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chHt
*- R

 

 

 

 

ON THE APPLICATION AND INTERPRETATION
OF COI-IERENT MOTION DETECTORS

By

Charles Paul Gendrich

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1991

/
r

I/IA'JKJV

ABSTRACT

ON THE APPLICATION AND INTERPRETATION
OF COHERENT MOTION DETECTORS

By

Charles P. Gendrich

Coherent motions are understood to play an important role in enhancing the
momentum transport of turbulent wall-bounded shear flows, but determining whether
or not a coherent motion is present in a given volume of space at a particular time is
still a diffith task. Although most detection schemes were developed for use within a
specific region above the wall, most are ultimately used throughout the entire boundary
layer. Three different probe-based algorithms and three different visual detection
schemes are applied to combined flow visualization and spanwise vorticity probe data
taken in the near-wall region and at y/8 of 0.8. Several new performance parameters
have been developed, and they are calculated along with most of the commonly used
evaluation parameters as functions of detection threshold and Reynolds number or y+.
The one-to-one correspondence between probe-based detections and visual detections is
also evaluated using two parameters already in common use and a new parameter,
P(T,t), which is based on the number of event overlaps as a function of time during an
event. Inner, outer, and mixed variables are used whenever appropriate to scale all
results, but only two Reynolds number-independent curves are found which describe

the outer-region response of any detection algorithm as a function of threshold.

Copyright by
CHARLES PAUL GENDRICH
1991

ACKNOWLEDGEMENTS

I would like to thank the many people whose assistance and support have been in-
valuable to me while working on this project. My advisor, Dr. Robert Falco, provided
the initial impetus for this study, and he has constantly motivated me to think and
work beyond what has already been done by other researchers. Drs. J. Foss and M.
M. Koochesfahani reviewed the manuscript and conu'ibuted many useful insights and
comments. Dr. Joseph Klewicki has helped in more ways than I can count, let alone
list here; all I can say is "'l‘hanks, Joe! :-)" My parents and friends have contributed
considerable moral support when I was discouraged; without them this work could
never have been completed. I appreciate the comments of Drs. W. Tiederman, C.
Wark, I-I. Nagib, R. Blackwelder, and J. Wallace. Finally, I would gratefully like to ac-
knowledge the financial support of the U.S. Air Force, Bolling AFB, D.C., under con-
tract F49620-86-C—0127.

iv

Table of Contents

List of Tables ............................................................................................................. vii
List of Figures ............................................................................................................ viii
Nomenclature .............................................................................................................. xviii
1. Introduction ........................................................................................................... l
2. The Experimental Data and Their Analysis ........................................................ 10
2.1. The Data ............................................................................................................ 10
2.1.1. Inner-Region Data Parameters ....................................................................... 11
2.1.2. Outer-Region Data Parameters ....................................................................... 12
2.2. Acquisition of Hot Wire and Flow Visualization Data ................................... 13
2.3. Reduction of Vorticity Probe Data ................................................................... 15
2.4. Reduction of Visual Data .................................................................................. 18
2.4.1. Large-Scale Motions ....................................................................................... 19
2.4.2. Visual Detections of Ring-Like Motions in the Outer Region ..................... 21
2.4.3. Inner-Region Visually-Detected Events ......................................................... 23
2.5. Probe-based Event Detection Schemes ............................................................. 25
2.5.1. The uv-quadrant breakdown technique .......................................................... 26
2.5.2. The TERA technique ...................................................................................... 27
2.5.3. The u-level technique ..................................................................................... 27
2.5.4. Grouping of Events ........................................................................................ 28

2.6. Performance Parameters .................................................................................... 29

2.6.1. Long-time statistical performance parameters ............................................... 31
2.6.2. Visual-correspondence performance parameters ........................................... 34
2.6.3. Additional Considerations .............................................................................. 36
3. Evaluation of Visual and Probe-based Detection Schemes ................................ 39
3.1. Large-Scale Motion (LSM) Results .................................................................. 41
3.2. Ring-Like Motion Detection Results ................................................................ 44
3.3. Inner-Region Visual Detection Results ............................................................ 47
3.4. uv-quadrant Analysis Results ............................................................................ 51
3.5. TERA Analysis Results .................................................................................... 57
3.6. u-level Analysis Results .................................................................................... 62
4. Comparison of Visual- and Probe-based Detections ........................................... 68
4.1. Large-Scale Motions and the Probe-based Detectors ...................................... 71
4.2. Ring-Like Motions and the Probe-based Detectors ......................................... 75
4.3. Inner-Region Visual and Probe-based Detections ............................................ 8O
5. Summary and Conclusions ................................................................................... 85
Tables .......................................................................................................................... 97
Figures ........................................................................................................................ 101

References .................................................................................................................. 278

LIST OF TABLES

 

 

 

Table Page
Number Number Table Caption
2.1.1 97 Inner-region flow parameters
2.1.2 97 Inner-region combined data set lengths
2.1.3 ' 97 Inner-region time uncertainty - the length
of one time tick
2.2.1 98 Outer-region flow parameters
2.2.2 98 Outer-region combined data set lengths
2.2.3 ' 98 Outer—region time uncertainty - the length
of one time tick
3.1.1 99 Outer-region LSM detection performance indicators
3.2.1 100 Outer-region RLM detection performance indicators
3.3.1 100 Inner-region visual detection performance indicators

vii

LIST OF FIGURES

Figure Page
Number Number Figure Caption

 

2.2.1 101 The 7.3m boundary layer wind tunnel in Michigan
State University’s Turbulence Structure Laboratory
2.2.2 102 The spanwise vorticity probe

2.2.3 103 Camera and mirror setup

2.2.4 104 Laser and laser optics setup

2.2.5 105 Smoke injection slit configurations (after

Lovett, 1982)

2.3.1 106 Changes in spanwise vorticity statistics for
different averaging window lengths

2.4.1 107 Zones of a "Typical Eddy" (after SIgnor, 1982)
3.1.1 108 Outer-scaled LSM ensembles. Error bars indicate
25% of an ensemble’s standard deviation at each
point in time

3.1.2 109 Mixed-scaled LSM ensembles. Error bars indicate
25% of an ensemble’s standard deviation at each
point in time

3.1.3 110 Inner-scaled LSM ensembles. Error bars indicate
25% of an ensemble’s standard deviation at each
point in time

3.2.1 111 Outer-scaled RLM sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation
at each point in time

3.2.2 112 Mixed-scaled RLM sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation
at each point in time

3.2.3 113 Inner-scaled RLM sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation
at each point in time

3.2.4 114 Outer-scaled RLM ejection ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.2.5 ‘ 115 Mixed-scaled RLM ejection ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.2.6 116 Inner-scaled RLM ejection ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at

 

 

viii

 

Figure Page
Number Number Figure Caption
each point in time
3.3.1 117 Ensembles of inner-region visually detected sweeps.
Error bars indicate 25% of an ensemble’s standard
deviation at each point in time
3.3.2 118 Ensembles of inner-region visually detected ejections.
Error bars indicate 25% of an ensemble’s standard
deviation at each point in time
3.4.1 119 Number of uv-quadrant events vs. threshold level
(Inner-region data)
3.4.2 120 Number of uv-quadrant events vs. threshold level
(RLM data set)
3.4.3 121 Number of uv-quadrant events vs. threshold level
(LSM data set)
3.4.4 . 122 Inner-scaled total uv-quadrant event time vs.
threshold (Inner-region data)
3.4.5 123 Inner-scaled total uv-quadrant event time vs.
threshold (RLM data set)
3.4.6 124 Inner-scaled total uv—quadrant event time vs.
threshold (LSM data set)
3.4.7 125 Total uv-quadrant event time (Mixed scaling) vs.
threshold (Inner-region data)
3.4.8 126 Total uv-quadrant event time (Mixed scaling) vs.
threshold (RLM data set)
3.4.9 127 Total uv-quadrant event time (Mixed scaling) vs.
threshold (LSM data set)
3.4.10 128 Outer-scaled uv-quadrant total event time vs.
threshold (Inner-region data)
3.4.11 129 Outer-scaled uv-quadrant total event time vs.
threshold (RLM data set)
3.4.12 130 Outer-scaled uv-quadrant total event time vs.
threshold (LSM data set)
3.4.13 131 Inner-scaled uv-quadrant event frequency vs.
threshold level (Inner-region data)
3.4.14 132 uv-quadrant event frequency (Mixed-scaling) vs.
threshold level (Inner-region data)
3.4.15 133 Outer-scaled uv-quadrant event frequency vs.
threshold level (Inner-region data)
3.4.16 134 Inner-scaled uv-quadrant event frequency vs.
threshold level (LSM data set)
3.4.17 135 uv-quadrant event frequency (Mixed-scaling) vs.
threshold level (LSM data set)
3.4.18 136 Outer-scaled uv-quadrant event frequency vs.
threshold level (LSM data set)
3.4.19 137 Inner-scaled average uv-quadrant event length vs.

 

 

threshold (Inner-region data)

ix

Figure Page

 

Number Number Figure Caption

3.4.20 138 uv-quadrant average event length (Mixed-scaling) vs.
threshold (Inner-region data)

3.4.21 139 Outer-scaled average uv-quadrant event length vs.
threshold (Inner-region data)

3.4.22 140 Inner-scaled average uv-quadrant event length vs.
threshold (LSM data set)

3.4.23 141 uv-quadrant average event length (Mixed-scaling) vs.
threshold (LSM data set)

3.4.24 142 Outer-scaled average uv-quadrant event length vs.
threshold (LSM data set)

3.4.25 143 Average inner-scaled uv-quadrant event length over

y+ vs. threshold (Inner-region data)

3.4.26 144 Percent Reynolds stress "captured" during

uv-quadrant events vs. threshold (Inner-region data)
3.4.27 145 Percent Reynolds stress "captured" during

uv-quadrant events vs. threshold (LSM data set)

3.4.28 146 RMS (0, during uv-quadrant events normalized by

(02’ vs. threshold (Inner-region data)

3.4.29 147 RMS a), during uv-quadrant events normalized by

(02’ vs. threshold (LSM data set)

3.4.30 148 Average TKE during uv-quadrant events normalized by
TKE’ vs. threshold (Inner-region data)

3.4.31 149 Average TKE during quuadrant events normalized by
TKE’ vs. threshold (LSM data set)

3.4.32 150 Outer-scaled uv-quadrant sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.4.33 151 Mixed-scaled uv-quadrant sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.4.34 152 Inner-scaled uv-quadrant sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.4.35 153 Outer-scaled uv-quadrant ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.4.36 154 Mixed-scaled uv-quadrant ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.437 155 Inner-scaled uv-quadrant ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.5.1 156 Number of TERA events vs. threshold level
(Inner-region data)

 

 

 

 

 

Figure Page
Number Number Figure Caption
3.5.2 157 Number of TERA events vs. threshold level
(RLM data set)
3.5.3 158 Number of TERA events vs. threshold level
(LSM data set)
3.5.4 159 Inner-scaled total TERA event time vs. threshold
(Inner-region data)
3.5.5 160 Inner-scaled total TERA event time vs. threshold
(RLM data set)
3.5.6 161 Inner-scaled total TERA event time vs. threshold
. (LSM data set)
3.5.7 162 Total TERA event time (Mixed scaling) vs. threshold
(Inner-lesion data)
3.5.8 163 Total TERA event time (Mixed scaling) vs. threshold
(RLM data set)
3.5.9 164 Total TERA event time (Mixed scaling) vs. threshold
(LSM data set)
3.5.10 165 Outer-scaled total TERA event time vs. threshold
(Inner-region data)
3.5.11 166 Outer-scaled total TERA event time vs. threshold
(RLM data set)
3.5.12 167 Outer-scaled total TERA event time vs. threshold
(LSM data set
3.5.13 168 Inner-scaled TERA event frequency vs. threshold
level (Inner-region data)
3.5.14 169 TERA event frequency (Mixed-scaling) vs. threshold
level (Inner-region data)
3.5.15 170 Outer-scaled TERA event frequency vs. threshold
level (Inner-region data)
3.5.16 171 Inner-scaled TERA event frequency vs. threshold
level (LSM data set)
3.5.17 172 TERA event frequency (Mixed-scaling) vs. threshold
level (LSM data set)
3.5.18 173 Outer-scaled TERA event frequency vs. threshold
level (LSM data set)
3.5.19 174 Inner-scaled average TERA event length vs threshold
(Inner-region data)
3.5.20 175 Average TERA event length (Mixed scaling) vs.
threshold (Inner-region data)
3.5.21 176 Outer-scaled average TERA event length vs. threshold
(Inner-region data)
3.5.22 177 Inner-scaled average TERA event length vs threshold
(LSM data set)
3.5.23 178 Average TERA event length (Mixed scaling) vs.
threshold (LSM data set)
3.5.24 179 Outer-scaled average TERA event length vs. threshold

xi

Figure Page
Number Number Figure Caption

 

(LSM data set)

3.5.25 180 Average inner-scaled TERA event length over y+
vs. threshold (Inner-region data)

3.5.26 181 Percent Reynolds stress "captured" during

TERA events vs. threshold (Inner-region data)
3.5.27 182 Percent Reynolds stress "captured" during

TERA events vs. threshold (LSM data set)

3.5.28 183 RMS 0), during TERA events normalized by

(I); vs. threshold (Inner-region data)

3.5.29 184 RMS (a, during TERA events normalized by

(02’ vs. threshold (LSM data set)

3.5.30 185 Average TKE during TERA events normalized by
TKE’ vs. threshold (Inner-region data)

3.5.31 186 Average TKE during TERA events normalized by
TKE’ vs. threshold (LSM data set)

3.5.32 187 Outer-scaled TERA sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.5.33 188 Mixed-scaled TERA sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.5.34 189 Inner-scaled TERA sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.5.35 190 Outer-scaled TERA ejection ensembles. Error

bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.5.36 191 Mixed-scaled TERA ejection ensembles. Error

bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.5.37 192 Inner-scaled TERA ejection ensembles. Error

bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.6.1 193 Number of u-level events vs. threshold level
(Inner-region data)

3.6.2 194 Number of u-level events vs. threshold level

(RLM data set)

3.6.3 195 Number of u-level events vs. threshold level

(LSM data set)

3.6.4 196 Inner-scaled total u-level event time vs. threshold
(Inner-region data)

3.6.5 197 Inner-scaled total u-level event time vs. threshold

(RLM data set)
3.6.6 198 Inner-scaled total u-level event time vs. threshold

 

 

xii

 

3.6.28

 

 

Figure Page
Number Number Figure Caption
(LSM data set)
3.6.7 199 Total u-level event time (Mixed scaling) vs. threshold
(Inner-region data)
3.6.8 200 Total u-level event time (Mixed scaling) vs. threshold
(RLM data set)
3.6.9 201 Total u-level event time (Mixed scaling) vs. threshold
(ISM data set)
3.6.10 202 Outer-scaled total u-level event time vs. threshold
(Inner-region data)
3.6.11 203 Outer-scaled total u-level event time vs. threshold
(RLM data set)
3.6.12 204 Outer-scaled total u-level event time vs. threshold
(LSM data set
3.6.13 205 Inner—scaled u-level event frequency vs. tlu'eshold
level (Inner-region data)
3.6.14 206 u-level event frequency (Mixed-scaling) vs. threshold
level (Inner-region data)
3.6.15 207 Outer-scaled u-level event frequency vs. threshold
level (Inner-region data)
3.6.16 208 Inner-scaled u-level event frequency vs. threshold
level (LSM data set)
3.6.17 209 u-level event frequency (Mixed-scaling) vs. threshold
level (LSM data set)
3.6.18 210 Outer-scaled u-level event frequency vs. threshold
level (LSM data set)
3.6.19 211 Inner-scaled average u—level event length vs threshold
(Inner-region data)
3.6.20 212 Average u-level event length (Mixed scaling) vs.
threshold (Inner-region data)
3.6.21 213 Outer-scaled average u-level event length vs. threshold
(Inner-region data)
3.6.22 214 Inner-scaled average u-level event length vs threshold
(LSM data set)
3.6.23 215 Average u-level event length (Mixed scaling) vs.
threshold (LSM data set)
3.6.24 216 Outer-scaled average u-level event length vs. threshold
(LSM data set)
3.6.25 217 Average inner-scaled u-level event length over y+
‘ vs. threshold (Inner-region data)
3.6.26 218 Percent Reynolds stress "captured" during
u—level events vs. threshold (Inner-region data)
3.6.27 219 Percent Reynolds stress "captured" during
u-level events vs. threshold (LSM data set)
220 RMS to, during u-level events normalized by

(02’ vs. threshold (Inner-region data)

xiii

 

Figure Page
Number Number Figure Caption

3.6.29 221 RMS 0), during u-level events normalized by
0); vs. threshold (LSM data set)

3.6.30 222 Average TKE during u—level events normalized by
TKE’ vs. threshold (Inner-region data)

3.6.31 223 Average TKE during u-level events normalized by
TKE’ vs. threshold (LSM data set)

3.6.32 224 Outer-scaled u-level sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.6.33 225 Mixed-scaled u-level sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at

- each point in time

3.6.34 226 Inner-scaled u-level sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.6.35 227 Outer-scaled u-level ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.6.36 228 Mixed-scaled u-level ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.6.37 229 Inner-scaled u-level ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time '

4.1.1 230 P(D): Probability of an LSM detection occurring
during a uv-quadrant detection vs. threshold

4.1.2 231 P(D): Probability of an LSM detection occurring
during a TERA detection vs. threshold

4.1.3 232 P(D): Probability of an LSM detection occurring
during a u-level detection vs. threshold

4.1.4 233 P(E): Probability of a uv-quadrant detection
occurring during an LSM detection vs. threshold

4.1.5 234 P(E): Probability of a TERA detection occurring
during an LSM detection vs. threshold

4.1.6 235 P(E): Probability of a u-level detection
occurring during an LSM detection vs. threshold

4.1.7 236 PO”): Probability of a uv-quadrant ejection vs.
phase of an LSM smoke detection a) R9=730,
b) R9=1400, c) Ro=2380, d) R9=3120

4.1.8 238 P(T): Probability of a TERA ejection vs.
phase of an LSM smoke detection a) R9=730,
b) Re=1400, c) R9=2380, d) R9=3120

4.1.9 240 P(I'): Probability of a u-level ejection vs.

 

 

phase of an LSM smoke detection a) R9=730,

xiv

 

 

 

Figure Page
Number Number Figure Caption
b) R9=1400, c) Ro=2380, d) Ro=3120
4.2.1 242 P(D): Probability of an RLM detection occurring
during a uv-quadrant detection vs. threshold
4.2.2 243 P(D): Probability of an RLM detection occurring
during a TERA detection vs. threshold
4.2.3 244 P(D): Probability of an RLM detection occurring
during a u-level detection vs. threshold
4.2.4 245 P(E): Probability of a uv-quadrant detection
occurring during an RLM detection vs. threshold
4.2.5 246 P(E): Probability of a TERA detection occuning
during an RLM detection vs. threshold
4.2.6 247 P(E): Probability of a u-level detection
occurring during an RLM detection vs. threshold
4.2.7a 248 PO): Probability of a uv-quadrant ejection vs.
phase of an RLM smoke ejection (R9=730)
4.2.7b 248 P(T): Probability of a uv~quadrant sweep vs.
phase of an RLM smoke sweep (R9=730)
4.2.8a 249 P(T): Probability of a uv-quadrant ejection vs.
phase of an RLM smoke ejection (R9=1400)
4.2.8b 249 P(I'): Probability of a uv-quadrant sweep vs.
phase of an RLM smoke sweep (R9=1400)
4.2.9a 250 P(T): Probability of a uv-quadrant ejection vs.
phase of an RLM smoke ejection (R9=2380)
4.2% 250 P(T): Probability of a uv-quadrant sweep vs.
phase of an RLM smoke sweep (R9=2380)
4.2.10a 251 P(T): Probability of a uv-quadrant ejection vs.
phase of an RLM smoke ejection (R°=3120)
4.2.10b 251 P(T): Probability of a uv-quadrant sweep vs.
phase of an RLM smoke sweep (R9=3120)
4.2.11a 252 P(T): Probability of a TERA ejection vs.
phase of an RLM smoke ejection (Ro=730)
4.2.11b 252 P(T): Probability of a TERA sweep vs.
phase of an RLM smoke sweep (R9=730)
4.2.12a 253 P(T): Probability of a TERA ejection vs.
phase of an RLM smoke ejection (Re=1400)
4.2.12b 253 P(T): Probability of a TERA sweep vs.
phase of an RLM smoke sweep (R9=1400)
4.2.13a 254 P0): Probability of a TERA ejection vs.
phase of an RLM smoke ejection (Ro=2380)
4.2.13b 254 P(T): Probability of a TERA sweep vs.
phase of an RLM smoke sweep (R9=2380)
4.2.14a 255 PO): Probability of a TERA ejection vs.
phase of an RLM smoke ejection (Ro=3120)
4.2.14b 255 PO): Probability of a TERA sweep vs.

XV

 

Figure Page
Number Number Figure Caption
phase of an RLM smoke sweep (Ro=3120)
4.2.15a 256 PO): Probability of a u-level ejection vs.
phase of an RLM smoke ejection (R9=730)
4.2.15b 256 PO): Probability of a u-level sweep vs.
phase of an RLM smoke sweep (R9=7 30)
4.2. 16a 257 P(T): Probability of a u-level ejection vs.
phase of an RLM smoke ejection (R9=1400)
4.2.16b 257 P(T): Probability of a u-level sweep vs.
phase of an RLM smoke sweep (Rg=1400)
4.2.17a 258 P(I'): Probability of a u-level ejection vs.
phase of an RLM smoke ejection (R9=2380)
4.2.17b 258 P(I'): Probability of a u-level sweep vs.
phase of an RLM smoke sweep (Ro=2380)
4.2.18a 259 PO): Probability of a u-level ejection vs.
phase of an RLM smoke ejection (R9=3120)
4.2.18b 259 P(I'): Probability of a u-level sweep vs.
phase of an RLM smoke sweep (R9=3120)

4.3.1 260 P(D): Probability of an Inner-region visual
detection occurring during a uv-quadrant detection
vs. threshold

4.3.2 261 P(D): Probability of an Inner-region visual
detection occurring during a u-level detection vs.
threshold

4.3.3 262 P(D): Probability of an Inner-region visual
detection occurring during a TERA detection
vs. threshold

4.3.4 263 P(E): Probability of a uv-quadrant detection
occurring during an Inner-region visual
detection vs. threshold

4.3.5 264 P(E): Probability of a TERA detection occurring
during an Inner-region visual detection vs.
threshold

4.3.6 265 P(E): Probability of a u—level detection
occurring during an Inner-region visual detection
vs. threshold

4.3.7a 266 P(T): Probability of a uvoquadrant ejection vs.
phase of an inner-region smoke ejection (y+=14.6)
4.3.7b 266 PO): Probability of a uv-quadrant sweep vs.
phase of an inner-region smoke sweep (y+=14.6)
4.3.8a 267 P(T): Probability of a uv-quadrant ejection vs.
phase of an inner-region smoke ejection (y+=15.0)
4.3.8b 267 P(T): Probability of a uv-quadrant sweep vs.
phase of an inner-region smoke sweep (y+=15.0)
4.3.9a 268 PO): Probability of a uv-quadrant ejection vs.

 

 

xvi

2.6. Performance Parameters .................................................................................... 29

2.6.1. Long-time statistical performance parameters ............................................... 31
2.6.2. Visual-correspondence performance parameters ........................................... 34
2.6.3. Additional Considerations .............................................................................. 36
3. Evaluation of Visual and Probe-based Detection Schemes ................................ 39
3.1. Large-Scale Motion (LSM) Results .................................................................. 41
3.2. Ring-Like Motion Detection Results ................................................................ 44
3.3. Inner-Region Visual Detection Results ............................................................ 47
3.4. uv-quadrant Analysis Results ............................................................................ 51
3.5. TERA Analysis Results .................................................................................... 57
3.6. u—level Analysis Results .................................................................................... 62
4. Comparison of Visual- and Probe-based Detections ........................................... 68
4.1. Large-Scale Motions and the Probe-based Detectors ...................................... 71
4.2. Ring-Like Motions and the Probe-based Detectors ......................................... 75
4.3. Inner-Region Visual and Probe-based Detections ............................................ 80
5. Summary and Conclusions ................................................................................... 85
Tables .......................................................................................................................... 97
Figures ........................................................................................................................ 101

References .................................................................................................................. 278

LIST OF TABLES

 

 

 

Table Page
Number Number Table Caption
2.1.1 97 Inner-region flow parameters
2.1.2 97 Inner-region combined data set lengths
2.1.3 ' 97 Inner-region time uncertainty - the length
of one time tick
2.2.1 98 Outer-region flow parameters
2.2.2 98 Outer-region combined data set lengths
2.2.3 * 98 Outer-region time uncertainty - the length
of one time tick
3.1.1 99 Outer-region LSM detection performance indicators
3.2.1 100 Outer-region RLM detection performance indicators
3.3.1 100 Inner-region visual detection performance indicators

vii

LIST OF FIGURES

 

 

 

Ifigume JPage
liunflxnr liunflxn' IdgumelZapfion

2.2.1 101 Tire 7.3m boundary layer wind tunnel in Michigan
State University’s Turbulence Structure Laboratory

2.2.2 102 The spanwise vorticity probe

23L3 103 (huncnrandrnhnorsenqr

2.2.4 104 Laser and laser optics setup

2.2.5 105 Smoke injection slit configurations (after
Lovett, 1982)

2.3.1 106 Changes in spanwise vorticity statistics for
different averaging window lengths

2.4.1 107 Zones of a "Typical Eddy" (after SIgnor, 1982)

3.1.1 108 Outer-scaled LSM ensembles. Error bars indicate
25% of an ensemble’s standard deviation at each
jxfintinthne

3.1.2 109 Mixed-scaled LSM ensembles. Error bars indicate
25% of an ensemble’s standard deviation at each
jxfintinthne

3.1.3 110 Inner-scaled LSM ensembles. Error bars indicate
25% of an ensemble’s standard deviation at each
Ixfinthrtune

3.2.1 111 Outer-scaled RLM sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation
ateachrxfinthnthne

3.2.2 112 Mixed-scaled RLM sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation
ateachjxfinthrthne

3.2.3 113 Inner-scaled RLM sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation
ateachjxfinthrthne

3.2.4 114 Outer-scaled RLM ejection ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
cachjxfintintune

3.2.5 115 Mixed-scaled RLM ejection ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
eachjxfintintune

3.2.6 116 Inner-scaled RLM ejection ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at

viii

 

Figure Page
Number Number Figure Caption
each point in time
3.3.1 117 Ensembles of inner-region visually detected sweeps.
Error bars indicate 25% of an ensemble’s standard
deviation at each point in time
3.3.2 118 Ensembles of inner-region visually detected ejections.
Error bars indicate 25% of an ensemble’s standard
deviation at each point in time
3.4.1 119 Number of uv-quadrant events vs. threshold level
(Inner-region data)
3.4.2 120 Number of uv-quadrant events vs. threshold level
(RLM data set)
3.4.3 121 Number of uv-quadrant events vs. threshold level
(LSM data set)
3.4.4 122 Inner-scaled total uv-quadrant event time vs.
threshold (Inner-region data)
3.4.5 123 Inner-scaled total uv—quadrant event time vs.
threshold (RLM data set)
3.4.6 124 Inner-scaled total uv-quadrant event time vs.
. threshold (LSM data set)
3.4.7 125 Total uv—quadrant event time (Mixed scaling) vs.
threshold (Inner-region data)
3.4.8 126 Total uv-quadrant event time (Mixed scaling) vs.
threshold (RLM data set)
3.4.9 127 Total uv-quadrant event time (Mixed scaling) vs.
threshold (LSM data set)
3.4.10 128 Outer-scaled uv—quadrant total event time vs.
threshold (Inner-region data)
3.4.11 129 Outer-scaled uv-quadrant total event time vs.
threshold (RLM data set)
3.4.12 130 Outer-scaled uv-quadrant total event time vs.
threshold (LSM data set)
3.4.13 131 Inner-scaled uv-quadrant event frequency vs.
threshold level (Inner-region data)
3.4.14 132 uv—quadrant event frequency (Mixed-scaling) vs.
threshold level (Inner-region data)
3.4.15 133 Outer—scaled uv-quadrant event frequency vs.
threshold level (Inner-region data)
3.4.16 134 Inner-scaled uv-quadrant event frequency vs.
threshold level (LSM data set)
3.4.17 135 uv-quadrant event frequency (Mixed-scaling) vs.
threshold level (LSM data set)
3.4.18 136 Outer-scaled uv-quadrant event frequency vs.
threshold level (LSM data set)
3.4.19 137 Inner-scaled average uv-quadrant event length vs.

 

 

threshold (Inner-region data)

ix

Figure Page

 

Number Number Figure Caption
3.4.20 138 uv-quadrant average event length (Mixed-scaling) vs.
threshold (Inner-region data)
3.4.21 139 Outer-scaled average uv-quadrant event length vs.
threshold (Inner-region data)
3.4.22 140 Inner-scaled average uv-quadrant event length vs.
threshold (LSM data set)

3.4.23 141 uv—quadrant average event length (Mixed-scaling) vs.
threshold (LSM data set)

3.4.24 142 Outer-scaled average uv-quadrant event length vs.
threshold (LSM data set)

3.4.25 143 Average inner-scaled uv-quadrant event length over

y+ vs. threshold (Inner-region data)

3.4.26 144 Percent Reynolds stress "captured" during

uv-quadrant events vs. threshold (Inner-region data)
3.4.27 145 Percent Reynolds stress "captured" during

uv-quadrant events vs. threshold (LSM data set)

3.4.28 146 RMS 0), during uv-quadrant events normalized by

(02’ vs. threshold (Inner-region data)

3.4.29 147 RMS a), during uv-quadrant events normalized by

(02’ vs. threshold (LSM data set)

3.4.30 148 Average TKE during uv-quadrant events normalized by
TKE’ vs. tlueshold (Inner-region data)

3.4.31 149 Average TKE during uv-quadrant events normalized by
TKE’ vs. threshold (LSM data set)

3.4. 32 150 Outer-scaled uv-quadrant sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.4.33 151 Mixed-scaled uv-quadrant sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.4.34 152 Inner-scaled uv-quadrant sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.4.35 153 Outer-scaled uv-quadrant ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.4.36 154 Mixed-scaled uv-quadrant ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.437 155 Inner-scaled uv-quadrant ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.5.1 156 Number of TERA events vs. threshold level
(Inner-region data)

 

 

 

 

 

Figure Page
Number Number Figure Caption
3.5.2 157 Number of TERA events vs. threshold level
(RLM data set)
3.5.3 158 Number of TERA events vs. threshold level
(LSM data set)
3.5.4 159 Inner-scaled total TERA event time vs. tlueshold
(Inner-region data)
3.5.5 160 Inner-scaled total TERA event time vs. threshold
(RLM data set)
3.5.6 161 Inner-scaled total TERA event time vs. threshold
. (LSM data set)
3.5.7 162 Total TERA event time (Mixed scaling) vs. threshold
(Inner-region data)
3.5.8 163 Total TERA event time (Mixed scaling) vs. threshold
(RLM data set)
3.5.9 164 Total TERA event time (Mixed scaling) vs. threshold
(LSM data set)
3.5.10 165 Outer-scaled total TERA event time vs. threshold
(Inner-region data)
3.5.11 166 Outer-scaled total TERA event time vs. threshold
(RLM data set)
3.5.12 167 Outer-scaled total TERA event time vs. threshold
(LSM data set
3.5.13 168 Inner-scaled TERA event frequency vs. threshold
level (Inner-region data)
3.5.14 169 TERA event frequency (Mixed-scaling) vs. threshold
level (Inner-region data)
3.5.15 170 Outer-scaled TERA event frequency vs. threshold
level (Inner-region data)
3.5.16 171 Inner-scaled TERA event frequency vs. threshold
level (LSM data set)
3.5.17 172 TERA event frequency (Mixed-scaling) vs. threshold
level (LSM data set)
3.5.18 173 Outer-scaled TERA event frequency vs. threshold
level (LSM data set)
3.5.19 174 Inner-scaled average TERA event length vs threshold
(Inner-region data)
3.5.20 175 Average TERA event length (Mixed scaling) vs.
threshold (Inner-region data)
3.5.21 176 Outer-scaled average TERA event length vs. threshold
(Inner-region data)
3.5.22 177 Inner-scaled average TERA event length vs threshold
(LSM data set)
3.5.23 178 Average TERA event length (Mixed scaling) vs.
threshold (LSM data set)
3.5.24 179 Outer-scaled average TERA event length vs. threshold

xi

Figure Page
Number Number Figure Caption

 

(LSM data set)

3.5.25 180 Average inner-scaled TERA event length over y+
vs. threshold (Inner-region data)

3.5.26 181 Percent Reynolds stress "captured" during

TERA events vs. threshold (Inner-region data)
3.5.27 182 Percent Reynolds su'ess "captured" during

TERA events vs. threshold (LSM data set)

3.5.28 183 RMS (r)z during TERA events normalized by

(02’ vs. threshold (Inner-region data)

3.5.29 184 RMS 0), during TERA events normalized by

(02’ vs. threshold (LSM data set)

3.5.30 185 Average TKE during TERA events normalized by
TKE’ vs. threshold (Inner-region data)

3.5.31 186 Average TKE during TERA events normalized by
TKE’ vs. threshold (LSM data set)

3.5.32 187 Outer-scaled TERA sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.5.33 188 Mixed-scaled TERA sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.5.34 189 Inner-scaled TERA sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.5.35 190 Outer-scaled TERA ejection ensembles. Error

bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.5.36 191 Mixed-scaled TERA ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.5.37 192 Inner-scaled TERA ejection ensembles. Error

bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.6.1 193 Number of u-level events vs. threshold level
(Inner-region data)

3.6.2 194 Number of u-level events vs. threshold level

(RLM data set)

3.6.3 195 Number of u-level events vs. threshold level

(LSM data set)

3.6.4 196 Inner-scaled total u-level event time vs. threshold
(Inner-region data)

3.6.5 197 Inner-scaled total u-level event time vs. threshold

(RLM data set)
3.6.6 198 Inner-scaled total u-level event time vs. threshold

 

 

xii

 

3.6.28

 

 

Figure Page
Number Number Figure Caption
(LSM data set)
3.6.7 199 Total u-level event time (Mixed scaling) vs. threshold
(Inner-region data)
3.6.8 200 Total u-level event time (Mixed scaling) vs. threshold
(RLM data set)
3.6.9 201 Total u-level event time (Mixed scaling) vs. threshold
(LSM data set)
3.6. 10 202 Outer-scaled total u-level event time vs. threshold
(Inner-region data)
3.6.11 203 Outer-scaled total u-level event time vs. threshold
(RLM data set)
3.6.12 204 Outer-scaled total u-level event time vs. threshold
(ISM data set
3.6.13 205 Inner-scaled u-level event frequency vs. threshold
level (Inner-region data)
3.6.14 206 u-level event frequency (Mixed-scaling) vs. threshold
level (Inner-region data)
3.6. 15 207 Outer-scaled u-level event frequency vs. threshold
level (Inner-region data)
3.6.16 208 Inner-scaled u—level event frequency vs. threshold
level (LSM data set)
3.6.17 209 u-level event frequency (Mixed-scaling) vs. threshold
level (LSM data set)
3.6. 18 210 Outer-scaled u-level event frequency vs. threshold
level (LSM data set)
3.6.19 211 Inner-scaled average u-level event length vs threshold
(Inner-region data)
3.6.20 212 Average u-level event length (Mixed scaling) vs.
threshold (Inner-region data)
3.6.21 213 Outer-scaled average u-level event length vs. threshold
(Inner-region data)
3.6.22 214 Inner-scaled average u-level event length vs threshold
(1.8M data set)
3.6.23 215 Average u-level event length (Mixed scaling) vs.
threshold (LSM data set)
3.6.24 216 Outer-scaled average u-level event length vs. threshold
(LSM data set)
3.6.25 217 Average inner-scaled u-level event length over y+
' ‘ vs. threshold (Inner-region data)
3.6.26 218 Percent Reynolds stress "captured" during
u-level events vs. threshold (Inner-region data)
3.6.27 219 Percent Reynolds stress "captured" during
u-level events vs. threshold (LSM data set)
220 RMS a)IL during u-level events normalized by

(01’ vs. threshold (Inner-region data)

xiii

 

Figure Page
Number Number Figure Caption

3.6.29 221 RMS toz during u-level events normalized by
(01’ vs. threshold (LSM data set)

3.6.30 222 Average TKE during u—level events normalized by
TKE’ vs. threshold (Inner-region data)

3.6.31 223 Average TKE during u-level events normalized by
TKE’ vs. threshold (LSM data set)

3.6.32 224 Outer-scaled u-level sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.6.33 225 Mixed-scaled u-level sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at

- each point in time

3.6.34 226 Inner-scaled u-level sweep ensembles. Error bars
indicate 25% of an ensemble’s standard deviation at
each point in time

3.6.35 227 Outer-scaled u-level ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.6.36 228 Mixed-scaled u-level ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time

3.6.37 229 Inner-scaled u-level ejection ensembles. Error
bars indicate 25% of an ensemble’s standard deviation
at each point in time '

4.1.1 230 P(D): Probability of an LSM detection occuning
during a uv-quadrant detection vs. threshold

4.1.2 231 P(D): Probability of an LSM detection occurring
during a TERA detection vs. threshold

4.1.3 232 P(D): Probability of an LSM detection occurring
during a u-level detection vs. threshold

4.1.4 233 P(E): Probability of a uv-quadrant detection
occurring during an LSM detection vs. threshold

4.1.5 234 P(E): Probability of a TERA detection occurring
during an LSM detection vs. threshold

4.1.6 235 P(E): Probability of a u-level detection
occurring during an LSM detection vs. threshold

4.1.7 236 P(T): Probability of a uv-quadrant ejection vs.
phase of an LSM smoke detection a) R9=7 30,
b) R9=1400, c) R9=2380, d) R9=3120

4.1.8 238 PO): Probability of a TERA ejection vs.
phase of an LSM smoke detection a) R9=730,
b) Ro=1400, c) Rg=2380, d) R9=3120

4.1.9 240 PO): Probability of a u-level ejection vs.

 

 

phase of an LSM smoke detection a) R9=730,

xiv

 

 

 

Figure Page
Number Number Figure Caption
b) R9=1400, c) R9=2380, d) R9=3120
4.2.1 242 P(D): Probability of an RLM detection occurring
during a uv-quadrant detection vs. threshold
4.2.2 243 P(D): Probability of an RLM detection occurring
during a TERA detection vs. threshold
4.2.3 244 P(D): Probability of an RLM detection occurring
during a u-level detection vs. threshold
4.2.4 245 P(E): Probability of a uv-quadrant detection
occurring during an RLM detection vs. threshold
4.2.5 246 P(E): Probability of a TERA detection occurring
during an RLM detection vs. threshold
4.2.6 247 P(E): Probability of a u-level detection
occurring during an RLM detection vs. threshold
4.2.7a 248 P(T): Probability of a uv-quadrant ejection vs.
phase of an RLM smoke ejection (Ro=730)
4.2.7b 248 P(T): Probability of a uv-quadrant sweep vs.
phase of an RLM smoke sweep (R9=730)
4.2.8a 249 P(T): Probability of a uv-quadrant ejection vs.
phase of an RLM smoke ejection (R9=1400)
4.2.8b 249 P(T): Probability of a uv-quadrant sweep vs.
phase of an RLM smoke sweep (RQ=1400)
4.2.9a 250 P(T): Probability of a uv-quadrant ejection vs.
phase of an RLM smoke ejection (R9=2380)
4.2% 250 P(T): Probability of a uv-quadrant sweep vs.
phase of an RLM smoke sweep (R9=2380)
4.2. 10a 251 P(T): Probability of a uv-quadrant ejection vs.
phase of an RLM smoke ejection (R9=3120)
4.2.10b 251 P(T): Probability of a uv-quadrant sweep vs.
phase of an RLM smoke sweep (R9=3120)
4.2.11a 252 P(T): Probability of a TERA ejection vs.
phase of an RLM smoke ejection (R9=730)
4.2.1 lb 252 PO"): Probability of a TERA sweep vs.
phase of an RLM smoke sweep (R9=730)
4.2.12a 253 PO): Probability of a TERA ejection vs.
phase of an RLM smoke ejection (R9=l400)
4.2.12b 253 P(T): Probability of a TERA sweep vs.
phase of an RLM smoke sweep (R9=1400)
4.2.13a 254 P(T): Probability of a TERA ejection vs.
phase of an RLM smoke ejection (R9=2380)
4.2.13b 254 P(T): Probability of a TERA sweep vs.
phase of an RLM smoke sweep (R9=2380)
4.2.14a 255 P(T): Probability of a TERA ejection vs.
phase of an RLM smoke ejection (R9=3120)
4.2.14b 255 PO): Probability of a TERA sweep vs.

XV

 

Figure Page
Number Number Figure Caption
phase of an RLM smoke sweep (Ro=3120)
4.2.15a 256 P(T): Probability of a u-level ejection vs.
phase of an RLM smoke ejection (Ro=730)
4.2. 15b 256 P(T): Probability of a u-level sweep vs.
phase of an RLM smoke sweep (R9=730)
4.2.16a 257 P(T): Probability of a u-level ejection vs.
phase of an RLM smoke ejection (Ro=1400)
4.2.16b 257 P(T): Probability of a u-level sweep vs.
phase of an RLM smoke sweep (R9=1400)
4.2.17a 258 P(T): Probability of a u-level ejection vs.
phase of an RLM smoke ejection (R9=2380)
4.2.17b 258 P(T): Probability of a u-level sweep vs.
phase of an RLM smoke sweep (R9=2380)
4.2.18a 259 P(T): Probability of a u-level ejection vs.
phase of an RLM smoke ejection (R9=3120)
4.2.18b 259 P(T): Probability of a u-level sweep vs.
phase of an RLM smoke sweep (Ro=3120)

4.3.1 260 P(D): Probability of an Inner-region visual
detection occurring during a uv-quadrant detection
vs. threshold

4.3.2 261 P(D): Probability of an Inner-region visual
detection occurring during a u-level detection vs.
threshold

4.3.3 262 P(D): Probability of an Inner-region visual
detection occuning during a TERA detection
vs. threshold

4.3.4 263 P(E): Probability of a uv-quadrant detection
occurring during an Inner-region visual
detection vs. threshold

4.3.5 264 P(E): Probability of a TERA detection occurring
during an Inner-region visual detection vs.
threshold

4.3.6 265 P(E): Probability of a u-level detection
occurring during an Inner-region visual detection
vs. threshold

4.3.7a 266 P(T): Probability of a uv-quadrant ejection vs.
phase of an inner-region smoke ejection (y+=14.6)
4.3.7b 266 P(T): Probability of a uv—quadrant sweep vs.
phase of an inner-region smoke sweep (y+=l4.6)
4.3.8a 267 P(T): Probability of a uv—quadrant ejection vs.
phase of an inner-region smoke ejection (y+=15.0)
4.3.8b 267 P(T): Probability of a uv-quadrant sweep vs.
phase of an inner-region smoke sweep (y+=15.0)
4.3.9a 268 P(T): Probability of a uv-quadrant ejection vs.

 

 

xvi

 

 

 

Figure Page

Number Number Figure Caption

phase of an inner-region smoke ejection (y*=18.9)

43% 268 P(T): Probability of a uv-quadrant sweep vs.

phase of an inner-region smoke sweep (y+=18.9)
4.3.10a 269 P(T): Probability of a uv-quadrant ejection vs.

phase of an inner-region smoke ejection (y+=24.2)
4.3.10b 269 P(T): Probability of a uv-quadrant sweep vs.

phase of an inner-region smoke sweep (y+=24.2)
4.3.11a 270 P(T): Probability of a TERA ejection vs.

phase of an inner-region smoke ejection (y+=l4.6)
4.3.11b 270 P(T): Probability of a TERA sweep vs.

phase of an inner-region smoke sweep (y+=14.6)
4.3.12a 271 P(T): Probability of a TERA ejection vs.

phase of an inner-region smoke ejection (y+=15.0)
4.3.l2b 271 P(T): Probability of a TERA sweep vs.

phase of an inner-region smoke sweep (y+=15.0)
4.3.13a 272 P(T): Probability of a TERA ejection vs.

phase of an inner-region smoke ejection (y+=l8.9)
4.3.13b 272 P(T): Probability of a TERA sweep vs.

phase of an inner-region smoke sweep (y"=18.9)
4.3.14a 273 P(T): Probability of a TERA ejection vs.

phase of an inner-region smoke ejection (y+=24.2)
4.3.14b 273 P(T): Probability of a TERA sweep vs.

phase of an inner-region smoke sweep (y+=24.2)
4.3. 15a 274 P(T): Probability of a u—level ejection vs.

phase of an inner-region smoke ejection (y+=14.6)
4.3.15b 274 P(T): Probability of a u-level sweep vs.

phase of an inner-region smoke sweep (y+=14.6)
4.3. 16a 275 P(T): Probability of a u-level ejection vs.

phase of an inner-region smoke ejection (y"=15.0)
4.3. 16b 275 P(T): Probability of a u-level sweep vs.

phase of an inner-region smoke sweep (y+=15.0)
4.3.17a 276 P(T): Probability of a u-level ejection vs.

phase of an inner-region smoke ejection (y+=18.9)
4.3.17b 276 P(T): Probability of a u—level sweep vs.

phase of an inner-region smoke sweep (y+=18.9)
4.3. 18a 277 P(T): Probability of a u-level ejection vs.

phase of an inner-region smoke ejection (y+=24.2)
4.3.18b 277 P(T): Probability of a u-level sweep vs.

phase of an inner-region smoke sweep (y+=24.2)

xvii

5
re >ur" ”+”.el>§.

N

Symbo

r: “St-f'i-s fififilegmmb<

IC.‘

N<+VX£<FS

NOMENCLATURE

Interpretation
"A" is a vector
a short time average of the quantity "a"
indicates the long-time RMS of "a".
indicates "a" was normalized with U, and v
indicates the value of "a" in the free stream
indicates the total quantity "a"
capital "A” is the mean value of a
lower-case "a" is the fluctuating component of a
a(t) a A + a(t)

Interpretation
kinematic viscosity
density
the same as 839; the boundary layer thickness
boundary layer momentum thickness
shear stress at the wall
the vorticity vector
the streamwise vorticity component
the wall-normal vorticity component
the spanwise vorticity component

mean event frequency

a length scale normalized with U, and v
Reynolds number based on U,, v, and 0
time normalized with U, and v

streamwise velocity component

the velocity vector as a function of position
friction velocity, «Irma/p

free stream velocity

wall-normal velocity component
streamwise velocity component

streamwise coordinate (see Figure 2.2.1)
wall-normal coordinate (see Figure 2.2.1)
height above the wall normalized with U, and v
spanwise coordinate (see Figure 2.2.1)

xviii

CHAPTER 1

INTRODUCTION

Since the introduction of the Reynolds-decomposed Navier-Stokes equations,
researchers of turbulent flows have sought ways to predict values for the Reynolds
stress, -pt‘r'V, and thereby close the streamwise momentum equation. Some researchers
have marked the flow and examined films of what transpires inside and outside the
boundary layer. Visual studies by Kline, Reynolds, Schraub, and Runstadler (1967),
Corino and Brodkey (1969), Kim, Kline, and Reynolds (1971), and others have shown
that the majority of the turbulence production takes place during intermittently-
occuning processes located primarily within the inner region of the boundary layer].
These events appeared to have a limited spatial extent and an organized velocity or
vorticity field, so they were dubbed "coherent motions." For quantitative measurements
researchers have used hot wires, hot films, LIPA, LDV, and many other techniques to
obtain velocity time histories at one or more points within the flow. Studies of these
time series by Blackwelder and Kaplan (1972), Wallace, Eckelmann and Brodkey
(1972) followed by Willmarth and Lu (1973), Alfredsson and Johansson (1984),
Luchik and Tiederman (1987), Falco and Gendrich (1989), and others have led to the
development of numerous probe-based detection schemes which use fluctuating quanti-

ties like u, v, and uv to locate when turbulence-producing events occur. Combined

 

1Inthisstudytheouterorwakeregionofthebomdarylayerwillret‘ertothatregionwhere
02<y/8so.99. TheregiatbetweeuOSy/SSOJwillbecalledtheinnerorwallregion,
andtlteregionbelowyUJv=50willbecalledthenear-wallregim.

velocity and visual measurements have also been undertaken by Falco (1974, 1977),
Bogard (1982), Lovett (1982), Signor (1982), and others to investigate the velocity and
vorticity characteristics of visually detected events. All of these studies have in some
way addressed the question, "What characterizes a class of events which is important

to the production of turbulence in the boundary layer?"

"Coherent motions" are often thought to be associated with the production of
negative uv, since quadrants 2 and 4 in the uv-plane provide the largest contributions
to the long-time W correlation. In a more general sense, a "coherent motion" is simply
a convecting region in space which moves or rotates as a unit in a fashion different
from the surrounding fluid. Each realization of a well-defined "coherent motion" gen-
erally has a recognizable spatial extent and organization, although random fluctuations
in the surrounding fluid will cause differences between each realization. Laufer (1975)
suggests that the presence of organized vorticity is the hue hallmark of a coherent
motion. Kline (1988) summarizes much of the research on the many different
coherent motions which have been observed, studied, and classified to date. Although
random velocity fluctuations which produce Reynolds stresses are not necessarily
caused by a coherent motion, it is generally thought that coherent motions are respon-

sible for the enhanced convective processes present in a turbulent boundary layer.

"Coherent motions," however they are defined, occur intermittently throughout the
boundary layer and come in many shapes and sizesz. Therefore a "good" detector

must be able to determine both the start and stop times of an event3, not merely that

 

2 See for example how Signor (1982) usedarange of stapes, sizes and orientations to iden-
tify”typicaleddies'.

3 T‘hestarttimeofaneventisgenerally heldtobethattimeatwhichaneventreachesa
givenpointinspace. Thestoptimeofthateventisthetimeatwhichtheupstreamendofthe
eventreachesthatsamepoint.

an event has occurred. If detection of Reynolds stress-producing events in the inner
region is important, a detector must be able to locate both high-speed events (sweeps)
in addition to low-speed events (ejections), since almost 80% of the Reynolds stress
correlation in the inner region is the result of high-speed, wallward-moving events

(Brodkey, Wallace, and Eckelman, 1974).

Probe-based event detection schemes promised to provide the least ambiguous
way to locate a coherent motion. Conditional averages4 have most often been shown
as "proof" that a given probe-based detection scheme did indeed locate a specific and
unique mechanism which accounted for the majority of the turbulence production.
However some authors (Alfredsson and Johansson, 1984) have questioned whether
these conditional averages are the result of the detection criterion or if the various
methods are indeed detecting distinctly different types of eventss. Bogard and Tieder-
man (1987) go further, suggesting that a conditionally-averaged signal always bears
characteristics which can be directly related back to the detection criteria. They ques-
tion whether or not conditional averages derived from velocity-based detection

schemes are truly representative of the characteristics of a sweep or ejectioné. The

 

‘Conditional averagesbasedontheexistenceofaneventeanbecalculatedinoneoftwo
ways: Thefirstapproachistoalignthecentersoftheeventstobeaveraged. Theaverageat
eachpointintimebeforeandafterdtecenteriscalculatedouttothedesircdlengthoftheen-
semble. This kind ofplot is typically what has been used to decide on how long a VITA event
is. Thesecondappoachistoalignthestartingtimesoftheeventstobeaveragedand
"stretch" or "compress" the duration of each event so that the end times are also aligned.
Averages are then calculated at each normalized point in time. This type of conditional aver-
age is commonly used with detectors which produce unique start and stop times for each event.
The latter method will be referred to as event averaging or ensembling in this document. while
the phrase conditional averaging will refer to the former process, and the context of the phrase
willdefinetheconditionsunderwhichtheaveragesaretobecalculated.

5 1n thisdocument "eventtype" referstoaspecifickindofdetectionmadeonaspecificdata
set. For example, one type of uv-quadrant event is a sweep detected at Ro=312m this "event
type" is different from sweeps detected at R9=2380.

‘5 A sweep is a high-speed, wallward—moving event. An ejection is a low-speed event mov-
ingawayfrornthewall. Sweepsandejectionswillbediscussedmuchmorethoroughlyin
chapter 2.

RMS for each point of a conditional average gives a strong indication of how con-
sistently the same thing is happening at each point in time during an "average" event.
Unfortunately, very few authors have included this statistic when presenting their

ensembles.

The choice of thresholding constant7 has always been a source of uncertainty for
probe-based detection schemes. Quantities such as intermittency, event frequency or
inverse event frequencys, and mean event length have been examined as functions of
thresholding constant in the hopes that a plateau would appear, indicating that results
in this region should be independent of the threshold chosen. However, Chen and
Blackwelder (1978) have shown that when a simple threshold level is applied to a
function which has a continuous probability distribution, the frequency of the detec-
tions will decrease monotonically with increasing threshold. This conclusion has led
Blackwelder and Haritonidis (1983) and others to choose thresholds arbitrarily, arguing
that the results are indicative of trends, even if the calculated numerical values are
somewhat uncertain. Bogard and Tiederman (1983) and others prefer to select thres-
holding constants for probe-based detection schemes such that they generate the same

number of events as were detecwd visually.

Velocity-based detection criteria were set aside in favor of visual detections in

studies done by Offen and Kline (1973), Falco (1974, 1977), Signor (1982), Lovett

 

7 "Threshold" and "thresholding constant" will be uwd synonymously in this document.
'Thrednldlevel'wfllnfamtheacmalvalueagahutwhichcanpafimwaemade. Ingen-
eralthethreshold levelequalsthedtresholdingconstanttimestheRMSofthedetectedvan-
able.

8Themisnomer"meantimebetweenevents"hasfrequerttlybeenappliedtothisterrn. The
inverseeventfrequencyistherneantimebetweenthebegimingoftwoneighboringeventsof
thesarnetypewhilethemeantimebetweeneventsisobviouslyuteaverageumebetweenflte
endofoneeventandthestartofthenext.

(1982), and many others. Studies by Chen and Blackwelder (1978) and Subramanian,
Rajagopalan, Antonia, and Chambers (1982) have attempted to determine the relation-
ship between probe-based detections and detections based on the presence or absence
of heat-contaminated fluid coming away from the wall. This technique of heating the
viscous sublayer far upstream and then examining the fluid passing over the probe for
temperature gradients corresponds very closely to the large-scale motion visual analysis
presented in Chapter 2. It suffers from one of the same disadvantages, namely that
marked fluid must have been convected away from the wall at some point in time,

although it may no longer be part of an active coherent motion.

Visual detections, or detections based on the presence, absence, or concentration
gradient of a marker, do not suffer from the problems inherent in analyzing velocity
measurements, but that does not mean that there are no problems associated with this
detection method. The Schmidt number indicates the ratio between momentum
diffusivity and mass diffusivity. If the Schmidt number is significantly larger than
unity, marker will diffuse slower than momentum, and instances will occur in which
the marker looks like it is being distored although there is no longer any active distor-
tion occurring9. A well-defined visual detection criterion is difficult to establish; the
easiest one to use is the presence or absence of marker, but high turbulence levels
and/or long diffusion times make even this determination a difficult one. Films gen-
erally have to be analyzed by eye, and the subjective contribution of the people doing
the analysis is diffith to estimate. Furthermore, when combined anemometry and flow
visualization is performed, films are rarely exposed at the rate of one frame per digi-
tized data point. Therefore one must not only decide if an active event which was

really caused by the physical process under study has passed over the probe, one must

 

9 This is sometimes referred toas "fossil turbulence".

also attempt to estimate at what point between two consecutive frames the event actu-

ally began or ended.

Velocity-based detection schemes will in general produce results which are
dependent on the choice of threshold. Although only a subjective "thresholdin g level"
can be applied to visual detections made without image processing equipment, there
are a number of different ways in which a film can be analyzed. This will be dis-
cussed further in section 2.4, and three methods are presented there which vary in
complexity and applicability. Those three methods will be applied to a number of
different data sets and the performance of each will be evaluated in subsequent

chapters.

Combined velocity and visual data acquisition has led to the comparison of visual
and probe-based detection schemes. Bogard (1982) developed a way to measure the
long-time correspondence between visual and probe-based detections. This approach
has been applied by Luchik and Tiederman (1987) to uv-quadrant, VITA, and modified
u-level detections. Most two- or three-dimensional non-intrusive velocity measurement
techniques rely on visual data for the generation of velocity vector fields, so the same
film which was analyzed for velocity information can also be analyzed to locate
coherent motions of interest. These analyses rely primarily on the visual interpretation
of films, velocity maps, or circulation contours to find the boundary of an event. Falco,
Chu, Hetherington, and Gendrich (1988), Wark and Adrian (1990), and others are
currently attempting to locate and characterize coherent modons on the basis of two—
dimensional non-intrusive velocity field measurements. Economikos, Shoemaker,
Russ, Brodkey, and Jones (1990) are attempting to do the same using three-
dimensional velocity measurements. Problems include the fact that enormous amounts

of data are generated if these measurements are to resolve a significant volume of

space with fine temporal and spatial resolution, in addition to the fact that an a priori
concept of what comprises an important coherent motion must be used to locate an

event.

The attributes of a good event detector are difficult to quantify, resulting in part
from lack of , agreement regarding what exactly should be detected; therefore the per-
formance of a detector is difficult to rate quantitatively. A "good" detector is, in fact,
one which makes use of whatever information it is given to accurately locate the pres-
ence or absence of the physical structure of interest. A detector will obviously per-
form best if the event to be detected is well defined and a signal directly related to the
presence or absence of the event is available“). If performance is rated with quantities
which are uwd by the detector itself, the "performance" of the detector will be related
to the threshold chosen, and an optimal choice of threshold can always be found which
will maximize the detector’s performance. If a time series directly related to the phy-
sical mechanism of interest is available, it can be used as an effective indicator of a
detector’s performance. Previously-used performance criteria have consisted of inter-
mittency, average event frequency and average event length calculations. However, the
performance of detectors which are supposed to locate Reynolds stress-producin g
events should also be evaluated on the basis of how well they do that. Performance
parameters based on this and other concepts are developed in section 2.6; results of
their application to various inner- and outer-region data sets are shown in Chapter 3;

comparisons among the various detection criteria employed are presented in Chapter 4.

 

1° If the event to be detected is simply any motion which generates negative uv, then the
opdnmldetectorbunisdreuv-quadranttechniquewidraduesholdofo. Thisassumesof
course that time series of both the fluctuating spanwise and wall-normal velocities are avail-
able. Asmtedabovedtmgh,amodonwhichgeremeskeymldssuesshmtnecessmilya
"coherentmotion."

If it is known that an event to be located has a well-defined visual appearance,
good agreement should exist between visual and probe-based detection schemes
designed to find the same type of event. Conversely, if the visual appearance of a
well-defined probe-based detection has been determined. there should be good agree-
ment between both detection methods. The correlation between visual and probe-
based detections can be measured using the quantities P(D) and P(E) originally defined
by Bogard (1982)l 1. However, a more comprehensive approach would be to see at
which points during a visual detection probe-based detections are most (or least) likely
to occur. This performance indication concept is also developed further in section 2.6,

and the results of its application are shown in Chapter 4.

When the performance of one detector is to be matched to that of another, thres-
holds must be chosen for each detector as appropriate. Bogard, Luchik. Tiederman,
and others have preferred to match the number of events detected and thereby the
mean event frequency. However, other performance parameters as discussed above
might provide better indicators of what threshold(s) to choose when comparing two
different detection schemes. This concept will be explored in more detail in Chapter

4.

The average characteristics of a given detection method are best shown using an
ensemble of the variables of interest. However, equally important to the significance
of this plot is the standard deviation of the average at each point in time: This indi-
cates how widely variant the events are which comprise the ensemble. The ensembles
shown in this document will in general contain plots of u, v, uv, (oz, and vtoz versus

normalized time during the "average" event. Plots of v0)z are included since the

 

" See section 2.6.2.

transport of Reynolds stress, a(rvyay is proportional to VG; At this point in time, the
question remains open of whether the motions responsible for W or its u'ansport,
a(rvyay, are more important factors influencing the physics of the flow (see for exam-
ple Hinze, 1975, or Klewicki, 1989). It is hoped that the vrnz information provided in
these event averages will be of use in resolving this question, but unfortunately its

interpretation will remain beyond the scope of this document.

Kline and Falco (1979) posed questions regarding the scaling of events in both
the inner and outer regions. Will the detection schemes developed for use in the
near-wall region perform similarly in the outer region? Do events last longer and get
larger when they are detected further from the wall? Does the intensity of an "average"
event in the outer region scale with outer variables? Is an outer-scaled "average" event
independent of Reynolds number? It was also asked in that same document whether
something other than joint u and v signals can be used to detect events which produce
significant amounts of Reynolds stress. These comprise the remaining questions which

will be addressed in the coming chapters.

CHAPTER 2

THE EXPERIMENTAL DATA AND THEIR ANALYSIS

In this chapter data sets are described which permit the issues raised in the Intro-
duction to be addressed. These data sets comprise hot wire time series and related
films, both of which have been analyzed to produce detection time series indicating
when sweeps, ejections, and quiescent periods occurred. The data reduction techniques
used to reach this point are described in detail in this Chapter. Parameters for evaluat-
ing the long-time performance of each detector are developed, in addition to three
parameters which indicate how much overlap there is between the detections of two

different schemes.

2.1 THE DATA

Combined flow visualization and hot wire data were obtained in 1979-1982 by D.
Signor and J. Lovett, working with R. E. Falco at the Michigan State University Tur-
bulence Structure Laboratory. A total of eight different data sets are available, four
taken in the inner region of the boundary layer and four in the outer region. Lovett

was responsible for taking the inner region data (Lovett, 1982), and Signor took the

10

ll

outer region data (Signor, 1982). For the most complete information regarding these
data sets and the related data acquisition processes, please see the appropriate docu-

ment.

2.1.1 Inner-Region Data Parameters

The inner region data sets were taken at an average Reynolds number based on
momentum thickness (R,,) of 720; the probe was positioned between 14.6 and 24.2
viscous units from the wall. The fiee stream velocity (U...) varied slightly from data
set to data set, but it was always approximately 1.0 m/s. The friction velocity (U,)
varied from 0.0497 to 0.0512 m/s. These values are summarized in table 2.1.1.

Data storage limitations prohibited the acquisition of very large contiguous data
records. Consequently a number of shorter records were taken, checked for errors, and
combined to form the data sets which were actually analyzed. The analog to digital
converter (AID) sampled each each of the four anemometers at 500 to 750 Hz. This
produced combined data sets which ranged from 39 to 108 seconds in length,
corresponding to 6400-18000 t+ and 360-1733 tU../8. These data are summarized in
Table 2.1.2.

The probe-based event detection schemes applied to the data produced start and
stop times as events of interest passed the probe. These time determinations are at
best accurate to one time tick, and the absolute time corresponding to one tick is
inversely proportional to the sampling rate. The uncertainty associated with the deter-
mination of start and stop times ranges then from 1.3 msec to 2.0 msec, corresponding

to 0.21-0.33 t“ and 0018-0031 tU.,/8. These data are summarized in Table 2.1.3.

12

Considerations regarding the uncertainty in the start and stop times of visual detections
will be presented in section 2.4.

2.1.2 Outer-Region Data Parameters

The outer region data sets were all taken at y/5 = 0.8 with R9 varying from 730
to 3120. The flow parameters for all four data sets are summarized in Table 2.2.1.
Between 5 and 42 individual data runs were taken at each Reynolds number, and these
individual runs comprise the combined data sets which were analyzed. Two different
analyses were performed on the visual data; one type of analysis was applied to all of
the data available (see section 2.4.1), while the other was applied to approximately
12% of the data (section 2.4.2). Two different combined data sets were created then
from all of the data available at each Reynolds number, giving data sets which ranged
in length from 2 seconds to 2.5 minutes (Table 2.2.2). A higher digitizing rate was
used at higher free stream velocities, so the absolute uncertainty in start- and stop-time
determinations decreases at higher velocities. These uncertainty values and their vari-

ous dimensionless equivalents are shown in Table 2.2.3.

Klewickilz showed that first— and second-moment statistics for U, v, UV, and n,
will converge to 3% with data sets at least 1000 tU.J8 in length. Convergence to 10%
will generally be achieved with data sets which are 200 tU,,/8 in length, a level gen-
erally achieved by all the inner-region and large-scale motion outer-region combined
data sets but. not the ring-like motion data sets (Table 2.2.2).

 

‘2 Klewicki (1989). p. 164. Note that convergence to 5% for third- aid fourth-moment
statisticswillonlybeobtainedwithdatasetswhichare4000tUJ5inlength,alevelwhichis
achievedbynoneofthedatasetsusedinthissmdy.

13

2.2 ACQUISITION OF HOT WIRE AND FLOW VISUALIZATION DATA

As mentioned earlier, the most complete descriptions of the data acquisition
processes used are available in Signor (1982) and Lovett (1982); Signor was concerned
with the outer-region data, and Lovett was responsible for the inner-region information.
However, all of the data sets were taken in the same tunnel using the same laser and
optics to generate lvisual information; the same probes, cameras, and computers were
used to store the data. Therefore it makes sense to treat the inner- and outer-region

data acquisition all at once, noting differences where appropriate.

The tunnel used was the Michigan State University Turbulence Structure Labora-
tory 7.3-meter low—speed wind tunnel shown in Figure 2.2.1. Note that the flow was
tripped at the entrance of the first working section of the tunnel using either a 12.7
mm circular rod at the lower speeds or a 1.59 mm rod at the highest speed”. A four-
wire vorticity probe shown in Figure 2.2.2 was driven by four DISA 55M01 anemome-
ters whose outputs were connected to a simultaneous sample-and-hold circuit, digitized
by a 50kHz 12-bit AID converter, and stored on a PDP 11/23 computer. An MKS
Baratron model l46H-0.1 pressure transducer was used in conjunction with a total
pressure probe and static pressure tap to generate free stream velocity information for
calibrations. A clock which incremented after the computer digitized each data point
was positioned within the camera’s field of view, so that each frame of film can be

uniquely associated with a particular instant of the corresponding hot wire time series.

A Redlake Locam model 50—002 16mm pin-registered high-speed movie camera

was used with a Schneider-Dreuznach Zenon lens to film the outer region flow

 

'3 See Signa (1982), a 10.

14

visualizations. That same camera/lens combination was used to shoot the y+=15 and
y+=18.9 data. A Photosonics model 35MM-4MLAC high-speed 35mm camera was
used to photograph the flow with the probe positioned at y+=14.6 and 24.2. Only side
views are available for the outer region flows; only plan views are available for the
y+=15 flows; but both side and plan views are present in the other three inner-region
flow visualization films. See Figure 2.2.3 for the camera and mirror setups which

were used to create the different views.

For the outer-region measurements the tunnel was illuminated using both
floodlights and a vertical laser sheet. The laser sheet was generated by sending the
beam from an 8-watt Coherent CR-8 argon-ion laser into the tunnel from below, where
it was focused onto a 3.5" cylindrical mirror. This is shown schematically in Figure
2.2.4. The laser sheet was aimed to pass as close as possible to the vorticity probe in
order to maximize the correlation between the visual information and the hot wire
data. The only problems arose when the laser sheet actually intersected a wire or two,
causing those wires to overheat and fail. The laser sheed did not otherwise affect the

hot wire measurements appreciably“.

For the inner-region films taken with the probe positioned at y+=15.0, the floor of
the tunnel was illuminated fiom above using three unfiltered floodlights. The y+=18.9
films were shot with red-filtered floodlighting of the plan view and laser-sheet illumi-
nation of the side view. Providing a red filter for the plan view eliminated the bright
blue line of the laser sheet from that view, but that reduced the overall illumination of
thefilm. Thesefilmshadtobepushprocessedwithacorrespondingincreaseinimage

 

l‘SeeIrovett(l982),p.49forrnoreinforrnationonthelaserandhotwiresetupand
qualification.

15

grain size. The uncertainty associated with analyzing the y+=18.9 films was much
larger than that associated with the y+=15.0 films because two views instead of one
were present in the former films which started with poorer image density and grain.
Poor image quality brought about the decision to use 35mm film for shooting the other
two probe positions. A red plan view, a blue side view, and a clock are visible in
these films, and the image density and grain are indeed improved over those obtained
at y+=18.9.

Smoke was injected upsueam of the measurement point using two slits for the
inner-region data sets, one far upstream and a tangential slit approximately 80 I“
upstream of the probe. For the outer-region data sets only the far upstream slit, posi-
tioned approximately 4.27 m upstream of the measurement point, was used. See Fig-
ure 2.2.5 for a graphic description of the different types of smoke injection slits used

and their positions in the tunnel.

2.3 REDUCTION OF VORTICITY PROBE DATA

The vorticity probes used by Signor and Lovett are similar to those described by
Foss, Klewicki, and Disimile (1986). The calibration scheme used is a variation of the
"effective angle" technique”. Applying this calibration technique, the effective angle
of the X-wires was determined, along with Collis and Williams coefficients for each of
the four wires. These coefficients were applied to the raw data using the programs

 

‘5 This technique is described in Klewicki (1989) pp. 3444-, Signor (1982), Lovett (1982),
andFalco(1980). Ithmalsobeenrecently evaluatedinastudybyBrowne,AntoniaandChua
(1989).

16

CONVOL and COM“, creating time series of the velocities for each wire at each
sampled instant in time. From this point on the data were processed using modified
versions of programs created by Klewicki to compute long-time statistics for the data
and to create time series of velocities, spanwise vorticity, spatial and temporal deriva-
tives, and various combinations of the above. The processes and assumptions used in
these programs are most completely described in Klewicki (1989), along with the

inherent uncertainty in the computed values, however a brief summary follows.

The time series required for the detection and evaluation schemes described in
section 2.5 are u, v, uv, Bu/Bt, uBu/Bt, (oz, and vrez. The first two time series are
derived from the X-array signals, and the third time series is simply the product of the
first two. The time derivative of the u signal is calculated by computing a local 5-
point least squares fit to a second-order model (u = a1+ a2: + a3t2) and then
differentiating the model. The calculation of dulay, one component of (oz, was based
on a 2-point finite difference approximation using the fluctuating part of the velocities
fiom the parallel array. The calculation of avlax was analogous to that of Bu/Bt, that
is, a local 5-point least squares fit of a second order model was computed about the
point of interest, and then the model was differentiated. The v-component velocities
used are those calculated from the X-array data, and Taylor’s hypothesis is used to
convert time derivatives to streamwise derivatives. Klewicki (1989) notes that this
method of computing avlax is preferred to a multipoint finite difference approach,
since this method is less sensitive both to the choice of step size and to signal noise.
The vn)z time series was computed by multiplying v(t) and (1)2“) together at each

instant of time; the nan/8t time series is the product of u and Bu/at.

 

‘5 For a description of these programs, see Lovett (1982), pp. 56+ and Signa (1982), Ap-
pendix A, pp. 167-H. ‘

17

Since Signor and Lovett did not use the analog filtering circuitry which was avail-
able to Klewicki, they developed a number of ways to filter their data digitally. The
program VELRED (Lovett, 1982) first eliminated points in the u time series which
varied from the previous point by more than u’; these points were replaced by the
average of the 2 neighboring points. The v and uv time series were treated the same
way. The resulting u, v, and uv time series were then low-pass filtered (averaged or
smoothed)17 by replacing each tick with a local 5- or 7-point average centered on that
tick. These then were the time series used to compute spanwise vorticity, temporal
and spatial derivatives, and combinations thereof.

The following approach used less filtering than before while eliminating enough
low-frequency noise so that the resultant time series were adequate for analysis:
Values in the time series for each wire, i.e., the outputs of CONVEL, were checked
against the previous point in time for values which changed by more than 2 RMS of a
100-point average about the point of interest. Values which did change so radically
were replaced by the average of the two neighboring values in the appropriate time
series; this occurred 2864 times out of a total of 878340 data points or 0.33% of the
time. The resultant time series were processed as described at the start of this section
to generate the u, v, uv, and other time series required for the probe-based detectors

and the effectiveness analyses.

After each time series was calculated, it was seen that appreciable jitter was still

present in the signals. Using an n-point average to smooth the final time series was an

 

1" It shouldbenotedthatthissortoflow-pass filtering prohibitsdirectcalculation ofcutoff
fieqwmiesmflikedratwhichcanbepafonnedwhenmmlogfiltefingisused. Cutofffrequen-
cies could have been estimated by calculating and comparing "before" and "after" power spec-
traoftheuandvtimeseries.

18

available option, but it was apparent that the choice of averaging window length would
have an effect on the long-time statistics of the resultant data. It was also readily
apparent that smoothing the jittery data would significantly change the statistics of
those data without giving any indication of whether this was due to the elimination of
noise or the introduction of biases by the smoothing process. Therefore smoothing
was applied to one of Klewicki’s 600,000-point vorticity-vorticity data sets18 all of
which exhibited smoothly continuous time traces for u, v, uv, and all. The long-time
statistics for the upper wire fluctuating vorticity time series ((0,0)) are shown in Figure
2.3.1 a-c as a function of smoothing window length; note that a smoothing window of
one corresponds to no smoothing at all. A window of 5 produced changes of less than
10% in the higher-order statistics”, so this is the window length which was subse-
quently used to smooth the final time series calculated from the unsmoothed data of
Signor and Lovett.

2.4 REDUCTION OF VISUAL DATA

The visual data obtained (films) were analyzed using a variety of methods which
will be described below. The determination of start and stop ticks for each event was
complicated by the fact that multiple hot wire data ticks were acquired during the
exposure of a given frame of film. Events with an unambiguous visual appearance pro-
duced the least uncertain start and stop times; see for example the large-scale motions

described in section 2.4.1. More ambiguous visual appearances produced less certain

 

‘3 Thespecificdatasetusedwas correlation 10, number 1.
19 Aflwtrratingtimeserieswasusedsothememwasalwayszero.

19

start and stop times, and this is quantified as well as possible below.

The atomized oil droplets ("smoke") used to visualize the flow averaged 1.0|.rm in
diameter and had a Schmidt number on the order of 38,000, indicating that these parti-

cles were satisfactory markers of convective processes but tracked diffusive processes

poorly.

The 35mm film was read using a NAC model PH-3SOB motion analyzer. The
16mm film was read using a NAC model DF-16C analysis projector whose images
were displayed on a ground glass screen and read from the reverse side to eliminate
the parallax errors associated with using a standard movie screen and viewing from an
angle. The 35mm analyzer displayed the images on its own screen; it was not used in

projection mode.

2.4.1 Large-Scale Motions

The side views present in all of the outer-region films show dark regions where
no smoke is present and lighter regions where smoke has been convected from the
injection slit far upsueam to the point at which the probe is positioned. If the atom-
ized oil droplets which comprise the smoke had had a Schmidt number of approxi-
mately one, the dark regions could be expected to contain the non-vortical fluid from
the free stream, while the lighter regions should contain the vortical fluid of the boun-
dary layer. Although it was expected that this would not be the case all the time, the
start of a large-scale motion event (LSM) was defined to be the time at which a light,
smoke-filled region started to pass over the probe. The end of an LSM was recorded
as the time at which a dark region started to pass over the probe.

20

The LSM visual analysis is simple and easy to perform. The fiaming rate of the
camera produced films in which between 4 and 12 data ticks elapsed between each
frame; between 2 and 4 data ticks were taken during each frame. This, in combination
with the unambiguous definition of an LSM, produced start and stop times which were
accurate to within :t2—6 data ticks (see Table 2.2.3 for the factors needed to convert

data ticks to seconds, t+, tU,,/5, and I’).

The relatively low ambiguity inherent in LSM visual detections is unfortunately
offset by a number of limitations. First, there is no provision for classifying an event,
so this analysis cannot be used to show whether modifications which induce changes in
the boundary layer structure are affecting the sweep process or the ejection process.
Second, application of this analysis to the near-wall region would be difficult, since the
presence or absence of marker there is rarely as unambiguous as it is in the outer
region. Third, this approach exacerbates non-unity Schmidt number effects since the
marker must be injected close to the working section inlet if it is to mark the entire
boundary layer. The entire development length is then available for the differences
between convection and diffusion of both marker and momentum to make themselves

apparent.

The simplicity of this approach makes it a desirable candidate for use in the outer
region if it can be shown that the disadvantages noted above do not affect the results
too much. Therefore LSM detections from the outer-region films were analyzed as
described in section 2.6, and the results from those analyses are presented in the next

chapter.

21

2.4.2 Visual Detections of Ring-Like Motions in the Outer Region

Falco (1974, 1977) and Signor (1982) proposed that vortex ring-like motions of
intermediate scale20 were a plausible mechanism for momentum transport in the outer
region of a turbulent boundary layer. Flow visualization and hot wire anemometry
were used in an iterative process to define the visual characteristics of this
intermediate-scale ring-like motion (RLM) which they called a "typical eddy." The
model RLM was then divided into eight separate zones as shown in Figure 2.4.1. The
existence of an RLM event in zones 1-6 passing over the probe was based in the shape
of the RLM with respect to the shape shown in Figure 2.4.1, the orientation of the
RLM, the existence of fluid motion within the eddy, and a location above y/5.=0.5.
The same criteria were applied to zones 7 and 8 for film taken at the two lowest Rey-
nolds numbers, but conditional sampling at the higher two velocities was performed
with reference to both the film and the u, v, uv, and rez time traces.21 The start of an

RLM event was recorded as that time at which the structure intersected the vorticity
probe.

Signor’s grand ensembles of u and v as a function of zone within the model
coherent structure22 were used in conjunction with the usual concept of a sweep and
ejection to determine which RLM detections could be classified as a sweep and which
as an ejection. Without this step RLM detections cannot readily be compared to the

results of detection schemes which locate sweeps and ejections.23 The average

 

3° ”Intennediateseale'inthiscaseissomethingontheordaofS/lo. Intheflowsstudied
dreavaageveruealextauofatypicaleddywasofthesameorderastheTaylormicroscale
(Tennekes and Lurnley, 1972, p. 66).

2‘ SeeSigna (1982), pp. 21-23.

2' These are Figures 3.35 and 3.36, p. 99 and 100, in Signor (1982). Note that the data
ficmallfourReynoldsnumberswereensembledtopmducetheseplots.

23 It would be possible to compare the detections from each zone to sweep, ejection, inward

22

streamwise velocity in zones 1 and 2 was always higher than the mean; in the other 6
zones it was generally less than the mean. The average wall-normal velocity in zones
1 and 2 was generally negative, while in the other 6 zones it was positive. Events
from zones 1 and 2 were therefore generally high-speed and wallward moving, so they
were called sweeps. Events from the other zones were generally low-speed and out-

ward moving, so they were called ejections.

The same film was used for both RLM and LSM analysis. Therefore an uncer-
tainty of between i2-6 ticks existed because of the way the film was exposed. The
event was well defined, and the selection criteria were applied conscientiously. How-
ever, the blurring in the higher-velocity films which required the combined use of film
and hot wire data for identification also increased the uncertainty in the start and stop
times of those events. For R9=730 and R9=1400 the start and stop times are therefore
uncertain to :l:2 and 3 ticks, respectively. The other times are probably uncertain to i7
ticks at Ro=2380 and t8 ticks at R,=3120. Using values from Tables 2.2.3 and 3.2.1,
the uncertainty in average RLM event length is between 0.3% and 1.2%.

The RLM visual analysis is both complex and time consuming. With adequate
illumination and framing rates, its uncertainty is comparable to that of the LSM visual
analysis, but blurred images in combination with the tight RLM sampling criteria pro—
duce both a higher uncertainty in start and stop times and a larger rejection rate than
that obtained for the LSM approach. However, the RLM analysis relies on the relative
motion of smoke particles from frame to frame to verify that each RLM is active when
it reaches the probe. This reduces the effect of a high Schmidt number on the results,

 

interaction, and outward interaction detections due to other schemes. However, since the focus
ofmismkismsweepsurdejecfiamuseemsmembkndeminewhichkm
zonescmtainevmuumbehavelikesweepsaMejecdmfacanpmimnpmposes.

23

since it has been shown that the particles used were small enough to mark convective
processes within the flow, while the time between frames (12 data ticks or less) was
short enough so that diffusive processes would not be a significant factor in that inter-
val.

2.4.3 Inner-Region Visually-Detected Events

The velocity signatures of sweeps and ejections were used to define the visual
characteristics of those events when their effects penetrated into or rose out of the
visualized inner-region of a turbulent boundary layer. The visual detections were
based primarily on the plan view of atomized oil droplets ("smoke") used to mark the
viscous sublayer. The concentration of smoke in the sublayer was greater than the
overlying fluid, so a high-speed, wallward-moving event appears to move the smoke
particles out of the way, creating a region darker than its surroundings which rapidly
advances on and passes the probe. Low-speed, outward-moving events appear as bright
areas (most often ”ridges") which move slowly over the probe. The side view,
illuminated by laser sheet, was used as a secondary source of information when it was
available. Ejections in the side view appear as slow-moving bright regions rising away
from the wall and passing over the probe.

The existence of an event at the probe was based on a number of criteria: Was
the smoke moving faster (or slower) than it did in the surrounding fluid? Was the
smoke density just upstream of the probe steadily decreasing (or increasing) from

frame to frame? Did the event intersect the X—array?“ The start of an event was

 

24'I‘hiscriteriawasappliedsincetheX-arraywasthesourceofuandvinfonnation. As
noted insection 2.3, thepatallel arraywasonly usedfor calculating ail/3y.

24

recorded as that time at which the boundary of the higher-velocity (or lower-velocity)
region intersected the X-array. The end of a sweep was occasionally difficult to deter—
mine, since strong sweeps did have the ability to remove all of the smoke from the
region around the probe. The precise end of an ejection was difficult to determine on
those occasions when the smoke density slowly relaxed back to its average value.
Generally an accurate determination of start and stop times could be made by playing
a sequence of frames and looking for changes in particle velocities; when this did not

work, the existence of an event was noted but not used in the analysis.

It was recognized that this method of analysis had a certain amount of subjec-
tivity in it, so two methods were employed to improve the consistency of this analysis’
application. The first method involved reading the same film at different times and
comparing the results. During the first two weeks of film analysis, this author read
many films, but the same film (5200 frames)” was read every other day. That day’s
results were compared with those of the previous reading. After the same events were
found in two consecutive readings and their start and stop times agreed to 1:1 tick, film
analysis started all over again; old results were discarded, and only subsequent results
were saved. In the second method, two practiced film readers analyzed the same film,
and the results were compared”. The same events were located, with a couple excep-
tions,andtheirstartandstoptimesagreedtoi3ticks.

Framing rates and film speed varied from data set to data set, so the uncertainty
of the start— and stop-time determinations also varied. Sometimes the film was still

accelerating up to speed within the camera during the initial frames of a data run;

 

25 This was the y+=15.0 film.

26MythanksgotoDr.Falcowhotookthetimetositandstareatfilrnswithrne. Weused
the firstfilm ofthe y+=18.9 data setfor this.

25

event times could generally be determined to within 10 data ticks for this part of a
film. Sometimesthecamerawasstartedlateorranoutoffilmearly; inthese instances,
quiescent periods were recorded during those times for which no visual information
was available. If more than 40% of the data run was affected in this way, the entire
data run was discarded”. The y+=14.6, y+=18.9, and y+=24.2 data sets all were filmed
with approximately 8 data ticks between frames when the camera was up to speed
Three or four data ticks were taken while each frame was exposed, giving a total
uncertainty in start and stop times for these data sets of 21:6 ticks. Approximately 4
data ticks elapsed between frames of the y+=15.0 film, and two to three ticks were
taken during each frame. Therefore the total uncertainty in start and stop times from
this film is about 13.5 data ticks. Using information from Tables 2.1.3 and 3.3.1, the

uncertainty in average event length varies from 0.6% to 3.1%.

2.5 PROBE-BASED EVENT DETECTION SCHEMES

Three of the more frequently used probe-based coherent event detection schemes
have been implemented in this study. A goal of the implementations has been to use
detectors which are capable of locating the start and stop times of coherent motions
which contribute to Reynolds stress production. Since it has been shown that sweeps
are responsible for the majority of the Reynolds stress production in the near-wall
region (Brodkey, Wallace, and Eckelman, 1974), each detector as implemented must
provide for the detection of high-speed events, a constraint which led to a modification

of the u-level technique. The detectors as used in this study will be described below

 

7’ Thisincludesloutof9ofthey+=l4.6datamns,noneofthey+=15.0dataruns,none
of the y+=18.9.data nuts. and 4 out of 18 of the y+=24.2 data runs.

26

in some detail. The computer programs used to generate detection time series were
presented in Gendrich, Falco, and Klewicki (1989); specific questions regarding the

implementations used in this study may be answered by referring to that document.

2.5.1 The uv-quadrant breakdown technique

Perhaps the most common detector used when time-resolved streamwise and
wall-normal velocity measurements are available is the uv-quadrant breakdown tech-
nique first proposed by Wallace, Eckelman, and Brodkey (1972) and subsequently
expanded by Willmarth and Lu (1972). The start of an event is said to occur when the
product of u times v exceeds a given threshold”, equal to cu’v’. The u and v time
series are used to classify events as sweeps, ejections, inward interactions, or outward
interactions. A sweep is a high-speed coherent event moving toward the wall, so a
sweep is an event that has u>0 and v<0 by definition. Similarly, ejections have u<0
and v>0; both u and v are negative during an inward interaction; and both are positive
during an outward interaction. Since this study focuses on the nature of sweeps and

ejections, the detections from quadrants 1 and 3 will not be analyzed.

 

2‘3 Somewriteflasthethresholdingconstantsymbolforthisdetectiontechnique;thisisin-
tendedtorefertothesizeofthehyperbolic”hole'intheuv-planewhichiscreatedbynon-
zero thresholding constants. k is frequently used as the thresholding constant for the VITA
technique, L R! the u-level technique. Since thresholding constants are used similarly in all of
thesedetectimschemes,theywillallbecalledcinthisdocument NotethathO.

27

2.5.2 The TERA technique

The essence of the Turbulence Energy Recognition Algorithm was proposed by
Zoran Zaric’ in 1981 and simplified by Falco and Gendrich (1989). The underlying
idea of the TERA technique is that a turbulence event will produce a change in the
magnitude of the streamwise turbulence kinetic energy. This will be accompanied by
an increase in the magnitude of the temporal derivative of u2, and doth/at equals
2u8ul3t. Therefore the start of a TERA detection is said to occur when the magnitude
of Bulat exceeds the threshold level, c(8ulat)’. The event ends when both Ian/8d and a
short-time average of that same quantity fall below the threshold level.

Events are classified as a sweep or ejection based on the sign of u. High-speed
events (u>0) are called sweeps, and low-speed events (u<0) are called ejections. An
event is also said to end if 11 changes sign before the short-time average described
above falls below its cutoff level. The TERA implementation for this study does not

differ significantly from what was described in Falco and Gendrich (1989).

2.5.3 The u-level technique

The u-level technique was first proposed by Lu and Willmarth (197 3) and subse-
quently modified by Luchik and Tiederman (1987). Events started when u dropped
below -cu'; they ended when u rose above (-cu')/4. Since this approach forced u to be
negative, only low-speed events (called ejections) could be detected by this approach.
Therefore the modified u-level technique of Luchik and Tiederman (1987) did not meet
this study’s requirements for a detection scheme, i.e., the detector was not able to

determine the start and stop times of both sweeps and ejections.

28

The modified u-level technique was further modified for this study so that high-
speed events could also be detected. An event is said to begin when the magnitude of
it rises above the threshold level cu’, and it ends when M falls below one quarter of
the threshold level or when it changes sign. Events are classified as sweeps or ejec-
tions depending on the sign of u; low-speed events are called ejections, and high-speed

events are called sweeps.

2.5.4. Grouping of Events

All of the event detection schemes presented above have the capability of produc-
ing very short events or very short quiescent periods between events of a similar
nature. A grouping procedure similar in nature to that used by Bogard and Tiederman
(1986) was used to cluster shorter events which likely comprised one individual burst.
Bogard and Tiederman (1986) used the probability distribution of their ejection statis-
tics to decide on the grouping window to use. Falco and Gendrich (1989) showed that
the size of the grouping window had little effect on the correlation between TERA and
inner—region visual detections if the grouping window was 5 t+ or larger. Therefore
events of the same type separated by pauses shorter than about 5 t+ were connected
and the intervening pauses eliminated.

Very short events posed another problem. The signature of events one or two t+
in length is bound to be significantly different from that of more average events which
range from 100-400 t+ in length. The inclusion of many short events therefore has the
potential to affect the ensemble average appreciably. Furthermore, it is questionable
whether a very short detection was caused by noise in the signal or a real physical pro-
cess. Consequently, it was decided to eliminate very short detections after grouping

29

was applied to the signal but before ensembles and other results were calculated. This
was implemented by eliminating sweeps or ejections which were shorter than three
data ticks in length (less than 1 t”; see Tables 2.1.3 and 2.2.3).

2.6 PERFORMANCE PARAMETERS

Quantitative evaluation of a detection scheme’s performance depends on the avai-
lability of a signal which gives a good indication of the presence or absence of the
physical structure under study. This signal can be in the form of an intermittency
function, from a visual analysis for example, or it can be in the form of another time-~
resolved quantity like vorticity. If the signal used to locate events is also used to
evaluate how well the detections were made, the level of performance achieved will be
directly related to the choice of threshold. In this case one can easily optimize the
performance of the detector by making the correct choice of threshold. It is not frivo-
lous to obtain a signal which shows whether or not something is going on and then not
use that signal in the detector itself; simple detection schemes need to be evaluated on

the basis of more complex ones which give the most nearly correct detections possible.

This leads back to the question of what a coherent motion is, which one cannot
know until it has been detected and analyzed; yet the adequacy of the detections can-
not be evaluated until the motion has been characterized. A simple definition of an
interesting coherent motion is used in this study; more complex definitions will not
change the methods by which the performance of a given detection scheme is
evaluated. Iterating the process of defining an event, figuring out how to detect it, and
then evaluating how well those detections have been made should lead to the most

30

well-refined definitions of both the event and the best way in which to detect it.

As mentioned in the Introduction, previously used performance evaluations have
often consisted of only average event frequency and average event length calculations.
These values may give some information regarding a range of thresholds within which
the detected event lengths or frequencies are threshold independent, but by themselves
frequency and length are not good performance indicators: Even if the average length
and frequency of occurrence are known, it is possible to generate detections having

these characteristics which locate absolutely nothing of interest.

Sweeps and ejections are the focus of this study; consequently the definitions of
these events will be used to construct parameters which should aid in evaluating the
performance of the various detection schemes used. The nature of both events is that
the product of uv is negative; they are Reynolds stress producers. Ejections should
induce negative fluctuations in the spanwise vorticity as the more vortical fluid from
near the wall is convected upwards. Similarly, sweeps should induce positive fluctua-
tions in (0,. In either case the RMS of tr)z is likely to be higher during these events

than it is on average.

Other event definitions will suggest different performance indicators. For exam-
ple, if the event to be located has a well-defined visual appearance, the one-to—one
correspondence between visual and probe-based detections will be a strong indicator of
detector performance. The factors P(D) and P(E) as defined by Bogard (1982) indicate
the level of one-to-one correspondence between any two detection schemes. The fac-

tor P(T) as defined below gives a time-resolved29 indication of how well the detection

 

29 Actually, P(T) is an event-resolved indicator, since the average likelihood of a correct
detectionisdeterm'medateachpointintirnedminganevent’sensemble.

31

scheme under test locates the presence of the correct event when it is ”known” that
such an event is occurring. P(D) and P(E) yield scalar quantities, while P(T) yields a
time series; all of these will be dependent on the threshold level chosen for the probe-
based detector. One-to-one event correspondence will be dealt with in section 2.6.2
and applied in Chapter 4. Some additional analysis concerns will be dealt with in sec-
tion 2.6.3.

2.6.1 Long-time statistical performance parameters

Old and new performance parameters are defined here which can be used to rate
how well a detector locates the presence of a sweep or ejection. The older parameters
will be presented first, followed by ones specific to the nature of the sweep and ejec-
tion as discussed above. The mean event frequency indicates how many events occur
per unit time. It is calculated by dividing the number of detected events by the total
data set length:

= (# of events)x(sampling rate)
(total # of ticks in the data set)

 

When inner variables are used to normalize this value, f*= fle}; if outer variables are
used, the dimensionless quantity is f8/U... The mixed normalization factor is always

defined to be the geometric mean of the inner- and outer-normalization factors, so in

 

this instance the mixed normalization factor is \I(v5)/(U?U.,). For comparison pur-
poses, results will only be given in dimensionless form, although all three normaliza-
tions will be presented.

The average event length is calculated by multiplying the average event duration

by an appropriate convection velocity. In the outer region it is generally assumed that

32

the convection velocity of a cohaent motion is approximately 0.90... Falco30 meas-
ured an average speed for pockets of 0.6U... In either case the convection velocity is
proportional to U... so as long as this speed is only weakly dependent on distance from
the wall, U. can be used to give event lengths suitable for comparison purposes. This
will permit us to determine whether or not a given normalization eliminates the depen-
dency of event length on Reynolds number or probe distance from the wall. Average
event lengths are then calculated by dividing the total detection time by the number of
events and multiplying by U..:

I: Sandividual event durations) xU
total number of events

 

Utlv is the inner-variable normalization factor, and 1/8 is the outer-region factor

used31.

Sweeps and ejections produce negative uv (by definition). A parameter which
indicates how often the detector is "ON" during periods in which negative uv is being
generated would be useful in evaluating the performance of that detector. Since large
magnitudes of uv contribute more to the long-time EV correlation, those times should
be weighted more heavily than ones which only produce minimal contributions to W.
This suggests that the percent of Reynolds stress "captured" should be defined as fol-
lows:

j u(t) v(t) dt

%negUV 3 MW“
I u(t) v(t) dt

Illtime

 

 

3° Private communication, 1988. See also Falco and Gendrich (1989).

3‘ It was suggested by C. Walk and H. Nagib of l.I.T. (private communication, 1990) that 9
wwldbeameaccmatdydetamhwdesfimateofmeoutenegionlengmxaledmnb. Un-
fmumately,mmffidmfinwwasavaihblemhmpaatemeirwggesfiminwmisstudy.

33

If sweeps actually convect fluid with a lower vorticity intensity, ltbzl, from the
outer region down to the level of the probe, they will cause positive fluctuations in
vorticity during an event (given our coordinate system and measurement location).
Ejections should behave in the opposite fashion, bringing up fluid with a higher vorti-
city intensity from nearer the wall, inducing a negative fluctuation which should show
up in the vorticity event average for ejections. A long-time performance indicator
which deals with the vorticity should deal with either the average fluctuation or the
average intensity of the fluctuations (RMS). Since the average fluctuation can be
shown in an ensemble, the intensity of the fluctuations will be the long-time perfor-

mance indicator used.

 

If high-intensity fluctuations are present, this parameter should be greater than one,
unless only the event under consideration produces all of the vorticity fluctuations
experienced by the probe or the vorticity changes occur before the detector turns "ON"
or after it has turned "OFF."

The energy associated with an event is a function of the the turbulence kinetic
energy and the enstrophy. Vorticity has already been dealt with above, but kinetic
energy has not yet been considered. Since the spanwise velocity, w, was not meas-
ured, only two out of three components of the turbulence kinetic energy are available.
Therefore the event intensity parameter to be considered will be approximated by
u2+v2, and this value will be non-dimensionalized by the long-time RMS of that quan-
tity.

(“2+ng mm,

(u2+v2)’

 

TKEparameters

34

Note that the quantities used in calculating the TKE parameter are the fluctuating
velocity components after the mean components have been subtracted out. Further-
more, the TKE parameter is based on the average value of the turbulence kinetic
energy during the events under consideration, not an RMS of that quantity. Therefore
strong events whose velocity components vary substantially from the mean during an
event will produce higher values for the TKE parameter than events whose velocity
components oscillate about the mean.

2.6.2 VisuaLcorrespondence performance parameters

Bogard (1982) proposed two different ways to gauge the long-time correspon-
dence between visual and probe-based detections. These parameters, called P(D) and
P(E), were the probability that a visual detection would occur during a given probe-
based detection and vice versa, respectively. P(D) and P(E) are defined as follows
(after Luchik and Tiederman, 1987):

 

_ ”-
P(E) 8 NE
_ N13v
9“” = is:

N5 is the total number of visual detections, ND is the total number of probe-based
detections, NED is the number of visual detections which correctly correspond32 to a

probe-based detection, and NDV is the number of probe-based detections which

 

32”Correct1:1correspondence'asusedinthisstudymeansonlythatthesarneeventis
detectedbybothmethodsatsorneoverlappingpointintinre. Nopenaltiesareassessedfor
detectingthewrongtypeofeventtxdetectingnoeventatall. P(E)andP(D)thereforehavea
rangebetweenzeroardone.

35

correctly

correspond to a visual detection. If either NE or ND is zero, both P(E) and P(D) are
defined to be zero.

A new quantity, P(T, t), is required to indicate how good the one-to-one
correspondence is at each point in time during an ensemble averaged reference detec-
tion. If we choose visual detections to be our reference, we can define P(T) as fol-
lows:

Nov at this t
Na

 

P(T, t) E

This variable shows the relative frequency of occurrence of probe-based detections as a
function of time during the reference (visual) detections. Within this context one can
think of P(T) as an event-resolved P(E) value. When P(T) equals P(E), all of the
probe—detected events which corresponded to any visual event overlapped at that
event-resolved point in time. PCT) in combination with the probe-based detection cri-
teria used will allow more specific limits to be set on flow variables at certain points
during the visual detection without needing to calculate the ensemble average of those
variables. For example, if a high-threshold uv-quadrant detection frequently occurs at
a given point during a visual event, one can conclude that the magnitude of uv at that

point is usually large.

The event-resolved correlation between visual events and probe-based detections
can show a number of interesting details regarding the relative location of those detec-
tions with respect to each other. If the P(T) plot is a horizontal line, the probe-based
detections either occurred at exactly the same point relative to the visual detections or

they must not be correlated with each other at all. That is, a horizontal line on a PCT)

36

plot indicates either perfect correlation or no correlation at all; P(D) will indicate
which. If P(T) varies significantly with time relative to the start and end points of the
"average” visual event, a certain level of correlation is present, indicated by PCB/P(E).
For example, given a P(D) of 43%, P(E) of 40%, and the PO) plot (threshold=0.7) as
shown in Figure 4.2.7a, one sees a) that 43% of the uv-quadrant ejections overlapped
with an RLM ejection, b) that 40% of these visual events overlapped with a probe-
based detection, and c) that three quarters of those overlaps occurred at 5I6“B of the
way through the visual event, at the peak in the plot where PCT) is about 30%.

2.6.3 Additional Considerations

Statistics are calculated for those periods during which detections are said to be
occuning. Therefore, one must consider how well those statistics will have converged
to their long-time values given the number of data points which are used. Using a
Weak Law of Large Numbers formulation and 95% confidence interval, Klewicki
( 1989) has calculated the convergence of different statistical moments for data taken
with these probes in flows between 1000<R9<5000. As long as the sampling rate is
large enough”, the number of samples required is not the prime concern; it is rather
the time over which values are summed. This is due to the fact that independent sam-
ples are needed to assure convergence of the statistics to their correct values. Normal-

izing these sampling times with outer variables provides a Reynolds number

 

33 The Kolmogorov frequency is an adequate lower bound on the frequency for the purposes
ofthis analysis.

37

independent approximation to how much data must be taken in order to assure a given

level of convergence for the statistics.

The mean and RMS velocity and vorticity statistics should converge to within 3%
by the time tUJS exceeds 1000. Velocity-vorticity correlations will probably not con-
verge until over 3000 tU../5 has elapsed. Skewness values require as much as 3500 to
6000 tU_/5 in order to converge to within 5%; flatness values generally require
between 2000 to 5000.

The performance indicators outlined above require only average and RMS values,
and convergence to 10% would be considered acceptable for the purposes of this
suldy. Convergence of velocity and vorticity average and RMS values to within 10%
should be obtainable with measurements taken over as little as 200tU,,/534. Therefore
if events have a length scale of 0(8), then averaging over 200 events should produce

statistics converged to i10%.

The scaling of events in the outer region35 of the boundary layer is to be con-
sidered in Chapter 3. Inner, outer, and mixed variables will be used to scale each vari-
able in the "average event" ensembles calculated from either visual detections or
probe-based detections made with a given thresholding level. The trends of each vari-
able during the ensemble will not be affected, but the scaling between data sets will
change. Since the length of each event is stretched or compressed until it fits into the

desired length of the ensemble, no special scaling will have to be done to the time axis

 

3‘ Klewicki (1989), pp. 164, 183-8, and private communication.

35 hm—regimevenmwiflnmbexaledsincediedamsaswaeanmkmmapproximately
the same Reynolds number (Ra-757%). This applies especially to Figures 3.3.1 and 3.3.2.

38

before ensembles fi'om different Reynolds numbers can be compared.

It is expected that the length of events in the inner region will scale with inner
variables, and that those events will grow larger the further they are from the wall. In
order to test this hypothesis, the inner-scaled average event length will be calculated
and then divided by the non-dimensional probe height above the wall. It should be
noted that some normalization needs to be used, since the flow parameters for each
data set are not quite identical, however the choice of normalization should not

significantly affect the results.

CHAPTER 3

EVALUATION OF VISUAL AND PROBE-BASED DETECTION SCHEMES

The event detection schemes described in sections 2.4 and 2.5 were applied to the
data sets described in sections 2.1-2.3, and the appropriate performance parameters
were calculated as described in section 2.6. Those results are presented in this chapter,

and Chapter 4 presents comparisons of the results from different detection schemes.

Results fiom all of the probe-based detection schemes depend on the thresholding
constant, c. This variable can take any non-negative value, and results were calculated
for increasing values of the thresholding constant until no events were detected for at
least three of the data sets used. This resulted in a thresholding range of 0—3 for the
u-level technique, 0-6 for the TERA approach, and 0-7 for the uv-quadrant analysis.

The TERA technique also depends to a certain extent on the choice of a short-
time averaging window length. Falco and Gendrich (1989) showed that using a win-
dow of St” or greater would create a situation in which the threshold has a much
greater effect on the results than the window length. Therefore the window was
chosen to be at least 5t+ (generally 25 ticks; see Tables 2.1.3 and 2.2.3) for this detec-

tor when applied in both the inner and outer regions.

39

4o

Long-time statistical performance parameters were calculated for all six detection
schemes employed“. Four inner- and four outer-region data sets37 were available for
analysis, and both sweeps and ejections were located by all except the LSM visual
detection method. For each performance parameter (e.g., inner-scaled average event
length) sixteen curves are required to describe the response as a function of threshold,
event type, and y+ or Re. It was found that this was too much to put on one plot, so
figures are divided according to whether inner-region or outer-region results are plot-
ted. Performance of sweep and ejection detections from the same data set are plotted
using similar symbols, and the same symbols are used consistently throughout all of
the figures. This means, for example, that results associated with sweep detections on
the y+=24.2 data set will always be plotted with the open diamond symbol, and the
corresponding ejection detection results will be shown by the crossed diamond symbol.

For each detection scheme the number of events and total event time will be
shown first in order to give an indication of the the statistical uncertainty present in the
subsequent results. Long-time average values will then be shown, including mean
event frequency, average event length, percent of Reynolds stress "captured," RMS
spanwise vorticity during events, and turbulence kinetic energy level. Finally, event
averages of u, v, uv, (oz, and vcoz will be presented in conjunction with the RMS for
each variable, to give an indication of the average events’ characteristics, and how
variable each turbulence quantity is during that particular kind of detection. Plots
which will be compared from detector to detector are in general plotted on coordinates

 

3‘ThesesixamdnlSM,RLMmdhna-ngimfisualde&dmmflhods,deuv—qua¢ant
breakdown technique, TERA, and the u-level technique.

37Table22.2:howsmadtearmeRfl400datasetisprobablynotlongenoughtogen-
erate long-time statistics significant to 10%, however this is also the case for the Ro=31m
RLMdataset. Itisseendlatsorneofdierestdtscalculatedfiommesedatasetsdomtcon-
fammuendsesmbfidwdbydeodterdamsemhowevadwsemflmxemvathdessshown
forcomparisonptnposes.

41

whose y-axes are scaled differently. This allows for the most precise determination of
Reynolds number or y” trends, but it enjoins caution when making comparisons from

plot to plot.

The performance parameters presented in this chapter will be evaluated on the
basis of Reynolds number or y” trend for a given type of event and whether or not
differences exist between results corresponding to sweep and ejection detections for a
given data set. The analysis results will be presented in the same order in which the
analyses were presented in Chapter 2. Sections 3.1-3.3 will be devoted to results from
the three different visual detection approaches, and sections 3.4 through 3.6 will con-
tain results from each of the different probe-based detection schemes.

3.1 LARGE-SCALE MOTION (LSM) RESULTS

The films resulting from Signor’s outer-legion ring-like motion study were
analyzed in 19845 by Falco, et. al. (unpublished) to determine the start and stop times
for LSM events as described in section 2.4.1. This analysis resulted in a database of
visual detections which corresponded to the entire available database of hot wire data.
The most detections (647) were available for the lowest speed (R9=730), and the
fewest were available for the shortest data set (37 detections for R9=l400). This gave
an outer-normalized total event time between 52 and 753 tU../8. Consequently we can
expect. fairly well-converged results for all except perhaps the R9=1400 data set. See
Table 3.1.1.

42

Rao, Narasimha, and Badri Narayanan (1971) suggest that the fiequency of
inner-region bursts should be Reynolds number independent when scaled with outer
variables; Blackwelder and Haritonidis (1983) suggest that inner variables will provide
a Reynolds number independent scaling, while outer variables will provide a non-
dimensional frequency which increases as R3". These detections were all made by
applying the VITA technique to inner-region hot wire data.

Since fewer than 200 LSMs were found at R9=3120, the frequency calculated at
that Reynolds number is only marginally significant; with only 34 events, the useful-
ness of the R9=1400 frequency calculations is doubtful. For the three longer outer-
region data sets then, inner scaling provides a dimensionless frequency which increases
then decreases with Reynolds number. Outer and mixed scaling give dimensionless
frequencies which decrease monotonically with increasing Reynolds number. It should
be noted thatthe probes used had a spatial scale shorter than the 20U1/v cutoff noted
by Blackwelder and Haritonidis (1983), therefore spatial averaging should not have
adversely affected these results.

The average event lengths scale poorly with inner or mixed variables, but when
scaled with outer variables, the average event is approximately one boundary layer
thickness in length38 and relatively Reynolds number independent. Even the R9=l400

events which were detected averaged around 18 in length.

 

3‘ Recall that a convection velocity of 1.0xU_ was used. A convection velocity of 0.9XU_
makestheouta-scaledlengthsveryclosetooneindeed,althoughtheRo=3lweventsarestill
a little longer than expected.

43

The most common long-time normalization of <uv> is to divide the average uv
during events by the long-time RMS of uv. This normalization is presented in Table
3.1.1 for comparison with the percent Reynolds stress "captured". LSM detections
capture between 45% and 60% of the Reynolds stress present in the outer region. The
average turbulence kinetic energy during LSMs is 77% to 89% of the long-time RMS
of the TKE. The RMS spanwise vorticity during LSMs from the three lower Reynolds
number data sets is close to the long—time RMS of (oz, while the RMS of (a2 during
R9=3120 LSMs is only half of (02'.

The event averages for an LSM detection are shown with outer, mixed, and inner
normalizations in Figures 3.1.1 through 3.1.3. One quarter of the ensemble’s standard
deviation at each point in time39 is plotted as an error bar about each curve. Unfor-
tunately the high variability of the LSM ensembles yields plots which have quite a
messy appearance; see for example Figure 3.4.32 in which there is quite a large range
of variability between the different quantities which were ensembled. The LSM
ensembles show a relatively constant RMS which for each variable is almost an order
of magnitude larger than the peak-to-peak variation in the average. The relative varia-
tion of the a), and v0)z ensembles is larger than the others, though. Furthermore, the
larger the sample size, the more nearly the ensemble average approaches zero as a

limit.

These results suggest that the typical LSM event is not an active producer of the

same kinds of turbulent motions throughout its entire lifetime. The high variability of u

 

39 The mean :t l/4 RMS for a Gaussian distribution gives limits within which only 20% of
the samples will fall. Although the distribution at each point in time of these ensembles is not
in general Gaussian, the high RMS values are strong indicators of the high variability of each
variable at each point in time.

44

and v throughout the life of an "average" LSM indicates that high-intensity turbulent
motions occur at random between the start and stop of an LSM. Outer scaling of the
ensembled quantities produces values whose maxima have approximately the same
magnitude; outer scaling does this better than mixed or inner scaling. However, the
event averages show no agreement or consistent Reynolds number trend between all
four data sets. This is probably attributable to the high variability shown by these

averages.

3.2 RING-LIKE MOTION DETECTION RESULTS

The results of Signor’s (1982) RLM analysis were converted into sweep and ejec-
tion start and stop times as described in section 2.4.2, and the long-time statistical per-
formance parameters associated with those detections are shown in Table 3.2.1. Since
six of the eight zones comprising a "typical eddy" are generally low-speed, outward-
moving regions, it is not surprising that ejections generally outnumber sweeps 4:1.
Unfortunately, even the ejections for each data set are fewer than 200 in number; the
outer-normalized total event time varies from 4-10 for sweeps and 23-58 for ejec-
tions“. The events presented below should be considered in this light; they represent
an indication of what this detection scheme might do on average if more samples were

available.

 

4° Detections from all four Reynolds numbers comprised Signor’s "grand ensembles," so
thoseresultsdidnotsufferfromapaucityofdataasdothese.

45

Falco (1974) and Signor (1982) observed that the intermediate-scale ring-like
motions which were observed had a length which was generally on the order of the
Taylor microscale. Therefore it is not completely surprising that a mixed-variable scal-
ing of the mean event frequency and mean event lengths produces results which exhi-
bit the least Reynolds number dependence. The mixed—scaled frequency for ejections
ranges from 100—124x10‘6; the corresponding sweep frequency range is 20—34x10“.
Mixed-scaled ejections are slightly longer than sweeps, and this is probably a conse-
quence of the length of zone 1 versus the other zones (see Figure 2.4.1). Since the
RLMs were contained within the LSMs“, it was expected that these events would be
shorter than one boundary layer thickness in length, and they are.

The RLM contains a fairly low percentage of the Reynolds stress generated in the
outer region, somewhere around 30%. Note that the 63% total detected in the RLMs
at Ro=3120 must be a consequence of the different data set lengths; the 139 LSMs
detected at this Reynolds number only contained 57% of the negative uv, and the
long-time RLM percentage must be less than or equal to this, since RLM detections
are a subset of LSM detections. Greater stresses are at work on average within an
RLM, as shown by higher fluctuations in (02 and higher average turbulence kinetic
energy levels. This is also indicated by the fact that the average magnitude of uv as

normalized by (uv)’ is greater for RLM’s (about 0.6) than it is for LSM’s (about 0.48).

Normalized ensembles of u, v, uv, (oz, and vtuz during an RLM sweep are shown
in Figures 3.2.1-3.2.3; the outer-, mixed-, and inner-normalized ejection event averages

are shown in Figures 3.2.4 through 3.2.6. High RMS levels are present once again,

 

“ Smoke is required to detect an RLM, and since presence of smoke is the only LSM
detection criterion, all RLMs must occur within an LSM detection time.

46

but the relative magnitude of the RMS compared to the peak of the average is lower
than it was for the LSM. The peaks in the RMS generally fall on local minima or
maxima in each plot; minimum RMS levels generally occur near zero-crossings. It is
interesting to note that the RMS values for sweeps are usually lower than the
corresponding ejection RMS values, even though (or perhaps because) there are
significantly more ejections than sweeps. The negative average values for it during
sweeps at R9=2380 are accompanied by the highest RMS values of all four data sets.
This is not inconsistent with the results of Signor (1982), but it certainly is unexpected.
As mentioned earlier though, Signor’s results (especially Figure 3.33) are averaged
over all four Reynolds numbers and have a correspondingly higher number of sam-
ples.

The rotational nature of the RLM tends to induce a sign change in v during the
event, at which point uv goes to zero. This is doubtless a contributor to the reduction
in Reynolds stress captured during RLMs versus LSMs. The positive to, fluctuations
for the R9=730 and 2380 sweeps are not expected based on a consideration of Figure
2.4.1; fairly strong vorticity fluctuations of the sign of the mean are expected from
both zones 1 and 2. However, those results are consistent with Figure 3.40 in Signor
(1982). The negative peaks in the (l)z ensembles for both sweeps and ejections are also
consistent with Signor’s results. Note in Figure 2.4.1 that positive vorticity fluctua-
tions are expected only from zones 7 and 8, while zones 3-8 have the u and v averages
characteristic of an ejection. The contributions from the events of zones 1, 7, and 8
are undoubtedly the largest cause of the high RMS values present in the a), ensembles
for both sweeps and ejections. The large variability in it during an RLM at the
different heights associated with the different zones probably causes the very high vari-

ance seen in the <u> plots.

47

The RLM is a more active event on average than the LSM, and it appears to cap-
ture about half of the Reynolds stress which is present within the LSM. As noted in
section 3.1 though, the LSM accounts for less than 60% of the negative uv present at
y/5=0.8. The peak level of vorticity within an RLM averages 2 to 4 times higher than
that present in the LSM, with a corresponding increase in the RMS vorticity. The
RLM ejection generally has more energy than the corresponding LSM or RLM sweep.
Once again outer variables produce normalized ensembles whose minima and maxima
are of approximately the same magnitude. While there is poor agreement between the
average behavior of u, v, uv, (t)z and vol)z during sweeps at the four Reynolds numbers
considered, those variables do have similar trends during the average RLM ejection
event. It should also be remembered that these results may be preliminary in nature

because of the relatively small number of events which were analyzed.

3.3 INNER-REGION VISUAL DETECTION RESULTS

The inner-region visual analysis described in section 2.4.3 was applied to all of
the film available, and 96-530 sweeps and ejections were located with the probe at
each different height above the wall. The shortest data set, y+=15.0, gave the fewest
detections, and the y+=14.6 data set was taken with the probe almost at the same
height above the wall in viscous units. Although the y+=15.0 results are shown, it is
expected that the y+=14.6 results will provide a more accurate indication of what

occurs around that location in the near-wall region“. The total detection times range

 

‘2 Recall that detections from the y*=l$.0 film had the least uncertainty with respect to start
andstoptimes. Theonlyproblem withthisdatasetisthatonlyonerolloffilmwasshot,so
the data set is smaller than one might like.

48

from 50—630 tU.,/8; the y+=18.9 ejection detections have a statistical significance

which is marginal. These data are summarized in Table 3.3.1.

Note that although the probes were moved, the event detection "point" was not.
Small differences might also be inherent in the results, since the Reynolds number of
these data sets did vary between 704 and 744. If the results are truly converged to
their long-term values, the inner-scaled frequency and event length values should be
accurate to :|:10%. Results which vary by more than this amount should be due to
differences in temporal and spatial resolution between the films which comprise the

visual record of these data sets. These differences were discussed in section 2.4.3.

Blackwelder and Haritonidis (1983) show that bursting frequency increases from
the edge of the viscous sublayer out to y+=40, giving values for f* between 0.0018 and
0.0028. The events detected were ejections, and both the bursting frequencies and
trend agree very well with the y+=l4.6 and 18.9 data shown in Table 3.3.1. As noted
in section 2.4.3, there were problems with film graininess and temporal resolution
which limited the scale of events that could be detected when the probe was positioned
at y+=24.2. This should have resulted in fewer events with generally longer length
being detected, and one can see here that the y+=24.2 frequency is indeed lower than
what was expected. More sweeps than ejections were located using the inner-region

visual analysis, resulting in a higher sweep detection frequency.

Ejections not only occurred less often, they also had a shorter average length than
the visually detected sweeps. In appearance the sweeps most often looked like "pock-
ets" as described by Falco (1980) and Lovett (1982). Ejections most often looked
either like a ridge of low-speed fluid pushed up and out by a sweep or like a long
streak which frequently appeared to be induced by a motion on one side or another

49

which contained streamwise vorticity”. Although the streaks were significantly longer
than the streamwise spatial extent of the "pockets," it seldom happened that a streak
moved lengthwise over the X-array while continuing to develop. This is what caused
the calculated length of an "average" ejection to be shorter than the "average" sweep.
The events detected at y+=18.9 were shorter than the corresponding events at 14.6, but
those lengths seemed to increase marginally from 18.9 to 24.2. This apparent length
increase was probably due to the analysis difficulties discussed above and in section

2.4.3; an increase in length was the expected effect of these analysis problems.

Visually. detected ejections capture about a quarter of the Reynolds stress in the
near-wall region, while sweeps account for another 40% or so. This is a little more
than the RLM and LSM detections in the outer region and corresponds roughly to the
performance of the uv-quadrant technique with a threshold of 1. Both sweeps and
ejections contain spanwise vorticity fluctuations which are about as intense as the
long-time RMS of (oz. The average turbulence kinetic energy associated with an ejec-
tion is higher than the TKE RMS and increases with distance from the wall, while the

sweep’s average TKE is less than the RMS and decreases with increasing y“.

Ensemble averages of u, v, uv, (oz, and val, during inner-region visual detections
are shown in Figures 3.3.1 and 3.3.2. The level of variance in these averages as indi-
cated by the RMS of those values is high, but again not as high as that for the LSM
ensembles. This detection scheme was designed to locate sweeps and ejections on the
basis of visual information, and the ensembles show that this is indeed what was done

on average. The average streamwise velocity of these motions is higher around y+=15

 

‘3 Here is a good instance of two uniquely identifiable motions which contribute to ulr-
bulence production, have attributes of an "ejection", yet have quite dissimilar physical charac-
teristics like spatial extent and temporal duration.

50

than it is further out in the boundary layer; the wall-normal velocity is highest at
y+=18.9. The ti)z plot shows that on average an increase in vorticity“ occurs just
before the passage of a sweep at the lower probe positions. This correlates nicely with
the observation that an ejection often preceded a sweep, and that ejection can be
expected to have a higher vorticity intensity than the mean. A decrease in vorticity is
associated with the passage of a visually detected sweep when the probes are higher
up, although the magnitude of this change is less for the y+=24.2 case. This tends to
support the observation that these visually detected events most often looked like the

"pockets" described by Falco (1980) and Lovett (1982).

Peaks in the v ensemble reveal that visual detections tend to miss the earlier part
of the event. The smoke which was observed in order to make the visual detections
marked only the viscous sublayer, whereas the probes were always located above
y+=7. Sweeps, moving wallward as they do, should have passed the level of the
probes before reaching the viscous sublayer where they would act on the smoke.
Therefore it is logical that the v excursion for sweeps should begin well before the
start of a visual detection. It is however surprising that the wall-normal velocity also
tends to be fairly high by the time a visual ejection starts, and that the v peak at
y+=18.9 occurs before the start of visually detected ejections. This suggests that the
motions which are classified as ejections by probe-based schemes might not originate
in the viscous sublayer; rather an upward motion starting further out entrains fluid

from the sublayer which subsequently appears to be an ejection.

 

‘4 Recall that the mean shear stress produces an average spanwise vorticity which is nega-
tive, therefore negative excursions of to, about the mean produce an increase in the magnitude
of the spanwise vorticity.

51

There are a number of other possible explanations for the behavior of the v
ensemble during ejections: The inertia of the oil droplets might have induced a delay
in the response of those particles, but that should also have caused non-zero u and v
ensembles at the end of the visual events which is not the case. The uncertainty associ-
ated with determining the start and stop of a visual event might have been biased
toward later in the event, although that should. also have resulted in an offset at the
end of the event which isn’t apparent. The criteria for locating the start of an event
might have been applied too strictly, forcing the presence of strong motions to cause
the smoke activity which was required before an event was said to .exist. However,
even the latter explanation does not account for the fact that the peak in the y+=l8.9
ensemble occurs before the start of the event. Therefore, it seems most likely that the
explanation at the end of the previous paragraph is the correct one, that is, events fre-
quently originating above the viscous sublayer entrain fluid from the sublayer to pro-

duce the visual signature which the present analysis classifies as an ejection.

The "average" inner-region visually detected event is a fairly vortical structure
which loses its turbulent energy as it gets closer to the wall. The sweeps usually
penetrate to at least y*=15, and the ejections tend to rise at least that high but not usu-
ally up to yT=l8.9, although the strongest vertical motions are generated at that point,
occuning before the start of the average visual ejection. A total of 60% to 70% of the
Reynolds stress generated in the near-wall region is contained within events located by
applying the inner-region analysis described in section 2.4.3. The requirement that an
event be active before it is said to exist results in an asymmetric ensemble, with peak

values in u and v occurring near the start of an "average" event.

52

3.4 uv-QUADRANT ANALYSIS RESULTS

The uv-quadrant analysis technique was applied to both the inner- and outer-
region data sets, and the results from these analyses are shown as a function of thres-
holding constant in the figures of this section. Figures 3.4.1 - 3.4.3 show the number
of events detected when this technique was applied to the data sets used for inner-
region, RLM, and LSM visual detections. Note that fewer than 200 events are
detected for the y+=15.0 data set, but the corresponding results will be included any-
way. For thresholding constants larger than 1.0, fewer than 200 of each type of event
are detected at any probe height in the inner region. In the outer region that point is
reached after c exceeds 3.6. Outer-region events must be of shorter duration45 than
inner-region events detected with the same threshold, since fewer events in the inner
region produce total event times of greater than 200 tU.,/8 until c goes above 1; the
corresponding outer-region threshold limit is 0.7. As expected because of the brevity
of the RLM data sets, this analysis produced only a very limited number of events to
be compared with the RLM detections in Chapter 4. Total event times are shown

under inner, outer, and mixed normalizations in Figures 3.4.4-3.4.12.

Note that when the threshold is zero, the number of sweeps for a given data set is
approximately the same as the number of ejections. As the threshold increases, fewer
sweeps are eliminated in the near wall region, in contrast to the wake region where
fewer ejections are eliminated. Since the Reynolds stress is the detected variable in
this scheme, an incremental increase in the thresholding level should eliminate fewer
events from the quadrant containing the Reynolds stress peak. Therefore the event fre-

quency as a function of threshold is a result of the detection criterion used and the

 

‘5 That is, outer region events are of shorter duration under outer variable normalization.

53

probe location.

The number of events and the total time during which a detector is "ON" are
functions of the data set length as well as threshold, so agreement between data sets is
not expected. As noted earlier though, it is expected that inner-region event frequency
(Figures 3.4.13 - 3.4.15) should be approximately constant for a given threshold when
sealed with inner variables. The sweep and ejection frequency for each data set is
about the same, but neither good agreement nor the slight increase with y+ which was
observed by Blackwelder and Haritonidis (1983) using the VITA technique is seen

with this technique using any scaling.

In the outer region however, inner variables do appear to do a good job of scaling
uv-quadrant detection frequency (Figures 3.4.16 - 3.4.18), with the exception of the
R9=2380 data. Note that the sweep frequency is lower than the ejection frequency in
the outer region for uv thresholding constants greater than 1.0, and recall that we

expect frequency results to be significant through thresholds of 3 or so.

Event lengths (Figures 3.4.19 - 3.4.24) were scaled with inner, outer, and mixed
variables. It can be seen that sweep events are longer than ejection events for y’SlS.
Inner-scaling suggests that inner-region events get shorter with increasing y", however
this trend is not observed under mixed or outer normalizations. One expects the
inner-region event length to scale with inner variables, though, and the lack of agree-
ment noted above may be a result of the event convection velocity chosen. As indi-
cated earlier, ‘it was assumed that convection velocity is only weakly dependent on dis-

tance from the wall. R. E. Falco46 argues that coherent motions would not remain

 

‘6 Private communication.

54

recognizable as such if they experienced a convection velocity which varied
significantly from top to bottom. A. N aguib“7 indicates his data support the notion
that convection velocity is not approximately constant at 0.6U.. throughout the near-
wall region“. If convection velocity does indeed increase with distance from the wall,
it might be seen that average event length scales with inner variables and is not a func-

tion of distance from the wall (Figure 3.4.25).

The essence of the uv-quadrant breakdown is that events are classified by the
magnitude of the Reynolds stresses they generate. The events considered here are only
those which generate negative uv, and the percentage of the negative uv "captured" by
these events is shown in Figures 3.4.26 and 3.4.27. The first of these figures shows
good agreement with results from y+=50 presented by Alfredsson and Johansson
(1984). Note that those authors plotted the total -W as a consequence of +138% from
quadrants 2 and 4 and -38% from quadrants 1 and 2; their 78% contribution from the
second quadrant49 would be shown as 57% in Figure 3.4.27. These results are undeni-

ably a consequence of the detection criterion used.

The RMS vorticity fluctuations are shown in Figures 3.4.28 and 3.4.29. It is clear
from Figure 3.4.28 that both sweeps and ejections in the inner region, with the excep-
tion of ejectidns occurring at y“=l4.6,so produce spanwise vorticity fluctuations which

are about as intense as the long-time RMS of 0),. Figure 3.4.29 offers a much less

 

‘7 Private communication, supported by comments from C. Wark and H. Nagib.

‘3 It is interesting to note that Naguib uses the uv-quadrant breakdown with a threshold of 3
to detect events downstream of a wall-mounted shear stress sensor. He calculates convection
velocity for sweep events by noting the average time required for them to travel from the
upstream detection point to the one downstream.

‘9 Alfredsson and Johansson (1984). P. 331.

5° The y+=150" values do not show good agreement with the y’=14.6 results, however this
may be due to the different data set lengths as discussed above.

55

straightforward interpretation. Among the ejection detections, vortical intensity varies
by a factor of five as it increases from R9=3120 to 730 then to 2380 and 1400. The
a)z RMS associated with R9=3l20 sweep detections increases initially but then falls,
while the vortical intensity of R9=2380 and 730 sweep detections increases monotoni-
cally with threshold. About the only consistent conclusion which can be drawn from
Figure 3.4.29 is that for thresholds of 0.9 or higher, ejections have larger fluctuating

spanwise vorticity intensities than sweeps in each data set.

The turbulence kinetic energy of events detected by the uv-quadrant technique is
shown in Figures 3.4.30 and 3.4.31. Events corresponding to the quadrant in which
the Reynolds stress peak is located should, on average, produce a greater level of
TKE”. As noted above, sweeps are the dominant Reynolds stress producers at y"$15,
so the results shown in these two figures are simply what was expected based on the

detection criterion and the distribution of the detected variable as a function of y+.

Calculating event averages requires that a threshold be chosen which can be
applied at the four different Reynolds numbers to be plotted. Some authors (e.g.,
Bogard and Tiederman, 1984) have chosen their threshold levels so that the number of
probe-based detections is the same as the number of visual detections. Authors who
are not looking for a high level of correspondence with visual data (e.g., Alfredsson
and Johansson, 1983) tend to choose higher thresholds in an effort to select only the
strongest events for analysis. To achieve the same number of probe-based detections
as visual detections would require a threshold of 0.2 in the inner region, 2.0 for the

ring-er motion data, and a value increasing with Reynolds number from 0.2 to 3.0

 

5‘ Recall that in the absence of the spanwise fluctuating velocity component, w, TIE is cal-
culatedasthesquareofuplusthesquareofv.

56

for the large-scale motion data. The statistics based on number of events (as Opposed
to total detection time) were well-behaved generally up to thresholds of 3, and stronger
events were more interesting than weaker ones, so a threshold of 2.45 was used to cal-

culate the event averages shown in this section.

Ensembles of the uv-quadrant sweep detections are shown in Figures 3.4.32-
3.4.34, while the ejection ensembles are presented in Figures 3.4.35-3.4.37. The detec-
tion algorithm used specifies that the magnitude of uv will have a given value at the
start and end of an event. Therefore the uv plot crosses the start and stop time marks
at the threshold level, resulting in a variance for uv which is zero at those times with a
peak in the middle of the event. Both u and v had to be fairly large for their product
to exceed the threshold, and this resulted in a significantly lower variance for <u> and

<v> when compared to the visual detection ensembles.

Outer scaling of both sweeps and ejections produces v ensembles which are
noticeably grouped into two curves, R9=730 & 1400 and R9=2380 & 3120. The low
variance for all of these curves suggests that this is more than just coincidence, that
uv-quadrant events in the outer portion of the boundary layer have <v> magnitudes
which scale with the free stream velocity and that those relative magnitudes become
larger at higher Reynolds numbers. Inner scaling produces a clear Reynolds number
trend in the v ensembles while causing the <uv> curves to group in the same way that
the <v> curves did under outer scaling. It was not expected that any variables would
cause universal scaling of the <uv> curves since the threshold level is the product of
u’ and v’, both of which are Reynolds number-dependent quantities (Klewicki, 1989).-52
Inner scaling is the clear choice for <uv>, and it should be related to a Reynolds

 

52 See also Wei and Willmarth (1990).

57

number shift in it? statistics at y/8=0.8, but inner scaling effectively eliminates com-

parisons of toz and v0), ensembles.

The (t)z variance is fairly large, especially for the ejection detection ensembles.
However, all four Reynolds numbers follow the same trend (seen best under outer
scaling in Figures 3.4.32 and 3.4.35), that of a strong vortical pulse at the start of the
event which relaxes toward zero. Recalling that Q, is less than zero in the near-wall
region, the negative vorticity fluctuation during an ejection is likely to result from the
upward convection of more intense (Dz from nearer the wall at the start of the event.
Similarly, inward convection of less vortical fluid from outside the boundary layer dur-
ing a sweep would result in the positive fluctuation observed on average at the start of

a sweep.

The "average" uv-quadrant detection is either a sweep or ejection whose fre-
quency, event length, turbulence kinetic energy, and u, v, & uv event averages can be
directly related back to the distribution of Reynolds stress throughout the boundary
layer and the choice of thresholding constant. The outer-region event is characterized
by a fairly strong initial peak in the spanwise vorticitys3 which relaxes toward zero as

the event progresses.

 

53Notetluttheto,peakislargerthantheRMSoftheaverageatthatpointinthenormal-
izedeventtime.

58

3.5 TERA ANALYSIS RESULTS

The TERA analysis was applied to both the inner- and outer-legion data sets
described in Chapter 2, and the results of these analyses are shown in this section. All
but the shorter 3 data sets (R9=1400, y+=15.0 and 18.9) produced an adequate number
of events (Figures 3.5.1 - 3.5.3) for thresholds up to 2 in the inner region and 3.5 in
the outer region. As was the case with the uv—quadrant analysis, slightly lower thres-
holds (just less than 2 for both inner and outer regions) produced total event times
(Figures 3.5.4 through 3.5.12) which exceeded 200tU../8 in duration.

No set of variables scales the inner-region detection frequency (Figures 3.5.13 -
3.5.15) so that it is independent of y", although outer scaling does appear to minimize
the differences. One can see most readily in Figure 3.5.14 the effects of grouping on
the frequency of TERA detections. Note that the frequency of y+=14.6 ejections,
y+=15.0 ejections, and y+=24.2 sweeps increases initially with increasing threshold.
This is accompanied however by a steadily decreasing total event time. The cause of
this is a combination of grouping and low threshold: At low threshold events are long
and close together, so the grouping process joins them up into a number of very long
events. As threshold increases, fewer of the events are close enough to be grouped, so
the total number of bursts detected increases, while the total event time goes down.
The apparently constant frequency of the y+=14.6 sweep, y+=15.0 sweep, and y+=24.2
ejection detections may also be a result of the grouping process and not some underly-
ing physical mechanism. As shorter events are eliminated with increasing threshold,
some grouped events are splitting up, thereby creating a relatively constant total

number of events, again with steadily decreasing total event time.

59

Outer-region TERA detection frequencies (Figures 3.5.16 - 3.5.18) behave in a
fashion very similar to the outer-region uv-quadrant detection frequencies. They scale
well with inner variables for thresholds of one or more. Sweeps occur less often than
ejections, and the R9=2380 detections seem to occur more often than any others.
High-speed events in the outer region seem to have less turbulence kinetic energy than
their low-speed counterparts, and the Turbulence Eenergy Recognition Algorithm

detects this.

Inner-region event lengths (Figures 3.5.19 through 3.5.21) seem to scale well with
inner or mixed variables, but again the events further out in the boundary layer appear
to be shorter than those nearer the wall. This may be a result of the convection velo-
city chosen; see the discussion in section 3.4 above. The strongest events appear to
have relatively constant lengths varying with y“ and ranging from 30 to 80 viscous
units (0.2-0.4 5)“. However, this appearance may be deceptive because of the rela-

tively few number of events detected at thresholds above 2.

Inner scaling of outer-region sweep detections (Figure 3.5.22) produces good
agreement between the Ro=730, 1400, and 3120 results. Mixed scaling (Figure 3.5.23)
produces relatively good agreement between all data sets except R9=3120. In any
event, TERA-detected sweeps in the outer region are longer than the corresponding
ejections, and those sweeps appear to have a length scale of around 50 viscous units.
It is interesting to note that under outer scaling (Figure 3.5.24), all events tend to a
length between 0.05 and 0.15.

 

5‘ Recall that the convection velocity used was 1.00..

60

Since TERA-detected inner-region events decrease in length with increasing y+, it
is not surprising that event length divided by height above the wall (Figure 3.5.25) is

strongly dependent on y’.

It is very interesting to note that at a threshold of zero, the TERA detector was
"ON" approximately 50% of the time in both the inner and outer regions”. During
this time, 100% of the total Reynolds stress was generated in both regions (Figures
3.5.26 and 3.5.27). Although wall-normal velocity information was unavailable to the
TERA detector, its negative uv performance is very similar to the uv—quadrant tech-

nique.

The intensity of the spanwise vorticity fluctuations during detected events is
shown as a function of the TERA thresholding constant in Figures 3.5.28 and 3.5.29.
In the inner region sweeps appear to have a higher level of vorticity fluctuation, but
this level increases for all detected event types well past the limit of statistical
significance (c=2). In the outer region TERA-detected sweeps and ejections stemming
from the same data set have about the same level of vorticity fluctuations, but no clear

Reynolds number trend is seen.

It is not at all surprising that the turbulence kinetic energy (TKE) of TERA-
detected events increases with increasing threshold. TERA detections are based on the
temporal derivative of the streamwise TKE, so requiring a higher level of this value at
the start of events must result in a higher level of TKE during the event. The thres-
hold dependence of this result is a consequence of the detection criterion, but the dis-

tribution of TKE between high-speed and low-speed events and the differences

 

55 Compare for example, Figures 3.5.3 and 3.5.5 with Tablet 2.1.2 and 2.2.2.

61

between those distributions from the inner to the outer regions is caused by the physics

of the flow.

The plots of Reynolds stress "captured" and turbulence kinetic energy present
during uv-quadrant and TERA detections show clearly that there is a strong correlation
between high TKE and large Reynolds stress values. Regardless of whether one looks
for a large magnitude for uv or a(u2)/8t, one will find both high Reynolds stress and
high TKE levels. This seems to be a result of the flow physics more than a conse-

quence of the detection criteria employed.

Once again it was impossible to choose a threshold level for creating ensembles
which would give the same number of events as were detected visually, although a
threshold of 1.5 yielded approximately the same total number of TERA detections as
LSMs at R9=730. The 1.5 threshold was also generally within the level of statistical
significance both in terms of total detection time and in terms of the number of events
detected, so that value was used to create Figures 3.5.32 through 3.5.37. It can be
seen in those figures that outer variables scale these variables best for comparison pur-

poses, especially e), and will.

The u trace is the one most directly influenced by the detection criterion used; the
characteristic upward (or downward) slope through the beginning of the event, peak,
and slow decline through the end are all a result of how the start and end of an event
are defined. On the average the wall-normal velocity, v, behaves opposite u, and this
behavior is not "programmed in" by the detection scheme. However the RMS values
show that v occasionally does have the same sign as u for both sweeps and ejections;
the higher average v peak shown in Figures 3.5.35-37 is simply accompanied by

higher RMS levels. The behavior of v strongly affects the average and variance in

62

plots of uv and veal.

Inner scaling produces the same kind of grouping in the <u> curves which was
seen in the <uv> curves for uv-quadrant detections. This is seen in the good agree-
ment for the R9=730 & 1400 <u> plots versus the R9=2380 & 3120 plots. Further-
more, the v and uv ensembles for TERA ejections exhibit the same Reynolds number
trend when scaled on inner variables (see Figure 3.5.37). The tlueshold level for the
TERA detector is based on nan/8t, suggesting that the Reynolds number dependencies
noted above are related to a correlation between the long-time nan/3t, u, v, and uv
statistics at y/5=0.8. If no such correlation exists, then the observed trends must be

related to changes in the outer-region motions detected by the TERA algorithm.

What is an "average" TERA event? At lower threshold levels TERA events con-
tain a great deal of Reynolds stress. At higher threshold levels both sweeps and ejec-
tions throughout the boundary layer are about around 50 viscous units long56. TERA-
detected events have high vorticity fluctuations around an essentially zero mean value,
implying uniform distribution of positive and negative spanwise vorticity fluctuations
during an "average" event. Even strong TERA-detected sweeps do not usually
penetrate to y+=15; strong TERA ejections do not generally rise above that level. In
Reynolds stress capture and TKE versus threshold performance, the TERA detector is
very similar to the uv-quadrant approach, but this is not entirely reflected in the "aver-

age" events calculated using event-based conditional averaging.

 

5‘ That is, assuming a convection velocity of 0.6U_ in the inner region and 0.9U. in the
outer region.

63

3.6 u—LEVEL ANALYSIS RESULTS

The u-level analysis as modified to detect sweeps (see section 2.5.3) was applied
to all the data sets available, and those results are presented in this section. The
number of events (Figures 3.6.1 through 3.6.3) is of the same order of magnitude as
the number of events detected by the TERA and uv-quadrant techniques. This means
that something other than number of events must used to pick a thresholding constant
with which to generate ensembles, since it is impossible to pick one threshold which
will provide the same number of u-level detections as visual detections for all data
sets. A threshold of 0.5 or less provides more than 200 events and more than
200tU../5 for most of the inner region data sets; 1.3 is a reasonable cutoff to use with
the detections made on the LSM database. Normalized total detection times are

presented in Figures 3.6.4 - 3.6.12.

Inner-region event frequency (Figures 3.6.13-3.6.15) is once again an irregular
function of y+ which does not scale with inner variables as noted by Blackwelder and
Haritonidis (1983). Outer variables provide reasonable agreement between the inner 2
and outermost event detection frequencies, but the cause of the y+=l8.9 behavior
remains an enigma. Note that the sweep event frequency is the same as the ejection
event frequency regardless of threshold; the number of sweeps detected does not
decrease faster than the number of ejections as it did with the TERA and quuadrant

detection schemes.

Outer-variable scaling of outer-region detections gives a dimensionless event fre-
quency which decreases with increasing Reynolds number. Other than that, no con-
sistent Reynolds number trends are the result of scaling with inner, outer, or mixed

variables. Outer-legion event frequencies are shown in Figures 3.6.16 through 3.6.18.

64

Note that all of the inner- and outer-region event frequencies are steadily decreasing

functions.

Average event lengths are shown in Figures 3.6.19-24. The most curious result is
the fact that the average event length is relatively constant for each event type, regard-
less of thresholding constant. Also, all sweep detections are at least as long as the
corresponding ejection detections, regardless of probe height. It was seen that the
number of events and therefore event frequency both decrease steadily as threshold
increases, yet the remaining events have the same average length. This stands in con-
trast to the results of Luchik and Tiederman (1987) who found that a parabolic profile
best described the average event frequency. (They didn’t report on event length, how-

ever.)

None of the scalings used generated a dimensionless frequency which was either
independent of probe height or consistently dependent on y+ or R9. The u-level detec-
tions are long events, 350-550 viscous units in length in the inner region and 250-650
viscous units in the outer region. In the inner region between 1.5 and 3 boundary
layer thicknesses pass during the average u-level detection; in the outer region the
average length is 0.45 - 1.38. Inner-scaled event lengths in the inner region already
have approximately the same value, although the ejections located further than y+=15
from the wall tend to be shorter than the rest. Normalizing these values by height
above the wall (Figure 3.6.25) creates a non-dimensional length which is inversely pro- '
portional to y+, just as it happened with the uv-quadrant and TERA detections.

At zero threshold the u-level detection function is on 100% of the time, detecting
either a sweep or an ejection. Consequently, at zero threshold the u-level technique

must detect 100% of the Reynolds stress generated throughout the boundary layer.

65

More interestingly, over 80% of the total Reynolds stress57 is still being detected at
threshold levels of up to 0.7 in both the inner and outer regions (Figures 3.6.26 and
3.6.27).

The inner-region to, fluctuation intensity during events is about the same as the
long-time RMS of (l)z in the inner region, regardless of threshold. Outer-region sweeps
detected with threshold levels of l or less have an RMS which is about 80% of the
overall vorticity intensity, while the vortical intensity of ejections is 120%-l30% of the
long-time RMS. However, this does not apply to the Re=3120 data set, even though
such large irregularities in a), intensities are not observed with the uv«quadrant and
TERA techniques”. In any event: u-level detections seem to have vorticity fluctua-
tiOns which are generally of the same order as the long-time to; values at each probe

location and Reynolds number.

The mean turbulence kinetic energy plots (Figures 3.6.30 and 3.6.31) are almost
identical to those associated with the TERA detection scheme, and they are also a
result of the detection scheme itself. As noted above, the level of TKE with respect to
threshold is a function of the detector, but the distribution of TKE between high-speed
and low-speed events must be a result of the flow physics and not the detection cri-

teria. Requiring higher levels of u during an event will inevitably raise the turbulence

 

57 The total Reynolds stress captured is the sum of the contributions made by both sweep
and ejection detections made on the same data set.

58 Close examination of Figure 3.6.29, the u-level ensembles, the profile of or, during VITA
detections, the VITA sweep ensemble, and the (toga-”Ito; calculated on the basis of the
RIM data set (Table 3.2.1) suggests that there are one or two points late in the R.=3120 data
set at which a massive jump in vorticity occurs. This point occurs within detections made only
by the VITA and u-level techniques, but it is buried in over 50,“)0 data points, so it has not
been found yet. It is apparently these one or two points which cause such strange behavior in
the VITA and u-level event averages, as well as the excessively high to" value which makes
the normalized to, RMS during R9=3120 events so low.

66

kinetic energy associated with those events, since TKE is directly related to the square
of the streamwise velocity fluctuations. These figures show results one would expect

from this detection algorithm.

A threshold had to be chosen before the ensembles for the u-level detector could
be calculated. It was decided to use the highest threshold which still permitted over
80% of the Reynolds stress to be "captur " by u-level detections. The threshold 0.7
was also acceptable in terms of number of events and total detection time. That thres-
hold was low enough so that the anomaly which affects the vorticity RMS for sweeps
was still included. However, eliminating the (Dz anomalies would have required a
threshold in excess of 1.8, and that would have produced unacceptably low total event

times.

The event averages of the outer region u-level sweep detections are shown in Fig-
ures 3.6.32-34; the corresponding ejection plots are presented in Figures 3.6.35 through
3.6.37. Outer variables once again provide the best normalization for comparing mag—
nitudes of (t)z and vtoz, and it is not at all surprising that outer variables scale <u> best
at y/8=0.8. Inner-variable scaling produces the same Reynolds number trends dis-
cussed in the two previous sections, including the grouping of <uv> and <v>, although
those are not variables used by the detection algorithm. One notable difference is the
fact that outer variables scale the <uv> ejection ensemble fairly well, a feature not

present in TERA or uv-quadrant detections.

Similar to the TERA detection scheme, the average character of the u signal is
determined by the detection criteria used: At the start and end of the event, u is equal
to the threshold levels used to initiate and terminate events, so the RMS of the average

goes to zero: at these points. The magnitude of u is large during an event, peaks

67

before the midpoint, and relaxes to zero slightly after the event ends. The average
trend of v during an event is such that Reynolds stresses will be produced most of the
time. The RMS of the v average is large though, indicating that v occasionally has the
same sign as u. Although the shape of the Reynolds stress curve is similar to that
associated with the "average" uv-quadrant detection, the level of the standard deviation
is the same while the average value is one order of magnitude smaller (compare Figure
3.4.32 with 3.6.32). The shape of the R9=3120 (t)z plot has already been discussed

above.

The "average" u-level event is a long event, regardless of the threshold used.
Like TERA detections, u-level events contain a very large percentage of the Reynolds
stress generated when lower threshold levels are used. Unlike TERA though, the u-
level detector is always "ON" at thresholds of zero, so not only is all of the negative
uv "captured". then, but all of the positive contributions to the Reynolds stress correla-
tion are also accounted for. The "average" u-level ejection has a higher level of vorti-
city fluctuations above y+=15 than the corresponding sweep. It is quite interesting to
note that the spanwise vorticity intensity during u-level events is generally independent
of threshold (Figure 3.6.29). Even strong u-level sweeps do not usually get down as
far as y*=15, while strong u-level ejections do not generally rise above that level.
Like uv-quadrant and TERA detections, a u—level event will have a level of turbulence

kinetic energy which is directly related to the thresholding constant used.

CHAPTER 4

A COMPARISON OF VISUAL- AND PROBE-BASED DETECTIONS

Several different notions of what characterizes an important event have led to the
development of methods to detect those motions as well as parameters to measure how
well those detections were performed. The best-defined average characteristic of the
motions studied is the streamwise velocity signature, which generally was a result of
the detection scheme applied59, although even the u-signature was poorly defined in
the case of the LSM. In broad terms, the detection schemes have been applied in an
attempt to locate the presence of sweeps (high-speed, wallward moving events) and
ejections (low-speed, outward-moving events). Ensembles have shown that these are
indeed the "average" events being detected, so the question naturally arises as to
whether or not the some events are being detected by these different approaches.

If one knows that a particular scheme does indeed locate the physical process of
interest but wishes to use a simpler detector to locate those same events, the problem
of threshold choice for the second detector scheme arises. Bogard and Tiederman
(1983), Luchik and Tiederman (1987), and others have chosen thresholds for the
second detector such that the number of events and thereby the mean event frequency

 

’9 In the instance that detections were made visually, the apparent velocity could be directly
relatedmdebest-definedchmactaistic,wluchmthiscasewasvisudinnaune.

69

are the same. However, one cannot argue that the same events are being located sim-
ply because the same number of events have been found. If one wishes to compare
long-time statistical quantities in order to optimize threshold choice, it would make
sense to compare parameters which are related to the physics of the events to be
detected, e.g., the percentage of Reynolds stress located.

The other method available to optimize threshold relies on an evaluation of the
one-to-one correspondence between detections made by the two schemes under exami-
nation. P(E) and P(D) give an indication of the long-time correspondence; P(T) gives
an indication of the event-resolved correspondence between detections. The general
problem with these three, although it applies particularly to P(E), is that the longer the
events are which the second detector locates, the greater the likelihood that there will
be some overlap with an event found using the first scheme. It will be seen in coming
sections that P(E) and PG) have their highest peaks when the second detector’s thres-
hold is zero. Therefore, something other than maximizing these two functions must
form the basis for the choice of threshold if P(E) and P(T') are to be used. Luchik and
Tiederman (1987) selected thresholds which gave the same average event frequency,
but this was also the point where P(E) and P(D) had the same value. Since P(T) gives
information about how often detections occur before, during, and after the reference
events, the combination of a high peak during and low peaks before and after could be
used to set limits on the threshold for the second detector.

Reynolds stress-producing events are obviously located best by the uv-quadrant
technique, but events which produce high uv magnitudes are not necessarily "coherent
motions." Economikos, Shoemaker, Russ, Brodkey, and Jones (1990) have recently
been working on the assumption that the general location of a coherent motion is best

detected visually, after which the velocity and vorticity fields associated with that

70

region in space are determined. In any event, the velocity and vorticity signatures
associated with a coherent motion cannot be determined from an a-priori examination
of only those time traces. Therefore if the goal is to locate a particular coherent
motion, it makes sense to start with visual detections and compare the long-time per-
formance and event-to-event correspondence of those visual detections with probe-
based detection schemes that are intended to locate the same kind of event“). In this
chapter that approach will be taken, and the correspondence of probe-based detections
to the three different kinds of visual detections presented in chapters 2 and 3 will be
evaluated.

For each of the three visual detection criteria applied in Chapter 3, the long-time
statistical performance of the visual detections will be compared with that of the
probe-based detection schemes in an effort to determine whether any threshold can be
chosen which makes the probe-based detector perform the same as the visual-based
detector, regardless of Reynolds number or probe height. The correspondence between
the visual detector and the three different velocity-based detection schemes will also be
evaluated. Altogether, this should give a good indication of how different the events
really are which these six detection methods locate.

 

60ltshouldbenotedhoweverthatthesecomparisonscanbeappliedtoanytwointerrnitten-
cyfimfimmofwhichmndaheadybeabbmbcatemeeventsofinterest. Forexam-
ple, it would be interesting to compare the zero-threshold TERA and uv-quadrant detection
cmespmdeweasimebofiofflmeappoachesderMofdeReynddssfieasmdn
boundary hyer with qrproximately the same level of intermittency.

71

4.1 LARGE-SCALE MOTIONS AND THE PROBE-BASED DETECTORS

Before addressing the one-to-one correspondence issue, it is useful to consider
what conclusions can be drawn regarding differences in detections based on differences
in the long-time performance parameters presented in chapter 3. As mentioned in
Chapter 3, it was impossible to select a thresholding constant for any of the probe-
based detectOrs used which consistently yielded the same number of events as were
detected visually. Referring to Figure 3.4.3 and Table 3.1.1, one can see that the total
number of events‘51 detected by the uv-quadrant technique with a threshold of 2.45 is
fewer than the number of LSMs detected at R9=730 or 2380, but it is more than the
number of LSMs detected at the other two Reynolds numbers. The TERA detector
with a threshold of 1.5 located approximately the same number of events as LSMs at
R9=730, although more events were located at the three other Reynolds numbers. The
u-level detector with a threshold of 0.7 located between two and three times as many
events as LSMs for all four Reynolds numbers. For all of the probe-based detectors
used, it would be impossible to match the number of detections to the number of
LSMs for more than one data set at a time. Since mean event frequency is directly
proportional to the number of events detected, the fiequency of LSM detections will be
higher (or lower) than that of probe-based detections at a given Reynolds number if

more (or fewer) LSMs were detected.

The inner-scaled average LSM length varied from 300 to 1500, a range even
wider than that exhibited by the u-level detections. The TERA and uv-quadrant

 

5‘ '"I‘otal numberofevents" referstothesmnofthenumberofsweepsandthenumberof
ejectionsforthosedetectors whichcanlocateboth. Recallthattheensemblespresentedin
Chapter 3 were made with the following thresholds: uv-quadrant, 2.45; TERA, 1.5; u-level,
0.7.

72

detections were generally between 30 and 150 viscous units in length; the u-level
detections ranged between 150 and 700. Surprisingly, the average u-level sweep from
the Ro=730 data set was longer than the average LSM at that Reynolds number; other-
wise all of the probe-based events had an average length shorter than that of the
corresponding LSMs. In any event, mean event length cannot be used as an indicator
of the correct threshold to choose for any of the three probe-based detectors under con-

sideration.

For the uv-quadrant technique, a threshold of 1.9 would match the Reynolds
stress "captured" by this technique at R9=730 to that located by the LSM visual detec-
tions. However, that threshold is 2.3 for the R9=l400 data and about 1.5 for the
R9=2380 and 3120 data sets. For the TERA technique thresholds between 0.8 and 1.8
are required to match this parameter; for the u-level technique the threshold range is
15ScS2L

As noted earlier, the TERA and uv-quadrant techniques had very similar vorticity
intensity and TKE distributions at least up to the limiting thresholds for each detector
(Figures 3.4.29 and 3.5.29). At thresholds of zero, the vorticity and TKE levels are
about the same for these three detectors, but only the vorticity associated with
Rg=3120 ejection detections can be matched with LSM detections at that Reynolds
number for non-zero threshold levels. As with event frequency, a different u-level
threshold is required for each data set in order to match vorticity or TKE performance
with the corresponding LSM value. One can therefore conclude that none of the
parameters considered, including number of events and average event length, can be
used to decide on a threshold independent of R9 for any of the probe-based detection
schemes under consideration. Matching probe- and visual-based performance at one
Reynolds number (when possible) only produces a performance mismatch at the other

73

Reynolds numbers.

Although the magnitude of the average LSM streamwise velocity peak is a factor
of 2-4 times smaller than that obtained with the probe-based detection schemes used in
this study, the average LSM event is low-speed in nature. Therefore it was decided to
study the correspondence between LSMs and ejections located with the uv-quadrant,
TERA, and u-level techniques. The reader is reminded that a significant number of
events were detected up to thresholds of 3.5 for the uv—quadrant and TERA techniques;
the cutoff for u-level detections is about 1.3. Please recall also that only 34 and 139
LSMs were detected in the R9=1400 and 3120 data sets, respectively, versus over 500

events each for the other two Reynolds numbers.

P(D), the probability of a visual detection occurring during a probe-based detec-
tion, is shown as a function of threshold in Figures 4.1.1 through 4.1.3. The most not-
able feature of these plots is that the value is so nearly constant, remaining between
45% and75% fromzerouptothe thresholdlimitsforallthreedetectors. One should
also note however that the value of P(D) for a given data set does vary with threshold,
going up and down without any particular trends. Luchik and Tiederman (1987)
observed a steadily increasing trend for P(D) when visual detections were compared
with uv-quadrant, u-level, and VITA probe-based detections made at y+=30; this trend
is not apparent in any of these resultséz. The same authors also observed a linearly
decreasing trend in P(E) in their study, and while a strictly linear threshold dependence
cannot be seen in Figures 4.1.4 through 4.1.6, a monotonic decrease is present. Note
that P(E) does not start at 100% for any of the detectors, implying that events are

 

‘2 See however section 4.3 for a comparison between the inner-region visual detections
made in this study with probe-based detections made between y+-.-l4.6 to 24.2.

74

being located by all three probe-based schemes which occur entirely outside the
smoke-marked outer region of the boundary layer.

P(T) is plotted versus norrmlized event time in Figures 4.1.7-4.1.9 for a number
of different thresholds for each detector. The constant value of this function for the
uv-quadrant detections at Ro=730 and 2380 shows that a uv-quadrant event was just as
likely to occur at any point during an LSM as it was to occur before or after an LSM.
This implies that no correlation exists between uv-quadrant and LSM detections at
those two Reynolds numbers. While encouraging, Figures 4.1.7b and d are probably
misleading due to the small number of events which were used to create those plots.
Figures 4.1.8 and 4.1.9 show essentially the same trends as Figure 4.1.7, although the
zero-tlueshold mean value of P(T) is higher for both TERA and u-level events, reach-
ing as high as 50% for u-level detections at R9=2380.

In summary, a probe-based detection is likely to occur at any point during an
LSM; this is supported by the invariant nature of P(D) as well as Figures 4.1.7-9. The
jagged character of the P(T) plots from the R9=1400 and 3120 data sets, when com-
pared to the smooth nature of the other two P(T) plots, suggests that 140 events are
not enough to characterize this distribution, while 500 appears to be an adequate
number. None of the long-time statistical performance parameters considered, includ-
ing frequency and event length, suggest that there is a single threshold which will
cause any probe-based detection scheme to generate the same performance as LSM
detections for all Reynolds numbers.

75

4.2 RING-LIKE MOTIONS AND THE PROBE-BASED DETECTORS

A comparison similar to the one presented above was performed on the RLM
detections from section 3.2, and the results are given below. The reader is referred to
Figures 3.4.2, 3.5.2, and 3.6.2, as well as Table 3.2.1, in which it is shown that no par-
ticular type of visual detection exceeded 200 in number, and only zero threshold levels
produced more than 200 detections from any probe—based detector. As a consequence,
the results shown below will be more qualitative in nature than those given in sections
4.1 or 4.3.

A consideration of the different detection criteria employed should suggest
whether or not one can expect the visually detected events to be located by the probe-
based schemes under scrutiny. The RLM "sweeps" and "ejections" were derived from
visual detections of ring-like motions which were required to display an actively rotat-
ing character before the event was confirmed. Although the grand ensembles of RLM
zones 1 and 2 showed that these parts of an RLM were high speed and wallward mov-
ing on average, the rotational aspect of these detections (especially from zone 2) tends
to induce a sign change in v fiom the start to the end of a "sweep". The wall-normal
velocity during "ejections" is very similar to that during "sweeps" as seen in Figures
3.2.1-6. Although confusing at first, this is almost certainly a result of combining
zones 3-8 and calling them all "ejections." As summarized in section 3.2, the visually
detected events were generally high or low speed as appropriate to sweeps or ejections,
but v usually goes from negative to positive at some point during each event, with the

exception of detections from zones 7 and 8 where the opposite occurred.

The probe-based detection schemes under consideration do a good job of locating
only high-speed or low-speed events. The uv-quadrant technique does a very good job

76

of locating only those events which generate Reynolds stress. Since this kind of event
generally occurs near the start of an RLM "sweep" or the end of an RLM "ejection," it
is expected that P(T') between RLMs and uv-quadrant events will show peaks near the
start of sweep detections and the end of ejection detections. TERA events key on the
streamwise velocity and its derivative; peaks in the PG) between RLMs and TERA
events should occur throughout the entire event, since changes in it occur at the ends,
and large values of it generally are present in the middle of RLM events. The u-level
detector also uses large excursions in the streamwise velocity to locate events, so the
P(T) peak should occur in the middle of RLM events where u is generally a max-

imum.

The more complex nature of the RLM detections makes it unlikely that any of the
probe-based detectors under consideration will locate the same events, having approxi-
mately the same starting and ending points (which would be indicated if P(T) had the
appearance of a square-wave). However, a consideration of the average RLM and
probe-based detections suggests that P(T) peaks might occur at predictable locations
during the RLM detections. Since it is anticipated that the starting and ending times
of the visual and probe-based detections will in general be different, it is not reason-
able to assume that the performance parameters developed in section 2.6 will yield an

optimal threshold for any of the detection schemes under consideration.

With higher Reynolds numbers, lower uv-quadrant thresholds will allow the uv-
quadrant technique to "capture" the same percentage of negative uv as generated dur-
ing RLMs. However, in general this threshold is not the same for sweeps as it is for
ejections; the range is 0.4 to 3.7. The same is true for the TERA technique, although
the applicable threshold range is smaller, 0.5 S range is from 0.8 to 2.3. Essentially

the same problem occurs when one tries to match any of the three remaining RLM

77

performance indicators to those generated by another detection scheme: A wide thres-
hold range is required to match the different performance levels associated with all of
the available RLM event types.

The long-time correspondence between RLMs and velocity-based detections is
shown in Figures 4.2.1 through 4.2.6. The reader is once again reminded that Figures
3.4.2, 3.5.2, and 3.6.2 show these P(D) plots are the result of at most 200 probe-based
detections, while the P(E) figures (see Table 3.2.1) are based on between 13 and 111
visual detections, with the fewest events present in the R°=l400 data set. As with the
LSM, these P(D) values remain within a relatively constant range, although the range
itself is larger than it was for the LSM. The majority of the uv-quadrant detections
produce P(D) values around 40%, while the R9=3120 data set produces higher values
for both sweeps and ejections. The same is true of the TERA detections, but the range
for the lower Reynolds number P(D)s is from 20% to 60%. P(D) for u-level detec-
tions exhibits a steadily increasing trend similar to that shown by Luchik and Tieder-
man (1987); the minimum non-zero P(D) value is 38%. The P(E) values for the uv-
quadrant and TERA techniques once again decrease monotonically with threshold,
while P(E) for u-level detections decreases almost linearly. It is interesting to note
that P(E) for sweeps is invariably lower than P(E) for ejections from the same data set.
This suggests that RLM sweeps generally have lower streamwise velocity peaks than
RLM ejections, since the u-level scheme requires the same u magnitudes for sweeps as

for ejections.

Event-resolved probabilities of the correct event being located are shown for the
uv-quadrant technique in Figures 4.2.7 through 4.2.10. It was expected that uv-
quadrant ejections would be located most Often toward the end of an RLM ejection,
and at zero threshold the peak was indeed located there with a magnitude of 55%.

78

More encouraging is the fact that a peak exists at all, that Figure 4.2.7a is not
comprised of straight lines like Figure 4.1.7a. This variation, especially the fact that
the P(T) magnitudes are significantly lower at the ends of the visually detected events,
suggests that the correlation between RLMs and uv-quadrant detections is better than
that between LSMs and any probe-based detections. However, it is disappointing that
the peaks which are so evident at Reynolds numbers of 730, 3120, and even 1400 (see
Figures 7a, 10a and 8a),63 are not as apparent at R9=2380. Instead of a variation from
25% at the start of an event to 55%-65% near the end, Figure 4.2.9a varies only from
an initial value of 30% to a peak value of 40%.

The expected P(T) trend between RLM and uv-quadrant sweeps was for the P(T)
peak to be located near the start of the RLM event. Although this is the generally the
case, the P(T) plots are ragged, and this result may be more fortuitous than factual.

The prObability of TERA events occurring during RLMs is shown in Figures
4.2.11 - 4.2.14; the u-level P(T) plots comprise the next four figures. The u-level and
TERA plots for each event type are almost identical, with the exception of P(T) for
ejections at Ro=2380, where the magnitude of the u-level response exceeds that for the
TERA technique. Furthermore, these figures do not show the variation which was
seen in Figures 4.2.7-ll, but have instead almost the character of the LSM plots 4.1.8
and 4.1.9. The differences between the RLM and LSM plots for these two probe-
based detectors could very well lie in the fact that almost five times as many events
are in the LSM data sets at R9=730 and 2380. Insomuch as there is any peak to the
P(T) plots, the peak is located near the center of the RLM, as expected Also as
expected, this applies to both sweeps and ejections. Since the level of correlation is

 

63 Ordy38eveflsuepresentinflrePfl')disUibutionshowninFigure4.2.8a

79

about the same before, during and after an "average" RLM, one must conclude again
that a TERA or u—level detection is likely to occur at any point during this type of

visual event.

Considering the "average" RLM event and the probe-based detection criteria sug-
gested that the RLM is different in nature from those events located only on the basis
of their velocity signaulres. This might be different if a spanwise vorticity-based
detection scheme were used. A comparison of the performance indicators generated
by RLM, uv—quadrant, TERA, and u-level events yielded no Obvious threshold levels
to use with any of the probe-based schemes. The long-time correlations between
visual- and probe-based detections suggested that a relatively constant proportion of
the probe-based events overlapped at least. somewhat with a visual event; unfortunately
this was a fairly small percentage, on the order of 40%. P(D) for the u-level detector
with these data sets exhibited approximately the same behavior as shown by Luchik
and Tiederman (1987), although that similarity was not seen with the uv-quadrant
detections. Even with thresholds of zero, at most 80% of the visual detections
corresponded with the appropriate type of probe-based event, as shown in the P(E)
plots. The combination of P(E) and P(T) indicated that the overlap between uv-
quadrant events and RLMs almost always occurred near the end of the RLM, although
the extent of, the overlap was widely variable. Contrary to initial expectations, the
overlap between TERA or u-level and RLM events is likely to occur at any point dur-
ing the RIM.

80

4.3 INNER-REGION VISUAL AND PROBE-BASED DETECTIONS

The inner-region visual detections have also been compared with the probe-based
detections made from the same data sets, and those results are presented below. The
difference between these detections and the ones discussed above is that the data sets
were all taken at approximately the same Reynolds number (R937 20), but the probe
was positioned at four different heights above the wall. Although the hot wires were
moved, the visual detection point did not shift; the plan view was almost exclusively
used to determine when events were occurring. The visual detection criteria were the
visual equivalents of what a sweep and ejection should be (see section 2.4.3), so these
detections should correspond most closely with the events located by the three
different probe-based detection schemes. However, little consideration could be given
to the vertical location or extent of the visual detections, so it is possible that the visu-
ally detected events did not produce velocity changes at the probe at the same times at
which the visual events were said to occur. A number of factors affect this issue,
including angular orientation and vertical velocity of the observed feature, height of
the probe, and the vertical extent of any overlying motions which caused or were
caused by the observed motion. Since the visual detections capture the entire event
regardless of vertical development with respect to the probe, it is not logical to assume
that the performance parameters of the visual-based detections can be "matched" to
those fi'om a given threshold for any probe-based scheme“. In section 3.3 it was sug-
gested that sweeps tended to remain above y+=15, while ejections did not usually
extend above that same point. Therefore it seems most likely that the best correlation

between visual- and probe-based detections will occur with sweeps at y+=18.9 and

 

64Thisisindeedthecase,withthresholdrangesbetweeuOand1.5requirledfortheTERA
and uv-quadrant techniques, between 0 and 1 for the u-level technique, depending on the
parameter.

81

24.2 and ejections at y+=l4.6 and 15.

A comparison of the ensemble averages shown in Figures 3.3.1 and 3.3.2 with
those shown in sections 3.4-6 suggests that there should be a good correlation between
u-level or TERA and visual dewcfions throughout the duration of the visual event. On
average the visual events generate a fairly constant level of Reynolds stresses before,
during, and after the events, therefore the correlation between visual and uv-quadrant
detections is expected to be poor. The uv ensemble shows that a slightly higher level
of uv is generally present near the beginning of the "average" visual events, so if there
are any peaks in the uv-quadrant P(T) distributions, it should be near the start of the
visual events.

Since sweeps move wallward, they should reach the outermost probe position
first; ejections should contact the innermost probe sooner than the others, assuming the
events started at about the same height and that that height was less than y+=l4.6.
This suggests that the P(T) profiles comparing inner-region visual events to detections
based on the streamwise velocity should have peaks which occur earlier for the y+=15
ejections and the y+=24.2 sweeps than for other event types. That is, with the probe in
the outermost position, the P(T) peak should occur closer to the start of the visual
sweeps than it does with the probe elsewhere, and similarly for visually detected ejec-

tions with the probe at its innermost position.

Long-time correspondence between visual- and probe-based detections are shown
in Figures 4.3.] through 4.3.6. Figure 4.3.1 shows that the visually detected ejections
above y”=l4.6 account for about half of all the low-speed events which generate Rey-
nolds stresses. Ejections at y+=14.6 and all of the visually detected sweeps account for

about 70% of the sweeps or ejections at that point which generate negative uv. Figure

82

4.3.2 shows that the strongest high-speed and low-speed events all correspond to visual
detections. The range on P(D) for TERA detections is fairly constant, between 40%
and 80% through the significant thresholding limit.

Only 65% to 90% of the visual events correspond to probe-based detections, even
at zero thresholds. Therefore, some of the visually located events of both types had
the wrong sign of u (and perhaps v, also) throughout their entire durations as measured
at the probe. Considering Figure 4.3.4, it is surprising that 83% of the visually detected
sweeps correspond to events in quadrant 2 of the uv plane at y+=15, although this is
offset by the 72% observed at y+=14.6. Recalling that the TERA detector is only on
50% of the time with c=0, while the u-level detector is always ”ON" with a zero thres-
hold, it is interesting to note that P(E) for both detectors at zero threshold is practically
identical for each data set; see Figures 4.3.5 and 4.3.6. The TERA algorithm with a
threshold of zero must therefore generate detections which correctly correspond to
every inner-region visual sweep with positive streamwise velocity fluctuations and
every visually detected ejection with negative streamwise velocity fluctuations. How-
ever, these are not the only TERA detections made with that threshold, as indicated by
the P(D) plot (Figure 4.3.3).

The event-resolved correlations between visual events and uv-quadrant detections
are shown in Figures 4.3.7 through 4.3.10. There is a surprisingly large variation in
P(T) from the start to the end of each event type, showing that uv—quadrant detection
overlaps are about twice as likely to occur near the start of all visual detections. The
variation in P(T) follows the variation in the uv ensemble for each event type as

shown in Figures 3.3.1 and 3.3.2, and in general the P(T) profiles are as expected.

83

Profiles of P(T) for TERA detections are shown in Figures 4.3.11-14. Over 85%
of the TERA events which overlap do so at the center of the corresponding visual
event, and the TERA events tend to occur earlier than the visual events as shown by
the high level of P(T) before and at the start of each average visual event. The strong
correspondence between TERA sweeps and visually detected sweeps must be tempered
by the fact that only 113 events comprise those P(T) curves. At the nearby y+=l4.6
location, 530 events give a much less pronounced profile. Although it was expected
that P(T) would have the highest peaks near the start of ejections at y+=15 and sweeps
at y+=24.2, it can bee seen that all of the P(T) peaks are about the same, with the
highesth magnitude present near the start of sweeps detected at y+=15.

The correspondence between u-level detections and inner-region visual detections
is shown in Figures 4.3.15 through 4.3.18. As with the TERA P(T) profiles, the peaks
are shallow and tend to occur near the start of the "average" visual events, regardless
of event type. The highest peak is once again present in the y+=15 sweep distribution,
potentially a result of P(E) for u-level detections being highest for y+=15 sweeps and
ejections. A difference between the P(T) profiles for the u-level technique versus the
other two techniques is the high level of correspondence between detections at higher
threshold levels. Over 90% of the c=l .6 probe-based detections which overlap with
visual events do so over the entire length of the visual event. The average length of a
u-level event is significantly larger than that of a visual events, so it is not surprising
that u-level detections tend to extend past both the start and end of the visual events

with which they correspond.

Consideration of the detection criteria and the ensembled inner-region visual
detections of sweeps and ejections suggested that a fairly high level of correspondence

would be present between these events and probe-based detections. A high level of

84

correspondence (over 75% with zero thresholds) was achieved, with velocity-located
events tending to overlap most often near the start of the visual events. However,
fewer than 80% (and as few as 45%) of the events located with a probe-based scheme
corresponded to visual events in the thresholding ranges for which a significant number
of events were available. P(D) had no consistent y+ or thresholding trends. Since
information regarding the vertical extent of the visual events was generally not used, it
was expected that a single thresholding constant would not work to generate probe-
based detections that had the same characteristics of the visual detections. This was

indwd the case.

CHAPTER 5

SUMMARY AND CONCLUSIONS

Six different coherent motion detection schemes have been applied to eight
different data sets, and the performance characteristics of those different schemes have
been compared. Outer region data in the range 730 S R9 5 3120 were used; inner
region data sets all had an average Reynolds number based on momentum thickness of
720, while the probe was positioned in the range 14.6 S y+ S 24.2. The performance
parameters used will be discussed below, followed by a summary of what those
parameters indicated when applied to the different detection sets. Visual detections
formed the reference data sets for the event-overlap analysis presented in Chapter 4.
The overall indications of P(T), a new parameter proposed in Chapter 2, will be dis-

cussed, in addition to some general comments on the detection schemes used.

Combined hot wire and flow visualization data taken in 1981 and 1982 by Signor
(1982) and Lovett (1982) comprised the raw data which was used in this study. The
hot wire data was processed by routines developed by Klewicki (1989) and Gendrich,
resulting in time series that were brief but adequate for the analyses to be performed.
All the routines which generated the probe-based detections were written by this author
and presented in Gendrich, Falco, and Klewicki (1989). The probe-based detections
are the result of applying the conventional uv-quadrant technique, the TERA technique,

85

86

and a modified modified u-level approach“ to all eight hot wire data sets. The outer-
region film was read by Signor, who located the presence of ring-like intermediate-
scale motions (RLMs, called "typical eddies" by Signor and Falco). Those same films
were read by Falco and others to determine the times during which smoke was passing
over the probe. These detections comprised the LSM database used in this study.
This author read the inner-region films to locate the presence of sweeps (high-speed,
wallward-moving events) and ejections (low-speed, outward-moving events) penetrat-
ing into or rising out of the viscous sublayer at the probe’s streamwise location. These

detections comprise the inner-region visual database used in this study.

Parameters were proposed in Chapter 2 which should indicate how well a given
detection scheme locates the presence of sweeps and ejections. These parameters
included the mean event frequency and length, in addition to a spanwise vorticity
parameter, a turbulence kinetic energy parameter, and a parameter indicating the per-
cent of Reynolds stress which was generated while the detector was "ON." Event fre-
quency and length were scaled using inner, outer, and mixed normalizations, and those
results were presented in Chapter 3. Neither of those parameters under any of these
scalings yields a parameter which is independent of Reynolds number or y". Ensemble
averages for the outer-region visual detections were also scaled using these normaliza-
tions. While it was expected that outer variables would best scale the minima and
maxima of all five variables, <u>, <v>, and <uv> scaled equally well with inner, outer,

and mixed variables.

 

65Thisversionoftheu-leveltechniquecouldlocatemestartandstoptimecofbothsweeps
andejections.

87

The vorticity parameter indicated the RMS of the spanwise vorticity fluctuations
during events, normalized by the long-time m,’. For each data set this parameter either
remained fairly constant or increased with threshold, but the performance tended to
vary irregularly with Reynolds number or probe height. The TKE parameter showed
the unsurprising result that the average of (u2+v2) increases with threshold for all three
probe-based detectors. However, the threshold dependence was a function of event
type (sweep or ejection) and not Reynolds number in the outer region for all three
detectors. Furthermore, the tlueshold dependence was linear with slope l for both the
uv—quadrant and TERA techniques. ‘

The percent Reynolds stress "captured" parameter varied predictably with thres-
hold for the uv-quadrant technique, since the Reynolds stress was the detected variable.
The inner-region variability of Reynolds stress with y“ accurately reflects the shift of
the uv-quadrant PDF peak from quadrant 4 below y+=15 to quadrant 2 above that
level. The u-level "% Reynolds stress" plots are very similar to those for the uv-
quadrant technique, although the O-threshold performance of the u-level technique can
be predicted from the fact that the u-level detector is always "ON" when c is 0. It is
more remarkable that the TERA plots are also similar to the uv-quadrant plots, dupli-
eating the 100% captured result at zero threshold, even though the TERA detector is
only on approximately 50% of the time then.

Criteria were suggested for determining adequate sample size on the basis of the
number of events located and the total event time. The distributions of u, v, uv, and
to, in the data sets considered indicate that convergence of the mean and variance to
110% of the true values can be achieved with 95% confidence in the results if samples
from 200tUJ8 are present in the summation. It was apparent from the results
presented in Chapter 3 that data sets longer than the ones used are required to provide

88

better statistical convergence and a higher level of certainty in the ensemble averages
shown. Longer data sets would not, however, guarantee that the variance of those aver-
ages would be reduced“. To a rough approximation, 200 events should provide
enough data so that the event length and event fiequency also converge to within 10%
of the true values. Results from Chapter 4 suggests that 140 events are too few, while
500 seem to be adequate to characterize the one—to-one correspondence between events

located by two different detection schemes.

Ensemble averages for u, v, uv, (n, and v0)z were presented for sweeps and ejec-
tions located by each detector. As discussed in the Introduction, it has been suggested
that the choice of detection criteria strongly influences the "average" characteristics of
the located events. The symmetry (or asymmetry) of the detection criteria certainly
seems to cause the ensemble of the detected variable to be symmetric (or asymmetric).
The low variability of <u> during TERA events suggests that the ensemble of a vari-
able related to the one which forms the basis for detections is influenced by the detec-
tion criteria. On the other hand the TERA detector had no information regarding v
during detections, yet v was almost always positive during ejections and negative dur-
ing sweeps. It seems most probable that this is an indicator of a correlation between
nan/8t and v rather than a result predicated by the choice of detection criteria.

The variability“ of each ensemble average was shown as a function of normal-
ized event time in the ensemble plots of Chapter 3. The limits thus depicted represent

bounds on the maximum likelihood region within which the true average value should

 

66Sinceonlythetoppa'allelwireoftheR..=l400datasetgeneratedbaddata,itwouldbe
posaibkneanddelengmofmmdamwasfmuLSMmdprobe-baseddetecfimuem

67OnequarteroftheRMSoftheaverageateachpointintirnecornprisedthevariability
whichwasshownintheensernbleplots.

89

fall. Alternatively, these regions can be seen as indicators of how widely variant the
different time signatures are which comprise the event’s ensemble. Note that the
ensemble averaging process appears to be an unbiased but not consistent estimator for
the expected value of a particular variable at a given normalized event time, since the
variance does not tend to zero as the number of events in the average increases. This
is either due to the estimation technique or the lack of convergence for the expected
value itself. Since the expected value of a random variable is well defined, perhaps
the process of stretching variable-length events to one size should be evaluated with
this problem in mind. In any event, the RMS was generally much larger than the
average value, even with as many as 650 events present in the ensemble. Although
there was so much variance about the average value of an ensemble, the ensembles of
a visual event were successfully used in conjunction with the detection criteria of a
probe-based scheme to predict when the greatest number of probe-based detections

were likely to overlap with the visual event; see for example sections 4.2 and 4.3.

The one-to—one correspondence between visual and probe-based detections was
considered in Chapter 4 using P(D), P(E), and a new variable, P(T, t), as the evalua-
tion parameters. Visual data provide more complete information regarding the spatial
organization of motions in the flow than do multipoint hot wire measurements. Conse-
quently, visual detections frequently comprise the reference database against which
probe-based detections are compared In keeping with this common practice, visual
detections were used as the basis for comparison in this document. However, sweeps
and ejections were the events which we wished to locate, and they have a well-defined
Reynolds stress signature which is accurately detected by the uv-quadrant technique.
It might be worthwhile to consider the correspondence between uv-quadrant detections
and those made by other detection schemes, perhaps as a function of two different
threshold levels“. This is particularly indicated for the TERA detector, whose long-

 

,5' InthiscaseP(E)andP(D)becomesurfacecinthethreshddspace. P(T,t)wouldbecorne
avohmeukrespmsepbtmlleesaduednflfmmofdedcwcmmuldbedecidedmm

90

time performance parameters correspond very closely to those of the uv-quadrant tech-

nique.

As seen in Chapter 4, the long-time overlap parameters P(D) and P(E) were not
smooth, monotonic functions of threshold for any of the combinations of probe-based
and visual detectors considered in this document. This stands in contrast to the results
of Bogard (1982) and Luchik and Tiederman (1987); it is perhaps caused by the brev-
ity of the data sets which were used in this study. P(T, t) was a well-behaved function
of normalized event time and threshold, except at the highest threshold levels where
the number of overlapping events was very small. Falco69 suggests that P(T) should
be redefined to indicate how many out of all the overlapping events overlap at each
given point in time. This modified version of P(T) would then be defined as:

Nov“)
N DV overall

 

P(TZr t) '3'

where NDv(t) is the number of probe-based detections which correctly correspond to a
visual detection at a given point in normalized event time, and Nov overall is the total
number of probe-based detections which correctly correspond to a visual detection.
Unfortunately P(T‘?) no longer indicates the overall correlation between visual and
probe-based detections in addition to the variance of that correlation over the ensenr-

ble, both of which can be read from P(T') plots.

The LSM results suggest that the LSM visual analysis should not be applied
when the marker used has a Schmidt number significantly different from unity. In this
particular instance (Schmidt number greater than 30,000), events which happened

 

advance.
‘9 Private communication.

91

upstream of the probe could move the smoke around and lose their momentum through
diffusion long before the smoke could relax back to its undisturbed condition. Classi-
fying events on the presence or absence of smoke resulted in detections which
occurred at random with respect to uv—quadrant, TERA, and u-level detections. The
percent Reynolds stress capnrred is approximately equal to the percentage of time that
the detector is "ON" (see Table 3.1.1). The spanwise vorticity parameter is approxi-
mately constant at l. The ensemble averages of fluctuating parameters are very close
to zero when compared against the variance of those same variables. These are
approximately the results one would expect when making random detections averaging
18 in length in the outer region of the boundary layer.

The RLM detections are based on the same data that produced the LSM detec-
tions (i.e., the same films were used), but the key difference is the requirement that the
smokemustbeseentomoveinadistinctmannerfromframetoframe.Itispractically
certain that the smoke did not mark all of the coherent convective processes occurring
in the outer region of the boundary layer, so it is quite likely that ”typical eddies" are
also present in the unmarked regions of the flow. If the entire flow field were marked
with smoke, all of the RLMs in the flow could be ' located; alternatively, use of a
marker with a Schmidt number of 1 would probably alleviate this problem.

The kinematic constraint on the RLM is vortical in nature, so the comparison
drawn between probe-based detections and those visual results was slightly forced,
since those results had to be cast into a classification scheme based on linear instead of
angular momentum. Future studies might consider the correspondence between the
different zones of a "typical eddy" and various probe-based schemes in an effort to
determine the correlation between those vortical processes and what is typically

classified as a sweep or ejection.

92

The inner-region visual detection technique described in Chapter 2 was demon-
strated as capable of locating the start and stop of sweeps and ejections. The temporal
gradient in the smoke intensity and the motion of a distinct region faster or slower
than its surroundings were used as the indicators of whether or not an active event was
passing over the probe. A small percentage of "ejections" were located whose absolute
velocity never fell below the mean, although subsequent examination of the time traces
revealed there was always a decrease in the streamwise velocity magnitude (and an
increase in the wall-normal velocity) during these events. "Sweeps" with a similar
problem were also detected. It seems most likely that these detections resulted from
considering only the temporal gradient of the smoke intensity and not the absolute

intensity itself.

Plan views of the flow were used to make the dewcfions, because that information
was available for all of the data sets of interest. Although it was diflicult to infer
event height above the wall on the basis of the plan view, that view did give the best
indication of the spanwise and streamwise extent of the active events. There was a
very poor correlation between dark (no smoke) regions in the side view and sweeps
detected using the plan view. Bright ridges rising out of the sublayer as seen in the
side view always corresponded to ejections in the plan view”, but the plan view gen-
erally indicated the event started before and ended after the side view’s ridge inter-
sected the probe. This suggests that the plan view is the best view to use when atom-
ized oil droplets are the marker and inner-region sweeps and ejections are to be
detected.

 

7°nteydidaslmgasmelasetsheetwasposiuooedrightoexttomex-army. Thisispart-
lydcpendentonthedefinitionofulejecfion(see2.4.3)andthegaraaflymnowaspectofthe
ejections.

93

None of‘the detectors located all of the same events, as seen in Chapter 4. The
percent Reynolds stress "captured" and TKE parameter plots were the only Reynolds
number independent parameters calculated. The former is directly related to how
effectively a detection scheme locates sweeps and ejections, so it is an appropriate
parameter to use when attempting to match the performance or threshold of two
different detectors. Unfortunately, neither percent Reynolds stress "captured" nor the
average turbulence kinetic energy during events was independent of Reynolds number
as far as the outer-region visual detections were concerned. Although either of those
two parameters could be used to match performance among the probe-based detection
schemes, no parameters could be used to match probe-based detections at a given

threshold to any visual detections.

Kline and Falco (1979) suggested that the "intensity" of an event in the outer
region should scale with outer variables. If "intensity" is understood to be the tur-
bulence kinetic energy in the flow, lz‘z(u2+v2-l-w2), then the intensity does not become
Reynolds number independent when normalized with U3. It does, however, scale with
the RMS of the TKE, at least in the approximation that the TKE is equal to %(u2+v2).

Consideration of the performance of the uv-quadrant detector led to the conclu-
sion that the amount of negative uv "captured" during uv-quadrant events is a result of
the tlueshold chosen and the PDF of u versus v. For uv-quadrant events the depen-
dence of frequency, turbulence kinetic energy, and event length on threshold seems to
be a function of the probe height and the detection criterion, in combination with the
distribution of u versus v. As discussed above, the uv ensembles are a consequence of
the detection criterion. The uv initial and final values are dictated by the start/stop
limit, and the upward slope] peak in the middle character follows from requiring the

events to have uv magnitudes greater than the start/stop criterion.

94

The TERA detection criteria cause the threshold dependence of the turbulence
kinetic energy during events; the higher the threshold, the higher the change in TKE at
the start and during events, leading to higher overall TKE levels. However the distri-
bution of TKE between high-speed and low-speed events seems to be a consequence
of the flow physics. Event averages of it during TERA events are the consequence of
thestartandstopcriteriainthesamewaythat<u>and<v>ensemblesarecausedby

the uv—quadrant criterion.

The u-level technique as modified by Luchik and Tiederman was further modified
for this study in order to detect sweeps as well as ejections. The performance of this
version of the u-level technique as indicated by the parameters presented in this study
is similar to that of both the uv-quadrant and the TERA techniques. Furthermore, the
u-level technique is the simplest of all 6 detection methods considered, both in terms
of data required and the analysis of that data. However, it should be noted that u-level
events are significantly longer than those located by all except the LSM approach,
even in the inner region of the boundary layer where events are most likely shorter
than one 8 in length.

Grouping was applied to all probe-based detections, and this also had an impact
on the apparent performance of the detectors. Long events which were close together
tended to group. As threshold was increased, those events grew further apart and
could no longer be grouped This caused an apparent increase in number of events
and event frequency, although the total detected time continued to decrease. The
resultant dependence of event frequency on threshold was a combination of the detec-
tion criteria, which had to permit long events, and grouping.

95

Outer-scaled event lengths provided a check on the hypothesis that events are
around one boundary layer thickness in length; it turns out that almost all detected
events were less than one 8 long on the average, with the shortest events occurring in
the near-wall region. Plots of event length versus y+ were shown in Chapter 3, with
the conclusion that events as detected by the three probe-based schemes considered do
not get longer the further they are away from the wall. This was true regardless of
threshold and regardless of the detection scheme“. It is important to note, though, that
the event convection velocity was assumed to be constant in the near-wall region, so
this conclusion follows directly from the inner-scaled average event duration. If the
convection velocity is dependent on y+, events may indeed grow larger the further they
are away from the wall.

If a coherent motion is simply one which generates Reynolds stresses, then the
parameter presented in Chapter 2 which best evaluates a detector’s performance is
obviously the percentage of negative uv "captured” by the detector. The best detector
of these events is the uv-quadrant breakdown technique, however it was seen in sec-
tion 3.5 that the TERA technique is very similar to the uv-quadrant approach with
respect to this performance parameter. Kline and Falco (1979)72 posed the question of
whether or not something other than high uv could be used to detect ”significant
motions" in the flow. If a significant motion is one which generates Reynolds stresses,
then the TERA approach, which requires only streamwise velocity information, can be
used to detect those motions. The exact relationship between TERA and quuadrant

detections as indicated by P(D), P(E), and P(T) still must be determined, though.

 

7‘ Since the irmer-region visual analysis did not generate infatnation regarding event size as
afunctionofdismncefiommewalhhlfmmfimfiomdutanalysiscammtwnmbutemm
arrswatothisquestion.

”Seexlineandlialoo(l979),p.ll.

96

Sweeps and ejections are simply-defined events, but five minutes’ contemplation
of flow visualization or u, v, and uv time traces will at least partially reveal the com-
'plexity of the motions within a turbulent boundary layer. In order to more completely
understand these motions, one must be able to distinguish between more than these
three states of Nature: (sweep, ejection, and quiescent periods}. As discussed by Kline
(1988), such distinctions are already being drawn, and detection schemes are being
designed to locate those events. In this document some new approaches to evaluating
the performance of a detector have been presented and compared to many of the older
performance parameters currently in use. The one-to-one correspondence of events
located by two different detection schemes has also been considered. It is hoped that
the new tools developed in this document will be of use in the community-wide efforts
to understand the interplay of coherent motions and the detectors designed to locate

and characterize them.

TABLES

97

Table 2.1.1 Inner-region Flow Parameters

 

 

 

 

 

 

 

 

 

 

 

 

x 105
U. 8 U1 v

y“ (m/s) (mm) (nu/s) (m2/8) Re

14.6 0.975 61.0 .0512 1.55 744

15.0 0.920 101.5 .0497 1.55 704

18.9 0.951 61.0 .0506 1.55 726

24.2 0.920 61.0 .0497 1.55 704

Table 2.1.2 Inner-region Combined Data Set Lengths

event total total total total
y+ type ticks sec t” tUJ8
14.6 S/E 65000 108.3 18309 1733
15.0 S/E 20000 40.0 6364 362
18.9 S/E 19500 39.0 6435 609
24.2 S/E 58800 78.4 12473 1 184

 

 

 

 

 

 

 

 

Table 2.1.3 Inner-region Time Uncertainty - the Length of One Time Tick

 

 

sampling 1 tick 1 tick 1 tick 1 tick

Y+ rate (HZ) (mice) (F) (tUJS) (1*)

' 14.6 600 1.67 0.282 0.0267 3.22
15.0 500 2.00 0.318 0.0181 3.54
18.9 500 2.00 0.330 0.0312 3.72
24.2 750 1.33 0.212 0.0201 2.36

 

 

 

 

 

 

 

 

98

Table 2.2.1 Outer-region Flow Parameters

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x 105
U. 8 U1 v

Re (tn/s) (mm) (m/s) (mz/s)

730 0.997 82.9 .0494 1.56

1400 1.86 102.0 .0811 1.55

2380 3.26 106.0 .136 1.55

3120 5.33 74.4 .196 1.55

Table 2.2.2 Outer-region Combined Data Set Lengths

event total total total total
R9 type ticks sec t+ tUJ8
730 LSM 153000 153.0 23900 1836
RLM 31500 31.5 4920 378
1400 LSM 22500 9.0 3813 168
RLM 13500 5.4 2288 101
2380 LSM 175500 35.1 42184 1081
RLM 36000 7.2 8653 221
3120 LSM 108000 6.8 16711 484
RLM 27000 1.7 4178 121

 

 

Table 2.2.3 Outer-region Time Uncertainty - the Length of One Time Tick

 

 

 

sampling 1 tick 1 tick 1 tick 1 tick

Re rate (H2) (msec) (F) (IUJS) (1*)
730 1000 1.00 0.156 0.0120 2.84
1400 2500 0.40 0.169 0.00747 3.50
2380 5000 0.20 0.240 0.00616 5.17
3120 16000 0.063 0.155 0.00448 3.79

 

 

 

 

 

 

 

99

Table 3.1.1 Outer-region LSM Detection Performance Indicators

(in)

 

 

 

parameter R9=730 R9=1400 R9=2380 R9=3120
number of events 647 34 557 139
total time (in) 9802 1170 24911 7497
total time (mix) 2717 246 3987 1276
total time (out) 753 52 638 217
frequency (in) 661e-6 256e-6 763e—6 199e-6
frequency (mix) 183e-6 54e-6 122e-6 34e-6
frequency (out) 507e-7 113e-7 195e—7 58e—7
event length (in) 306 789 1070 1470
event length (mix) 18.9 34.6 35.0 47.9
event length (out) 1.16 1.52 1.15 1.56
% "ON" time .410 .307 .590 .449
<uv>/RMS (uv) -0.408 -0.454 -0.426 —0.508
% (-) uv .447 .366 .591 .570

RMS cl)z 1.02 1.06 .953 .465

average TKE .774 .92 .837 .889
average strain .023 .024 -.020 -.001

 

 

 

 

 

(mix) indicates mixed variables were used.
(out) indicates outer variables were used.

indicates inner variables were used to normalize the results.

 

100

Table 3.2.1 Outer-region RLM Detection Performance Indicators

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R9=730 R9=1400 R9=2380 regim—
parameter E S E S E S E S
t of events 90 24 38 13 110 24 111 21
total t (in) 761 136 527 91 1696 283 1379 211
total t (mix) 211 38 111 19 272 45 235 38
total t (out) 58 10 23 4 43 7 40 6
freq (in) 446e-6 119e-6 477e-6 163e-6 734e6 160e-6 636e-6 120e-6
freq (mix) 124e-6 33e-6 100e-6 34e-6 118e-6 26e-6 108e-6 20e-6
freq (out) 343e-7 9le-7 210e-7 72e-7 188e-7 41e-7 184e-7 35e-7
ev len (in) 171 114 318 161 368 281 338 287
ev len (mix) 10.5 7.0 13.9 7.1 12.1 9.2 11 9.4
ev len (out) .649 .434 .611 .310 .395 .302 .360 .305
<uv>/RMS (uv) -.732 -.483 -.372 -.148 -.518 -.528 -.695 -.352
% (-) uv .265 .033 .268 .028 .240 .036 .587 .050
RMS to, 1.34 .832 1.32 1.21 1.07 .961 1.28 1.33
avg. TKE 1.15 .922 1.10 .973 1.04 .985 1.01 .642
avg. strain .434 -.293 .158 .237 .041 -.186 .202 .447
(in) indicates inner variables were used to normalize the results.
(mix) indicates mixed variables were used.
(out) indicates outer variables were used.
Table 3.3.1 Inner-region Visual Detection Performance Indicators
. y*=14.6 y"=15.0 y‘=l8.9 y'=fl.2
parameter E S E S E S E S
4 of events 490 530 96 113 157 220 271 352
total t (in) 4631 6638 867 2241 1062 2223 2565 5165
total t (mix) 1425 2042 207 535 327 684 790 1591
total t (out) 438 628 49 128 100 210 243 490
freq (in) 212e-5 230e-5 153e-5 180e-5 266e-5 372e-5 98e-5 127e-5
freq (mix) 653e-6 707e-6 364e-6 429e-6 817e-6 1150e-6 301e-6 391e-6
freq (out) 201e-6 217e-6 87e-6 102e-6 251e-6 352e-6 93e-6 12le-6
ev len (in) 180 239 167 368 127 190 175 272
ev len (mix) 12.7 16.8 9.3 20.4 9.0 13.5 12.6 19.5
ev len (out) .895 1.19 .515 1.13 .64 .96 .898 1.39
<uv>/RMS (uv) -.299 -.646 -.745 -.734 -.899 -.560 -.698 -.466
% (-) uv .245 .464 .155 .383 .25 .33 .285 .40
RMS (0, 1.04 .966 1.06 .987 1.06 .985 1.03 1.02
avg. TKE 1.11 .992 1.08 1.05 1.46 .72 1.31 .67
avg. strain -.147 -.13 -.128 -.080 .47 -.39 .197 -.126

 

(in) indicates inner variables were used to normalize the results.
(mix) indicatesmixed variables were used.

(out) indicates outer variables were used.

 

 

FIGURES

101

Plan View

Honeycomb I“ smoke slit

Screens (4) 2nd smoke slit

 

 

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Side View

NOTE 1: All dimensions are in millimeters. Drawing is not to scale.
NOTE 2: The data acquisition point is at the origin as shown above.
NOTE 3: The entrance contraction has an area ratio of 13:1.

Figure 2.2.1 The 7.3m boundary layer wind tunnel in Michigan State
University’s Turbulence Structure Laboratory.

102

 

V
N

X-array

 

A
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1.0 3.0

 

 

 

20

 

 

 

 

 

 

 

 

 

 

 

 

 

NOTE 1: All dimensions are millimeters. Drawing not to scale.
NOTE 2: Axes indicate directions only, not the location of the origin.

Figure 2.2.2 The spanwise vorticity probe.

103

Side View Mirrors
(most films)

   
    

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Red Filter

Top View Mirror \

     

Plan and
Clock View

Side View
(most films)

 

 

 

 

 

NOTE 1: The red filter was only used when the side view was present.

NOTE 2: The spanwise vorticity probe was located at the origin. The
laser sheet passed through the X-Y plane.

NOTE 3: Dark arrows indicate lines of sight.

Figure 2.2.3 Camera and mirror setup.

Cylindrical Mirror

 

 

Focusing Lens

 

 

 

Argon-Ion Laser

‘fi—F

 

Figure 2.2.4 Laser and laser optics setup.

105

1" smoke slit (see Figg 2.2.1)
y

L.

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Fairing

 

Smoke

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3’

L...

WWW/”W

Smoke Injected Tangential to the Flow

NOTE: Axes indicate directions only, not the location of the origin.

Figure 2.2.5 Smoke injection slit configurations (after Lovett, 1982)

 

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Figure 2.3.1 Changes in spanwise vorticity statistics for different averaging
window lengths.

0|

107

 

 

 

 

 

 

 

 

 

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Figure 2.4.1 Zones of a "Typical Eddy" (after Signor, 1982)

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Legend:

 

r=o 160 260
(start) Normalized event time

t=300
(end)

400

R0=730 —--R9=1400 —-R°=2380 —--R9=3120

Figure 3.1.1 Outer-scaled LSM ensembles. Error bars indicate 25% of an
ensemble’s standard deviation at each point in time

109

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 3.1.2 Mixed-scaled LSM ensembles. Error bars indicate 25% of an
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110

 

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Figure 3.1.3 Inner-scaled LSM ensembles. Error bars indicate 25% of an

2710 1:300
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400

ensemble’s standard deviation at each point in time

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R(start) Normalized event time (end)
Legend: R0=730 — — R0 =1400 — - Ro =2380 - - R 0:3120

Figure 3. 2. 1 Outer- scaled RLM sweep ensembles. Error bars indicate 25% of an
ensemble’ s standard deviation at each point in time

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

-15) L . :
-100 t=0 100 200 t=300 400
(start) Normalized event time (end)
R0=730 — — Re=1400 — - Re=2380 — - - Re=3120
Figure 3.2.2 Mixed-scaled RLM sweep ensembles. Error bars indicate 25% of an
ensemble’s standard deviation at each point in time

Legend:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Fi rgur e 3. 2.3 Inner -scaled RLM sweep en n.sembles Error bars indicate 25% of an
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114

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 3.2.4 Outer-scaled RLM ejection ensembles. Error bars indicate 25% of an
ensemble’s standard deviation at each point in time

115

 

 

-100 i=0 100 200 t=300 400
(start) Normalized event time (60d)
Legend: Re=730 — — Re=1400 —- Re=2380 ---- Ro=3120

Figure 3.2.5 Mixed-scaled RLM ejection ensembles. Error bars indicate 25% of an
ensemble’s standard deviation at each point in time

116

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~100 t=0 100 200 t=300 400
(Start) Normalized event time (end)
R0=730 — — R0=1400 — ' Re=2380 — ' ' R0=3120

 

Legend:
Figure 3.2.6 Inner-scaled RLM ejection ensembles. Error bars indicate 25% of an
ensemble’s standard deviation at each point in time

117

 

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Figure 3.3.1 Ensembles of inner-region visually detected sweeps. Error bars indicate
25% of an ensemble’s standard deviation at each point in time

118

 

 

<u>
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<uv>
<mz>
«to?

-100 t=0 100 200 t=300 400
(Stan) Normalized event time (end)
Legend: y*=14.6 — - y"’=15.0 — - y+=l8.9 — - - y+=24.2

Figure 3.3.2 Ensembles of inner-region visually detected ejections. Error bars indicate
25% of an ensemble’s standard deviation at each point in time

119

 

 

 

 

 

 

Number
of Events
5m + l l r l I l l
4’ Re ~ 720
+ y+ = 4.6, S
400 r + y+ = 14.6, E ‘
0 A y+ = 15.0, S
I A y" = 15.0, E
300 ~ ° + D y+ = 18.9, S _
o B y+ = 18.9, E
U . ° + 0 y" = 24.2, S
200 has . I, o y+=24.2,E _
A D +
33 D +
100 _ A E a t + d
A o t . * +
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O a + + + +
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.1

Number of uv-quadrant Events

vs. Threshold level (Inner-region data)

120

 

 

 

 

Number
of Events
350 I l l l l I
E; Ring-Like
300 — motions
x R0: 730,8
as v Re=l400,S
v R9=1400,E
200 1" o o Re=2380,S
‘9 69 R9=2380,E
150 _“ § 8 ¢ R6=3120,S
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v s i a ‘ . ‘ 2 2 é *
V"2§§v“vv;§““oualii
0 v ‘7 9 C:

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level
Figure 3.4.2

Number of uv-quadrant Events
vs. Threshold level (RLM data set)

121

 

 

 

 

Number
ovaents
12m I I T I I I I
a Large-scale
motions
1000 H
e, o Re=730,S
a a =730,E
.1 V! R =14OOS
9 9
800 .3 ° : # R9=14OO,E
a a =2380,S
600 r a 2 a Re=2380,E
a a R9=3120,S
E . 8 Re=3120,E
400 ~ 8 a ‘
a a
5 9 ° a 3
E g e a a a
l
200 2* 8 O 9 e a g a
a a o 8 e 9 e e E E a a n
E O a 8 O I
0 3"”«minimiiij738:3:5

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level
Figure 3.4.3

Number of uv-quadrant Events
vs. Threshold level (LSM data set)

10000

10

122

 

 

 

 

Ro~720
* + y+=14.6 S
2 + y+=14.6E
a i + A y+=15.0 S
3 : + ‘ y+=15.0E
H I ‘ + [3 y+= 8.9 S
D S " m +— 89 E
0 a O + y — .
[3 a t + 0 y+=24.2 S
2 ‘ i . . y+=24.2E
D A 0 o ...
a:
0 , +
I 8 o +
_ D Q o + +
. 6 9 ‘ i +
D ’ +
9 6 o *
. a D e .
D A . +
B 9 CI 9
A i as 3
o E .
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.4
Inner-Scaled Total uv-quadrant Event Time
vs. Threshold (Inner-region data)

 

10000

10

123

 

 

 

 

Ring-Like
motions
2: x R0= 730, S
ii 8 3* R0: 730,13
,( e v R9=1400,S
F? g 8 e V R9=1400,E
s: . § 63 O =2380,S
‘ v a z: 0 e e R9=2380,E
'vx‘gfa. ¢Re=3120,S
, ‘ g 63 a, ‘ R6=3120,E
v a O ‘ ’ e '
V K v I 9
H 9 g 1 ‘3 g
ii 9
i v * it 5 t
v . v ,g 6 t
3; o v 3‘ ..
v a x V v
V 7 $
m 1 1 X 1 1 v Y 1
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv—quadrant technique tlueshold level

Figure 3.4.5

Inner-Scaled Total uv-quadrant Event Time

vs. Threshold (RLM data set)

 

124

 

 

 

 

 

 

1mm) I I I I I I I
Large-scale
motions
o no: 730,3
db 3 R = 730 E
u e a
10000 : 1+ R =1400 S
9 9
Total 43 a . 8 3 Re =1400, E
Event 9 3 a Z ‘ a R9=2380’S
Time a a a a ‘ . R0=2380,E
II a 8 e g a ; - . E R0=3120,S
1000 4’ 1, g 9 8 a a a . e Re=3120,E
at # 0 a 8 8 e a 5 a
,t a e 8 a
1}2 1+ it ° 9 e - a
x—-1 ‘t W o . 6 8 g "
V 4+ a 8 g a
a 6 a: a ‘ a 8 g a B
100~ * .3 ° C ‘* 3. 3 z a . 2
4+ 8
II '3' O 0 ° * *‘
II a o o Q * s
10 1 1 1

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.6
Inner-Scaled Total uv-quadrant Event Time
vs. Threshold (LSM data set)

10000

Total
Event
Time

10

125

 

AA
VV

I

:83

 

 

.04-

DB

E1800++

l

EEO O*+

DDSOfi+

+
+

DDDB) «O

[1960*0

DDDBGO

DDEO O

0

m0

OOBDDD*+

Q +

o o +
E o o +

 

0.0

1.0

2.0

3.0

4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.7

Total uv-quadrant Event Time (Mixed Scaling)

vs. Threshold (Inner-region data)

 

Event

1000

100

10

126

 

 

 

 

Ring-Like
as motions
.. x R9: 730,3
3" o * Re: 730,E
ti é _

i‘ v R9—1400,S
@ v =1400,E
II a"
.7 Q ..g o [19:23:30.3
., , a e R0=2380,E
_ v . g a R9=3120,s
v v i O as {R9=3120,E
v Q é ..
9 x e x
8 x
V v v ‘I at e a"
O x v t . e 2 *
V 9 I ‘ e * X
a x V t f e x
0 v . g e 3‘
v . >< ' ’ i
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.8
Total uv-quadrant Event Time (Mixed Scaling)
vs. Threshold (RLM data set)

 

127

 

 

 

 

 

10000 7 1 I I I I I I
Large-scale
motions
Total n R = 730,8
Event 9-
. 1+ Re=l400,S
3 I: R9=1400,E
1000 i g a Re=2380,S
g ‘ . . Re=2380,E
2 ° ‘ a a: R =3120 S
E Q 0 s
x 21k “ a 2 e 8 R =3120,E
V 8 g a E B 9
1k 8 8 g Q g
:: ° a ‘ - i a .
it a a 8 e . a a E
100 H ‘t E a 9 3 9 o . E 0
++ * at O a 8 8 8 ‘ . a I B
§ 8 . a
it at 0 . 8 8 a» I
8 8 a I
a ' . 9 a
.t 3
o x 6 o a
a o z *
10 l l E O l6 ’ l 1 l

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.9
Total uv-quadrant Event Time (Mixed Scaling)
vs. Threshold (LSM data set)

128

 

 

 

 

1 000 I I T I I I I
Total I Re ~ 720
Event <> + y+ = 14.6 S
Time 0 it y+ = 14.6, E
U” A y+=15.o s
"T g + A y+ = 15.0 E
. a y+= 8.9 s
l . : as y+ = 8.9 E
H °.+ o w=uzs
1m 803+ 9 w=u25
CI
2 D f; ’ +
2 D g t + +
A a 8 ¢ . +
‘ 8 a o 9 +
A e B . +
3 +
10 1 l l . 1 L l l
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.10
Outer-Scaled uv-quadrant Total Event Time
vs. Threshold (Inner-region data)

 

1000

100

10

129

 

Y Wu 7“

A
'V

 

 

90

«i

Ring-Like
motions

G G <9 0 4 <1 3K X
gag! ”3’3"ch 7o

56

CD O
u II II II II n u
N
W
00
P
U)

09

l l 1 l l l

 

0.0

2.0 3.0 4.0 5.0
uv-quadrant technique threshold level

6.0

Figure 3.4.11

Outer-Scaled Total uv-quadrant Event Time

vs. Threshold (RLM data set)

 

130

 

1 (XX) I l l l l l l
Large-scale
Total motions
Event a O R = 730, 8
Time 9
U.» , 3 ++ R6 = 1400, S
x—a— . a a it R9=14m,E
2 a e R9=2380,S
as g a - R9: 2380,E
a .. “ . a R0=3120, s
100 " 8 ' - e R —3120 E
E a Q 6 — ’
E a
l} 9 . a
it 8 a . . . a
a e a
e . U
3 e . a
3 9 ‘ e ‘ a a
at a 8 . . a
at ° 8 8 . I a
Q o 9 a ‘ a
10 1 * l 1 9 ‘ l l BI

 

 

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.12
Outer-Scaled Total uv-quadrant Event Time
vs. Threshold (LSM data set)

131

 

 

Number
ovaents )(_V__
Total Sample U12
Time
,ms I I I I I r I
Re~720
£3 + y+=14.6,S i
004 I y+=14.6,E
a A y+=15.0,S
A y+=15.0,E
003 _ D y+=18.9,S ‘
J 0 EB y+=l8.9,E
’ a. D o y+=24.2,s
.002 3 . e y“ =24.2,E a
<> A D
A 93 In
" t t 3 f a
.001 ~ : o 1' + a a _
o o + 1‘
8 ° é «t g g a
o 8 I S
o 6 ° ’ E i Him—“444444

 

 

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.13
Inner-scaled uv-quadrant Event frequency
vs. Threshold level (Inner-region data)

132

Number
of Events x _V_ _5_
Total .Sample 012 Use

 

 

 

 

Time
.ml4 I I I 7 I r I
‘3 R9 ~ 720
.0012 - + y+=14.6,s
a i y+ = 14.6, E
.0010 r A y+ = 15.0, S
A y+ = 15.0, E
0008 B y"' = 18.9, S
' D 33 y"' = 18.9, E
q [3 0 y+ = 24.2, S
.0006 1L 8 o y"’ = 24.2, E
<> 3
‘ m
.0004 ... a s D a
0 o i B
O o + ‘i S
0002 r 3 . i t 2 2 B
3 3 z ‘ S
3 8
‘ 0 ‘ a i W

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.14
uv-quadrant Event frequency (Mixed-scaling)
vs. Threshold level (Inner-region data)

133

 

 

 

 

 

 

Number
of 1.3va x 5
Total Sample U“,
Time
om E T I l l l I
e Re ~ 720 _
a + y+ = 14.6, S
.0003 _ t y+ = 14.6, E l
A y" = 15.0, S
_ A y” = 15.0, E _
0 D y+ = 18.9, S
‘3 EB + = 18.9 E
.0002 0 Y ' -
<> y+ = 24.2, S
0 a o o y"' = 24.2, B
it t E q
1? +
0001 — e * + m -
. I: o * + E
0 3 a + + 3
_ ° . ‘ + B B A
8 2 3 z X
o 5‘ 8
° 3 ’ i 9 i W
0 i—I—I—I—t—l—o—
0.0 1.0 2.0 3.0 4.0 5.0 6.0

uv-quadrant technique threshold level

Figure 3.4.15
Outer-scaled uv-quadrant Event frequency
vs. Threshold level (Inner-region data)

134

Number
of Events X_V
Total Sample U:

 

 

 

 

 

 

Time
(”25 I I I I I 77
Outer-Region
.0020 f motions
D R9= 730,8
6 Re" 730,E
I+ R =l400 S
. ~ 6 ’
0015 # R9=l400,E
: a R9=2380,S
a . 9:2380,E
.0010 1p ‘ a Re=3120,S
a g 8 R9=3120,E
B Q :
.0005 — a a g . : . . .
E g a g ; é . .
fi 9 g
0 'g.;agg§lllouugg'lll
0.0 1.0 2.0 3.0 4.0 5.0 6.0

uv-quadrant technique threshold level

Figure 3.4.16

Inner-scaled uv-quadrant Event frequency

vs. Threshold level (LSM data set)

 

 

 

 

135

 

 

Number
mx _\.’__£_
TotalSample [1121]”
Time
.0004 7 I I I T 1 ' I
Outer-Region
” motions
0 Re=730,S
.0003 B R0=7309E
* R9=1400,S
q; # RO=I4OO,E
«2 R9=2380,S
o . R =2380E
_ ‘3 e 9
0°02 ' a R9=3120,S
It: 8 Re=3120,E
a * .
a * a g
.0001 - e 3. 2 a
a 6 a g ; f B I
a e . e a
>4 3 Z 8 2 E g g : 2 E a a I
B
0 MMZEZEJHEHSHH

 

 

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4. 17
uv—quadrant Event frequency (Mixed-scaling)
vs. Threshold level (LSM data set)

 

136

 

 

 

 

Number
Mxi
TotalSample U“,
Time
10 l I l l l l l
Outer-Region
motions
8~ 0 R9=730,S *
m Re=730,E
1+ R9=1400,S
6” O 4* R9=1400,E _
a a Re=2380,S
x105 1* . Re=2380,E
a Is: R0=3120’S
4* fi 0 9R9=3120,E “
é o m
S; ;; ‘ g
20 a ' a a a a a
e 8 g . it a a
3 e g o 0 . t 9 B a a
9a§°e§3’:é 8"“Inn
0 a a a 8 e g g g g g ‘ I a a

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.18
Outer-scaled uv-quadrant Event frequency
vs. Threshold level (LSM data set)

137

 

 

Total
WV ' x2221
Numberof V
Events
350 I I I I I I I
Re~720
300 it A + y"’-14.6,S ‘
+ y+-14.6,E
240 1: ‘ i A y+-15.0,S -
+ A A y+=15.0,E
‘3 D y"'=18.9S
.5 U B A A 9 _.
200 i? t as ea y+=18.9,E
° 0 + ‘ A A o y+=24.2,s
150~ ., a y E . A o y+=24.2,E -
D ; E! A
0 0 tag A A A
El
100* °g§geieggA J
“seisgéa;;;+...+
50h i § ° 0 80 3 o 9 A A +fi
‘ *I? D D 0 o A
? . C) o
0 w é: =- I—I—-—H—I+I—H‘

 

 

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.19
Inner—Scaled Average uv-quadrant Event Length
vs. Threshold (Inner-region data)

138

 

 

Total 2
mx 22221
Numberof 5v
Events
20’ l I I I I I I
R ~720
9 + y+=14.6,S
15 a, 4; y+=14.6,E
a; A y+=15.0,s
90 E; A y+=15.0,E
a; D y+=18.9,S
10H ° 3 g a 33 y+=18.9,E _
a 2 . <> y+=24.2,s
° 9 t B s a o.y+=24..2,E
33;. i; i a a
D A . 1 + + +
5H ‘ f 3 g S g g 2 El 8 t § + + + + + T
A 0 6 A 0 o 8 O +
’ ‘ 9? 9 fig 033 6
A B D 6
g 9
O a .A. Afig—g—I—H—g—g—u—m

 

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.20
Average uvoquadrant Event Length (Mixed Scaling)
vs. Threshold (Inner-region data)

 

139

 

 

 

 

 

 

Total
W .112
Numberof 8
Events
1.6 l l I l r I l
R ~720
~ 9

1'4 + +=l4.6,S
.. + y+=l4.6,E 4

1'2 A y+=15.0,s

A a A y+=15.0,E
1.0 E; t m D y+=18-9,S 4

ii a + EB y+=l8.9,E
.8 H A é a 0 y+=24.2,S -

‘ A g +—
§ 8 o y -24.2,E
D
.6 H 8 2 t E Q “
9 . 3 ° '2 S a

4 T Q Q a R [2 + + a
. ‘iisoég:633§:;+.++
.2 I“ A ‘ z z 9 a Z A D E 0 g 0 o .4
L i E? g . e a X 8
0 = =+a——U—l—I—I—I——u——I——m

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.21
Outer-Scaled Average uv-quadrant Event Length
vs. Threshold (Inner-region data)

140

Total
mm x__¢UooU
Number of V

 

 

 

 

 

 

Events
3m ’ I I I I I r m
Outer-Region
... motions
250 a Re: 730,8 ~
- a Re: 730,13
8 5 it R9=14m,s
200 . * * Re=1400,E -
t a . g . , Re=2380,S
. “ ; g a 9 e * - Re=2380,E
150— o 1: a t - . e a Re=3120,S -
a .8, ;:*;ffee°9 eR9=3120,E
T 3 a a a “ :t it ' . . f 9 e . e
100~ it I 9 ° ° . o 3 8 . 0 fi 9 2 e e r
O 4} it I I B * " ‘ 2 .
O a G E a U a g I a a * “ . ‘t O
0 IS! I g a fi = a Q a s:
50H 0 O O a E I 6 EH
0 D o o O o '3 E B a
O B o
o a B a
0 e c: " :ewaefi‘: ._.—M
0.0 1 .0 2.0 3.0 4.0 5.0 6.0 7 .0

uv-quadrant technique threshold level

Figure 3.4.22
Inner— Scaled Average uv-quadrant Event Length
vs. Threshold (LSM data set)

141

Total 2
3912013212 x 11221
Number of 5 v

 

 

 

 

 

 

 

Events
16 I I I r T I I
Outer-Region
14” motions ‘
a Re=730,S
12~ a R9=730,E —
I+ R9=1400,S
10 # Ro=l400,E u
“ e Re=2380,S
8 g . Re=2380,E _
I' a R9=3120,S
it ° 2* .. * e R =3120,E
GD . a 0
6* :e - ' t: *
a g g .
B o f? b g ' 3 '
44 g I: g . ‘ . 2 2 § : 3 a a a . . _.
0330..-.:‘ :ggggggfi
2_ a a a a o 8 a 8 a B 9 c.) ' e a: . . 2
a a B E E a Q 0 O
a a a a
O 4: # u 4: :4 4: : I+I—
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.23
Average Event uv-quadrant Length (Mixed Scaling)
vs. Threshold (LSM data set)

Total

Event Time
Number of 5
Events

U0.

142

 

 

 

 

 

 

 

1.0 I T I I I I I
Outer-Region
motions
0.8 ~ 0 R9: 730,3 -
a Re: 730,13
It R9=1400,S
0.6 .m 1* R9: 1400,13 a
a .. Re=2380,S
. . R9=2380,E
o a a 8 R9=3120,S
0.4 ,, o a a a . * e R9=3120,E d
” at g a at a . . I B .
. * * o “ at a . a
0.2 5 g C Q a ; g 3 g " ' i it s , ‘t : a I a - a a w
B a Q 8 a 8 3
8 a . a a g E 2 g 2 g a a g 8 g I a g g 8
a a a a a a a a a a a a a a . .
a a a a a
0 # 4: e e n a: g a+a~
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.24

Outer-Scaled Average uv-quadrant Event Length
vs. Threshold (LSM data set)

143

Total
Eve tjljime x2951:
Number of v y+

 

 

Events
25 I I I I I I I
R ~720
+ y+-l4.6,S
20 7: A + y+-l4.6,E -
‘ A A y+=15.0,S
+ e A y+=15.0,E
15“ A a y+=13.9,s -
t ‘ A m y+=18.9,1~:
a; + ‘ A 0 y"'=24.2,S
10$D$é+‘:A oy+=24.2,E -
C] + A
$0.0:‘iggetf ..
o o . D B a + + A
5*“ o o ’ g C] E g E CI 31 + X + + + + + "
° 83: :Hnfiééwa‘zfxm'r
o o 3 2 $ a z o a a a a 8 A
33 o 8 ° 0
0 = : =+I——I—a—H—I—~I—m

 

 

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.25
Average Inner-Scaled uv-quadrant
Event Length over y
vs. Threshold (Inner-region data)

144

 

 

 

 

 

 

juv<Oljuv<O
:23 mm-
1m% I I I I I I I
R ~720
80%? + y+=14.63
+ y+-14.6,E
A y+= .
60%: A y+=15.0E
z; a y+= .
,, 15$ . m y+=18.9E
40%“ + 6 . ’ <> y+= .
i 9 A g oly+=24.2E
‘ 9 .5
* 9 +
20%.“ i 6 a +
l’ U l + +
+ E g I + + +
l ’ G éfi + + + +
A. 385333l++++iil
0% 4 + —
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.26
Percent Reynolds Stress "captured" during

uv-quadrant events vs. Threshold
(Inner-region data)

 

14S

 

 

 

juv<0lfuv<0
during alltimes
CV61“
100% I I T I I I T
Outer-Region
motions
80% “ 0 R9: 730,8 ‘
G R9=730,E
++ R9=1400,S
60% 3. # R9=14OO,E .
. . U a R9=2380,S
. * E a . Re=2380,E
a . t‘ ' . Ea R9=3120,S
40% “ a . “ a a 8 a R9=3120,E ‘
a fi ‘ . a , a s
I . ‘ g a: 5
++ a ‘ a .
20%r I“. ‘..**383 _
I a . O ‘3 “ at a 8 8 0
“age .“:2~." a
0% H 5 B W

 

 

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.27
Percent Reynolds Stress "captured" during
uv-quadrant events vs. Threshold
(LSM data set)

3.0

2.5

2.0

(n’|(hum
___§$'vmé.

1.0

0.5

146

 

 

 

 

vs. Threshold (Innerregron data)

Re~720
_ + +=14.6,s
I y+=14.6,E
A y+=15.o,s
1* y+=1s.o,I~: o
g D y+=18.9,s '3
‘3 y:=18.9,E
0 C]
y =24.2,S
’ y+=24.2,E D D D
H C]
D
c] i
'3 I
A: f e A A A A A E a! A
t It i
xfiigg§2§§§$-:;Xf+++fif
0 E a 8 . A
AL 0 o +
A A 0 0 o o <> 0 o
A A ‘ ‘ ‘ ‘ A B O . U
-I ‘ ‘ A
A 0 §
O o o
O
l l l l l l l
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level
Figure 3..428
RMS (02 During uv-quadrant Events
Normalizedby 0)’

 

3.0

2.5

1.0

147

 

 

 

 

—1
—1

I

l

 

Outer-Region Motions
D R9=730.S at
I R9=730,E . a
g. Re=lm.s fi
. Re=l400.E -
. R9=2380,s . s a
. Re=2380.E . - ‘ “
a R9=3120.S ; a * a
8 R9=3120.E a a: a
a . ‘
O . *
a . ‘ at t a a a a
e 2 ’ ‘t a 2 a a ' a a '3 a a a
B
s a ‘ ° .
a a . e
e a a D G C O O
a * u» 3 a g it 0 O O a O
o 0
99968888 a are 8989 “’8
a a a a a '3 3 a a a a a
it
4t * 4+ ’3 a
l 1 l l l l l
1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 3.4.29

RMS (.02 During uv-quadrant Events

Normalized by (0’

vs. Threshold (LSM dazta set)

 

<u2-t-v2>lduring
___th
(u2+v2)’
6
+
t
5 H A
‘
:3
4 g a;
0
9
3 ..
2 H
3
E;
1 o
0
0.0

148

 

 

 

Re~720
y+—14.6,S
y+=14.6,E
y+=15.0,S
y+=1s.o,E A
y+=18.9,s . . A A
y+=18.9,E . . a 5153+ + *
y+=24.2,S 9 A A A Q +
y+=24.2,E ’ A a '5 a
0 at 5 D U
;Q a D D 0 D D D D ’
QQ D 2‘ O o
0 0 o o <> 0
n g g?
i m i o o
2 . ? a a 0 o ‘ § * t
A t D o o
o D 0
g] o

l l

 

1.0 2.0 3.0 4.0 5.0 6.0
uv-quadrant technique threshold level

Figure 3.4.30
Average TKE During uv-quadrant
Events Normalized by TKE’
vs. Threshold (Inner-region data)

 

149

 

 

 

 

 

<u2+v2>lduring
__ma.
(u2+v2)’
10 l . I l I I T T
Outer-Region
motions
0 R9: 730,8
8 _ 3 Re: 730,E ”a
g 6
++ R9=1400,S fi ‘
a: R =1400,E ., 9 9 a
9 9 I
a R0=238O,S * ’ O a B
6” - Re=2380,E ,, g S a a a
B: R9=3120,s . a 3 w
e Re=3120,E ' a " a
0 3 g 3 a a E Q E
a . a a B 8 o 0
4% i i . ‘ ° 3 ' a B “
. 9 . B a
. " ' ‘ 2 3 e ” “ ”
. u . g g 3
2“ I . ‘ a 9 ‘
. E
. a I
I
0 1 1 1 1 1 g 1
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 3.4.31
Average TKE During uv-quadrant
Events Normalized by TKE’
vs. Threshold (LSM data set)

150

 

 

 

 

 

 

  

 

      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q
Uoo
W
U... . {1L3 ‘1‘. 2.
‘fi'iI-Ha-Ha—H-Mrfivfi‘l
<uv> ’ _ 'I'E-I-E-I-§-I"*"I-..f
U02 - '--~... ’_
' «...k i"'I'"1'~I-'i---I—{---I---I—-I--I"I';I..r' '
"NI-1.}._I._{..}._I_{..§.—}—-I"
<_‘°z>_5_ ML I "" ' -~.. -~..
u... NEH mi'HHI‘HHI-l-Hi'liiH-Iigq. .1. H
-m?
H4
. . . " a 1 ~
<vco 6 fPIifTHfl§LfiThl¥ I" 1 ”TL.
11,; Fan... .-—- ,.- ..
t=0 ‘ 160 5 ‘ 260 t=300 400
(start) Normalized event time (end)

Legend: R0=730 — — Re=l400 -— - Re=2380 — - - R9=3120

Figure 3.4.32 Outer-scaled uv-quadrant sweep ensembles. Error bars indicate 25%
of an ensemble’s standard deviation at each point in time

 

151

 

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09:
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-2oo
4m
150:-
100;—
. .. MU»
<vm L5 =_ JJJILTJJ l 11.15 '- - ,
.. 1' 1 i , .
U... U3 4°; {INN}? H‘I 1111”. ._1:i_ff't
_m:_.1-..1. ._ _. . ._ -. . .
45): L L
-100 t=0 100 200 t=300 400
(start) Normalized event time (CHd)
Legend: Re=730 —— Re=1400 —- R9=238O —-- Re=3120

Figure 3.4.33 Mixed-scaled uv-quadrant sweep ensembles.

of an ensemble’s standard deviation at each point in time

Error bars indicate 25%

file

13

 

 

 

 

 

   

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Legend:

 

160 260 t=300

E
l
3
a;

t=0
(Start) Normalized event time (end)
R6=730 — — R6=1400 — - R°=2380 — " R0=3120

Figure 3.4.34 Inner-scaled uv-quadrant sweep ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

l9

sclé

153

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fl?
.4 . -
I“ J/I'IIa'fq
<uv>11'
U02 ,1. if
H1:1; lily-f
IT IFIYT fl'fl—‘m'
1:1 1*
<coz>5 T.—"' _-.—-
U00 I
L_ mitt}?
«(9&8 ' 1 1, . -—
0.3 "’l
—100 t=0 160 260 z=3oo 400
(start) Normalized event time (end)
Legend: Ro=730 -— Re=1400 —- Re=2380 --- Re=3120

 

Figure 3.4.35 Outer-scaled uv-quadrant ejection ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

154

 

 

   

_ -I--I- HJ
PM ‘H-fi‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

160 260 t=300 400
(start) Normalized event time (end)
R9=730 — — Re=1400 —- Re=2380 --- R0=3120
Figure 3.4.36 Mixed-scaled uv-quadrant ejection ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

 

Legend:

155

 

1.0. _:
U : I .’l} . O -1

 

 

 

      

  

I C105 L E: . ' . ’1’
if?“ IIIiii{tiriH-Itihl-nhi-‘M T”
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45x105§j I

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1071 we: .. - ..p—I {rag-LT “BLT" I'LTJIIIjTlI’I‘I . .
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-2.0x1055

2x105: _
5311. 1__I 111:1. 'Tzrr‘J.lj’JJTJTT—ITTLTTTF
:u-T,“7""" ..p'vjilllllt
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U“t - I __ 0 .. .l. .. :
#105: ‘ —_
4x105: . . ‘

-100 t=0 100 200 t=300 400

(start) Normalized event time (end)

Legend: Re=730 —— Re=1400 —- Re=2380 —-- Re=3120

Figure 3.4.37 Inner-scaled uv-quadrant ejection ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

156

 

 

 

 

 

 

Number
of Events
500 I I I I 1 I
Re ~ 720
+ y+ = 14.6, S
_ I I y'I’ = 14.6, E _
400 * A y+ = 15.0, s
' A y+ = 15.0, E
I + 3 ‘P + C) y+ = 18.9, S
300 b 0 + 83 y+ = 18.9, E ‘
0 . 0 ° 8 + 0 y+ = 24.2, S
I + + 0 _ y+ = 24.2, E
200 ” I . + ‘
a 8 D e o * . . t
A A 2 Z a 2 EB ° I 0
100 I. ‘ S 2 I; <1 * i + ..
t D e, B é O t
. 0 2 a ’
‘ ‘ Q U 6 E 2 E O ' ‘ 0 o
0 ‘ . WM
0.0 1.0 ‘ 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.1
Number of TERA Events
vs. Threshold level
(Inner-region data)

157

 

 

 

 

 

 

Number
of Events
3m I I I T I I
Ring-Like
_ motions -
250 x Re- 730,8
0 3% R9: 730,E
200 45 C: v R9=l400,S _
a: n v R6=1400,E
. o R9=2380,S
O —
150 i e e 119-2330,15 -
e ‘5 R9=3120,S
x 0 e 6 ’ R9=3120’E
100 r ‘ 9‘ : S e ‘
v V '3 >< . (E : 3
50 + " 3 5 u o ‘l : ii 2 ea 63 —
V O ! ¥ 2 V : . : 3! Q 6 § 3‘
a O V
v v c X x o t g It 0 § . 3
0 V3o23833;;;;;v’;;;
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.2
Number of TERA Events
vs. Threshold level

(RLM data set)

Number
of Events
12m 1 T I I T
0 .. Large-scale
1000 _ 3 motions
0 R9: 730,8
I . ° a Re: 730,13
800 r - 1+ R9=14OO,S
a . # Re=l400,E
a a e . a R0=2380,S
600 r a 9 . . R9=238O,E
+ l n B Re=3120,s
' . . o Re=3120,E
400 ~ 8 8 ° . I ‘
8 8 a
a 8 ° I
a 8
§ . a
0
- a a a
200 ° 0 z e e I a .
I) g 3 a a a o a . e 9 e e z u . .
0 IIi:f:§ag§;;;;:§;§as
0.0 1.0 2.0 3.0 4.0 5.0
TERA threshold level
Figure 3.5.3
Number of TERA Events

158

 

 

 

 

 

vs. Threshold level
(LSM data set)

 

159

 

 

 

 

 

Total U2
Event x—
Time
lomo 1 I I 1 r 1
+ ,1 R0 ~ 720
3 ' + + y" = 14.6, S
3‘ ; + + + y+=14.6,E
3 ° 9 + A y+ = 15.0, S
fig: , + + A y+=15.0,E
1 (xx) _ O i . + D y+ = 18.9, S —+
A 1:: g . . . + + 33 y+=18.9,E
A D , 9 + 0 y+ = 24.2, S
‘ 1:1 2 . . + ’.y+=24'2’E
A D o i . + +
1:) o g ‘ +
A i 2 9 + +
100 r- A 0 ° ‘ a O O + -<
0 o . I A . +
A D o + a! A A 9 + +
U o ‘ EB A . . +
A E A A o +
A U 0 + E A A X
A C] o + E X
1» m
10 1 1 1 1 1
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.4
Inner-Scaled Total TERA Event Time
vs. Threshold (Inner-region data)

160

 

 

 

 

 

Total U1?
Event x—
Time V
10000 I j I l I I
Ring-Like
:3 8 motions
x 8 X R9: 730,8
:13 e x R0=730,E
" o e v =14oo s
t x ’
V
1% JV ’ if 2 e V Re=1400,E ..
‘7 g ‘ .. e o R9=2380,S
v: :,. e a «9 Ro=2380,E
: z 0 . * ,. a =3120,s
a v 3 ‘ , *1 S e *.R9=3120,E
V V t x 6
x 0 v v t . a! i e
100 x 0 v ‘I ‘ 3: Q ..
"- ° x v u. a
v . 0 ' ‘ i 2
X o ' "‘ i e
V V v x ’ g
x o v o
9 x 0 v ”E g 5
g V X 0 V v ”t
e x o '
10 1 1 1 1 1 L
0.0 1.0 2.0 3.0 4.0 5.0 6.0

Fi

TERA threshold level

gure 3.5.5
Inner-Scaled Total TERA Event Tune
vs. Threshold (RLM data set)

161

 

 

 

 

 

Total U2
Event x—
Time
100000 1 1 l I 1 l
Large-scale
motions
0 R9: 730,8
0 3 a Re: 730,E
g z ++ R =1400 S _
a o 9
10000 1. g . . - . a: Re=l400,E
a Z . - . e R =2380,S
” o e g . - . - R9=2380,E
1; a . ' . . 121 Re=3120,S
it 0 § ' ‘ .
1000_ a a o :9 a a o . . 6Ro=3120,Efi
* ‘ ° 8 9 a a a ‘ .
it a O . a 8 8 z E . a
* a . 8 g a . o
it E a . 9 a . . a
” E :1 fl ‘ 9 8 I a .
a a ‘t a ” ° . . |
100 '— * E O a 94
it B O t a a
1+ 8 O “ * a
4+ 8 O " . .
E O 8 ‘ a
1+ * a O ‘t .
10 l l l l l l
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.6
Inner-Scaled Total TERA Event Time
vs. Threshold (LSM data set)

 

T01
Eve
Tir

10

1000

100

10

162

 

 

 

 

Re~720

+ y+ = 14.6, S

# y+ = 14.6, E

1L + A y+ = 15.0, S
j: 0 j A y+=15.0,E
° 3 + . a y+=13.9,s
pm 1 q
H 3 + 83 y+=18.9,E
A E a ’ . + + 0 y+=24.2,S

A E t . + o y+=24.2,E

A a 9 o + '
6 a + . +
A g 8 ° 0 + +
3 sis o +
__ A 1: A $ . + _
A D 6 Q . +
A C] 6 93 83 ° +
‘ D 2 B O O
A +
U o A 93 +
‘ [j ‘ A E! +
O i A A o g +

. . 1 ‘ 1 0 ° ‘ E15 1 ' + L
0.0 1.0 2.0 3 .0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.7

vs. Threshold (Inner-region data)

Total TERA Event Time (Mixed Scaling)

 

163

Total U 2 U00

 

 

 

 

 

Event x 4—
Time V 5
lax) i l I I I l r
g Ring-Like
.11 *6 motions
8 x R9= 730,8
# O X i * Re: 730,E
:; . o s v Re=1400,S
V t x ii ‘7 R0=1400’E
X t 0 5 x 0 Re=2380,S
., . : e .. e Re=2380,E
100 ~ :9 e .. a R9=3120,s ~
v " e *‘ “ R =3120,E
9 x 2 . $ at 9
v . $ !
3 X 0 v ‘ e 3K
x v ‘ 33 ”E x
a o v t e x ”E
X 7 . e
s :2 v I. ‘ f e ”E ..
10 a 0 v . Q g x
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.8
Total TERA Event Time (Mixed Scaling)
vs. Threshold (RLM data set)

164

 

 

 

 

 

Total 2
Event x ply-‘3
Time V 5
10m ' I l l I 1 1
Large-scale
motions
I G Re= 730.8
I m Re: 730,13
* a . ++ R9=14oo,s
" a - ’ 1.. R =14oo E 1
P 8 j 6 9
1000 e g , .. R0=2380,S
‘9 e , ’ g . R9=2380,E
1: ° 9 a 2 . a Re=3120,S
3 a o e . 2 a 8 R6=3120’E
at " a B '
4+ * a C . 9 a B
* C . 8 8 . 2 3
100 "’ g. a it a 3 8 a B a "‘
at t o a 8 8 . . I a
* a * II ‘t . . e 9 e . =
” 121 a ' g a 8 8 e . 2 o
* a o o “ 3 . 8 e ;
it E * a
a o O * 0
10 1 I 1 J ‘ 1 4
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.9
Total TERA Event Time (Mixed Scaling)
vs. Threshold (LSM data set)

16S

 

 

 

 

 

Total
Event x—fi
Time
1 m l l i l T l
+ R ~720
o t + y+ "' 14.6, S
0 * . y+ = 14.6, E
D 8 + + A y+=15.0,S
a ; + A y+ = 15.0.15
“ 8 ’ + a y+ =18.9,S
A a 0 t + E y+ = 18.9, E
’2 8 ° + 0 y+ = 24.2, S
100 L. A a + ' + o 31* = 24.2, E 1
‘ A D B . . +
A O 6
CI 8 o + +
“ A ° é . +
A R 0 g 0 +
a o a o +
A e 3; ° +
o 1 113 . +
A 3 o B o +
10 L L 1 1 1
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.10
Outer-Scaled Total TERA Event Time
vs. Threshold (Inner-region data)

166

 

 

 

 

 

Total
Event x—°a
Time
1 000 I I I I I I
Ring-Like
motions
x R9 = 730, S
9% R9 = 730, E
x v R9 = 1400, S
v R9 = 1400, E
" x 0 R9 = 2380, S
d3 "‘ e Re=2380,E
100 ~69 o 3‘ 0 Re=3120,S ‘
e X 3* v R = 3120, E
It: 9
8 “ x
ii c $ ,(
3 o 9 x
i 8 3%
z . c); e ”‘
3 ' : x e ”E "‘
v g e x
O ; G X
10 1 O . 1 1 1 1 1
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.11
Outer-Scaled Total TERA Event Time
vs. Threshold (RLM data set)

167

 

 

 

 

Total
Event x-—°°-
Time
1 000 I I I I I I
g Large-scale
a motions
: a 0 R9 = 730, S
o
. I a R6 = 730, E
a a ‘H’ R0 = 1400, S
a o a 1* R6 = 1400, E
g . ‘ a a Re =2380, s
8 ‘ a . R6 = 2380, E
_ a e ‘3 ‘ 9 a R9=3120,S 1
100 I s ‘ ° 5 9 R9 = 3120,13
1? a a
fi 9
fl 6 . G
8 a . E
a 9 . a
* a: a 8 . a
II 9 . a
g 8 8 . a
II a 8 . 3
a at * O 8 B
c, e ‘ a
10 T a T “ O ‘3 1 8 8 1 . ‘ 1 . 1
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.12
Outer-Scaled Total TERA Event Time
vs. Threshold (LSM data set)

 

168

 

 

Number
m xi.
Total Sample U12
Time
.0030 é I I I I I I
D
D Re~720
.0025 — a! . + y+=l4.6,S ‘
r a a I y+=14.6,E
0020 _ ‘ j a, a y+=15.o,s -
' “ ‘ A A 2 A y+=15.0,E
A In El y+=18.9,S
.0015 1 * ‘ U m a y+=13.9,1~: .
+ + + A 0 y+=24.2,S
o o + U a Q y+=24.2,E
o I + 93 I
.0010 b0 . o O 8 : E ._
o 6 53
o B as
o T O o 3 EB
.0005 L o ‘ 1. 9 4‘ + + a; _
o o g 8 0 g 2 g g
o ‘giia.ff::gga

 

 

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0
TERA threshold level
Figure 3.5.13

Inner-scaled TERA Event frequency
vs. Threshold level (Inner-region data)

 

xlO‘4

169

Number
of Events x L _5
Total Sample U1? U“,
T' e

 

 

 

 

 

 

1m
9 a I I I I I I
D
8 r 0 R6 ~ 720 "
B a + y+ = 4.6, S
7 h a m + y+ = 14.6, E 1
Z S A y+ = 15.0, S
6 h * A D 4‘ y+ = 15.0, E J
A [a [:1 y+ = 18.9, S
5 FA 1 ‘ EB y+ = 18.9, E ‘
I + 9 ¢ 3 A U 5’ <> y+=24.2,S
4 b o o + A 83 9 . y+ = 24.2, E d
3 '1) 0 9 O t + I: D a —4
o g . + m
2 _ o : t f 6 + a -
0 In
3 ' 2 + + a
1 8 I a a + + E
- . 8 § X X g B -1
i
O 9 § 2 g 2 E 3' SI 2 i I I a a
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.14
TERA Event frequency (Mixed-scalin g)
vs. Threshold level (Inner-region data)

170

Number
of Events x 5
Total Sample U...

 

 

 

 

 

 

Time
30 I I T I I r
n R 720

_ e “' _

25 : D + y+ = 14.6, S

8 a g + y+ = 14.6, E

"’ = 15.0 S
20 " B A Y 9 _4

D D ‘9 A y+ = 15.0, E

x1o-5 + a a y+ = 18.9.8
15 - * I 93 y+ = 18.9, E a

" + I : + D a 0 y+ = 24.2, S

A A 0 o ‘ + D ‘9 9 . y+ = 24.2, E
10 h“ o A A A ? l: + D B a

o 9 ° 9 +
3 t z; a B a
5 _ ‘ O I ’ I; + + a a .
A 2 2 2 Q E : : g: B
0 § g g g g 2 i Q g g a

0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.15

Outer-scaled TERA Event frequency
vs. Threshold level (Inner-region data)

171

Number
of Events x—Y-
Total Sample U1?

 

 

 

 

 

 

 

Time
.0020 I .l I I I I
Outer-Region
motions
G R — 730,8
”015 “' , . a Re: 730,13
5 ++ Re=l400,S
a 3‘ Re=1400,E
_ a ‘ . a Re=2380,S
.0010 a Q I . R9=2380,E
I; 2 . a R9=3120,S
I x 3 ‘ . e R9=3120,E
9 e 8 .
0005 - 5 a ‘ J
- é a a a .
a . . a g . . a
g a O a ‘ a
B ° . . 3 a 3 fi 5
0 93......i aziatg
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.16
Inner-scaled TERA Event frequency
vs. Threshold level (LSM data set)

172

Number
of Events x L _5
Total Sample U12 Um
e

 

 

 

 

 

 

T1m
30 l l l I I l
a Outer-Region
25 1 9 motions ‘
o a G R9=730,S
2 a R9=730,E
20 - II a ‘1’ Re=l400,S d
5 o . 9 a a: R9=1400,E
xlO' a e . I: e Re=2380,S
15 _ a g * . a . Re=2380,E _
T ‘t a: ‘ . a 8 R9=3120,S
. ° * . a e R0=3120,E
10 “’ 8 9 e g 2 ‘ n “
E E 8 a # 9 u
D e 2 Q C a
5 ~ 9 ” ° 2 e 8 ’ ; '.' a . ~
aégsa“ee;§;:!!!!
o E”g'aéia;:§§:f333
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.17
TERA Event frequency (Mixed—scaling)
vs. Threshold level (LSM data set)

173

Number

of Eveng x 8
Total Samme Uoo

 

 

 

 

 

 

Time
10 I I I f I I
Outer-Region
motions
8 ~ 0 0 Re— 730,8 -
o a Re: 730,E
' I+ R9=1400,S
6 __ a it Re=l400,E _
_5 a e R9=2380,S
x10 a a .. R9=2380,E
II * a 8 Re=3120,s
4 1: . . . 9 R9 =3120,E ~
0 B
. a 3: 3
8 a . z a
2 fifl a ; a i at a l _‘
e e 2 8 g o ‘ z . 9 a a
8 g a a O : a ‘ B Q E
. ‘ 3 a at a
0 “MEEEEVHH533““;
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.18
Outer-scaled TERA Event frequency
vs. Threshold level (LSM data set)

174

Total
Event jljime x2201}:
Number of V

 

 

 

 

 

 

Events
600 I I I I I
R9~720
+=14.68
5m _"* + y ,
4) + y+=14.6,E
+ A y+=15.0,S
400 15 t A y+=15.0,E
1:? 'CI y+=18.9,S
i 3 EB y+=18.9,E
300 - § ’i‘ 0 y+=24.2, S
o 9 y+=24.2,E
. a
o 4}
200»- ° 3 +
X , A +
o ; f g f3 9 A
100— ..n$*°z¢A....AAAAA
0 o 0 g 2 g g g a g + + § + + + + :
3 ° 3 9 G 5 Q S a a
0 :- L .2. L .4: ‘
0.0 1.0 2.0 3.0 4.0 5.0

TERA threshold level

Figure 3.5.19
Inner-Scaled Average TERA Event Length
vs. Threshold (Inner-region data)

175

 

 

 

 

 

 

Total 2
Event Time It Uoo U:
Number of 5 v
Events
40 I I I r I I
35 — Re~720 “
+ y+ = 14.6, S
30 — + I y+=14.6,E +
l A y+ = 15.0, S
25 _ S + A y+=15.0,E -
i D y+ = 18.9, S
20 _ E + B y“ =18.9,E _
o g 0 y+=24.2,S
* + +=24.2,E
15 r . o E + 9 * y ..
10 — 2 I 8 + J
0 I E a + +
‘ s * 9 + + Z A
5; H§?g§§§§§3iweifei
‘ ° ‘ I E Q 9 G 5 a E $
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.20
Average TERA Event Length (Mixed Scaling)
vs. Threshold (Inner-region data)

176

 

 

 

 

 

 

Total
Eve tiliime x Uoo
Numberof 5
Events
3.0 I I I I I
1, R ~720
2.5 i: + y+=14.6,s
+ y+=l4.6,E
+ A y+=15.0,S
2.0 ”E5 I; A y+=15.0,E
: + D y+=18.9,S
? EB y+=l8.9,E
1-5 "’“ a + o y+=24.2,s
A A a 0 _ y+ =24.2, E
o +
_ ° 8
1.0 ‘ ’9 . + +
0 4 8 +
O A g +
0.5 b ‘ o 1:. + + + 4‘
“ ‘ o E g $ i i 3 + + + +
‘ ‘ A 2 o g § I 2 0 g S A ‘5 ‘ 4* 4‘
‘ ‘ ‘ l g G g 9 I a a
0 e. é : a = .e
0.0 1.0 2.0 3.0 4.0 5.0

TERA threshold level

Figure 3.5.21
Outer-Scaled Average TERA Event Length
vs. Threshold (Inner-region data)

177

 

 

 

 

 

Events
6m I I I I I I
Outer-Region
500 ” motions
. 0 Re=730,S
a R =730E
_ a 6 ’ _
400 8 . +I =1400,S
at Re=1400,B
e , ... R9=2380,S fi
300 a . Re=2380,E
. .. ; 9 ‘ a R9=3120,S
a e ‘ e R =3120,E
200 — O a i * 8 . 9 -
a C a t g ; a . .
_ a I 0 g 6 ; ‘ g “ 3 a @_
100 3533§1;--:.;§a“°§3223
chansgeignnggm
0
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.22
Inner-Scaled Average TERA Event Length
vs. Threshold (LSM data set)

 

178

 

 

 

 

 

 

Tom 2
mx _U.._U1
Numberof 5v
Events

20 I I I I I I

Outer-Region

motions

0 R =7BOS
o . _

15 - a Re=730,E

9 ++ R9=1400,S

a; g ' 3* Re=l400,E

* e R9=2380,S
10* a 5 ' . R0=2380,E J

.. é ' , a Re=3120,S

9 e : 3 8 R9 =3120,E

. . * z .
5*— ” 2 ° 8 . = 2 I . § “ *t “
a 9 a g z e 9 e a . a I a 5 a a a
II a 8 0
8 a * ' a 2 9 g 9 I! I E ' ' 8 o
8 E a a g a B a E a g g a g l E g g s
O

0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.23
Average TERA Event Length (Mixed Scaling)
vs. Threshold (LSM data set)

179

 

 

 

 

 

 

TERA threshold level

Figure 3.5.24

Outer-Scaled Average TERA Event Length
vs. Threshold (LSM data set)

Total
EventTime J13
Numberof 8
Events
1.6 I I I I I I
1-4 ’ Outer-Region ‘
motions
1,2 1, a Re: 730,8 a
a Re: 730,E
1.0 — * Re=1400’5 ~
It Re=l400,E
08 _ a a R9=2380,S _
‘ a . R6=2380,E
° 8 R9=3120,S
0.6 — a e Re=3120,E ~
t 8
o * a '
0.4 1, g 9 , B . a -
a2;;;.‘**~..,_.
0.2» axgzgggfiééaSSSESSBzin a“
O “engaggtaggggafiiii?
0.0 1.0 2.0 3.0 4.0 5.0 6.0

 

180

Total

Event Time x 1100111
Number of v y+

 

 

 

 

 

 

Events
40 I I I r I I
J.
35 R6 ~ 720 ~
“ + y"' - 14.6, S
30 ” + + y+ = 14.6, E —
A A y+ = 15.0, S
25 - 4 A y" = 15.0, E _
U y+ = 18.9, S
+
2 48 Q a y = 18.9, E _
0 Z . <> y+=24.2,s
o o "’ - 24.2, E
15 — o 9 “ y ~
° f 3; +
10 — z . I] A z. ¢ a
o o g é B + A X g A A A A A A A
5 h o . . o a H g + + + + + i A A A I;
o o o o . g E 2 f + + + + +
0 o o o o o g g a g E g g E E E g“
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.25
Average Inner-Scaled TERA
Event Length over y+
vs. Threshold (Inner-region data)

181

 

 

 

 

 

 

 

Inv<0ljuv<0
6011318 alldmes
cvcms
1m% T I T I l I
Re~720
80% — + y+= 14.6, S a
+ y+=14.6,E
A y+=15.0,S
60% — A y"' = 15.0, E _
J» + + D y+=18.9,S
: 5 3 EB y+=18.9,E
I 3
409' _" v 6 E! A 0 y+=24.2, S d
0 20 8 o.y+=24.2,E
' <> 6 Z
t o ;;
20%~ a . + + «
1 a 2 A +
0 D a; , 9 + +
1 2 3 8 a 9 o g
‘ifigmflisiz‘l‘aaaii
0% 4
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.26

Percent Reynolds Stress "captured" during
TERA events vs. Threshold

(Inner-region data)

182

 

 

 

 

 

 

 

Iuv<0ljuv<0
dun’ns Illtimes
events
100% I I I T 7 I
Outer-Region
80% — motions -
a R = 730.3
a Re: 730,E
. ‘li R9=1400,S _
60% at ‘ . at Re=l400,E
‘ 2 .. . .. R9=2380,S
‘ s a . R9=2380,E
40% a " g i a R9=3120,S ~
g . g a
20% — 3 = . 5 . . -
a “ g
o . . a
a a . . g 8
g a a a O . . . E I w 2 a e e
0% 8 9 WOW
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.27
Percent Reynolds Stress "captured" during
TERA events vs. Threshold
(LSM data set)

 

3.0
2.5
m , I 2.0
. :25
(92’
1.5

1.0

0.5

183

 

 

 

 

__ + y+=l4.6,S _
I y+=l4.6,E
A y+=15.0,S
A y+=15.0,E A
_ D y+=l8.9,S A A A _
EB y+=18.9,E A A
0 y+=24.2,s A A A A A O
9 y+=24.2,E 8 ? D D o e 0 o
3 + + g + + + + +
._ S + v t o —I
A 2 + m In 8 g 0 * ¢ 0
‘4gfig ..,.,Uo..,.,...
A 3 3 a Q 9 E; Q Q EB 33 *3 B a a; In EB EB
a £8 a A g A
Q a B A ‘ a m [B H; 4
o T ‘ ‘ A ‘ A B
4} A A El
._ A A —4
‘ c: D Cl
0
u m o
J J A l ‘ l l
0.0 1.0 2.0 3.0 4.0 5.0 6.0
TERA threshold level
Figure 3.5.28
RMS 0) During TERA Events
bformalized by 0)’

vs. Threshold (Inner—region data)

 

3.0

2.5

, 2.0
a) I

z m

1.5

1.0

0.5

184

 

 

 

 

 

l I f T I T
a R =730.s ° . ‘
- R9=7301~3 ’ ‘
+ R8=1406.s a
— .. R0=14oo,1§ .3 .3 - e . - a
. =2380,S .
- R9=2380.E . . . .
a Re=3120.s 2 -
e R9=3120.E ‘ 2 a
._ a . t g 8 .l
a a “ B
t
o a
a x t 3 . U
C a at
,— . fl» - a a . w “ 4+ ll .1
a a: 3 t . a I g o B 9 5+) *
at a . o O O o O 15 ii
if
‘ I fi 0 a o
O
8
g a
'3' 8
.83322233888395 9 8
Has 8 e 8 8 ~
8
Outer-Region Motions
l L l l l l
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 3.5.29

RMS 0) During TERA Events
ormalized by (0;

vs. Threshold (LSM data set)

 

<u2+v2>l

185

 

 

 

 

during
__mnIL
(112+v2)’
6 I I I I T I
R ~720
+ y+=l4.6,S
_ + y+=14.6,E fl
5 A y+=15.0,S
A y+ = 15.0, E
D y+=18.9,S
4” ea y+=18.9,1~: ‘
<> y+=24.2,S t Z 3 A
0 y+=24.2,E A A 4> A +
3 k A A + .a
f3 + 0
¢ D E] D g
2 ._ + x A a i g g a E: 8 g o —
E 3 i 9 ' . " . ° '3 : a a .
g Q 0 O A L ‘ i + + t ’ t t
5 I é ‘ ‘ ‘ a . +
1 a a
a
0 1 l l l l 1
0.0 1.0 2.0 3.0 4.0 5.0 6.0
TERA threshold level
Figure 3.5.30
Average TKE During TERA

EventsNormalized by T'KE’
vs. Threshold (Inner-region data)

 

<u2+v2>|(luring
___EMIL
(u2+v2)’
6 l l l T l l
Outer-Region
motions 8
5_ o =730,S -
a = 730,E I. e 8
* R9=1400,S at a a
a R9=1400,E ,, g 2 2 ‘ .
4 - a Re=2380,S at 3 g i ‘ i' a
. R0=2380,E .. ; 9 ‘
a Re=3120,S 3! a
3- e R9=3120,E . | ‘ .3. a .. ;_
. ‘t ‘ a e a *
I *t E .3 +0
55 e33§3§°5° °°°
2b a 8 a 5 E 9 fl 3 i
l a a g a E 3
I g
9 a 5 II a
e . 3 2 a a
1 a g Q .I
° E
I
0 l 1 1 l l l
0.0 1.0 2.0 3.0 4.0 5.0 6.0

186

 

 

 

 

 

TERA threshold level

Figure 3.5.31
Average TKE During TERA
Events Normalized by TKE’

vs. Threshold (LSM data set)

187

 

A
a 1
V

C‘.
8

 

 

 

 

 

 

 

 

 

 

 

 

EB

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

<uv>

 

 

 

 

 

 

 

 

 

 

 

 

C‘.
3n

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LO:— ‘

U... E rr T n T .I .I T “ ""~ ---~——-« - ‘
LIJHT TR l:.l._ ... ‘ 0’ 'l TTJT TIT {II TTT LT] TJT T “1T .

:w I- HFHHI -If}..-4mIIIIII~IIIII=IIIIIIEI--II

 

 

 

m u o T ‘

W°I.I"..II..- I.. q
<vco W .5] L11"? ' .1qu Till} I T -
+3 :2; all; ”T" .1 ._ .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-omo
4mm, " _ .
-100 t=0 100 200 t=300 400
(Stan) Normalized event time (end)
Legend: R0=730 — — R0=1400 — ' R0=2380 — - ' R6=3120

Figure 3.5.32 Outer-scaled TERA sweep ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

 

<(D>

U..U W; P1
1

_ ”5* . l-H-Thl I, _ 1115;111le I I1
, -‘ 1'1 I . . n - ‘ I. 1

. .._. ., 1.11 I Lil I LLL
UooU. = .,
:m II iii? J

188

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.—

”HIIIMIIII

 

 

 

 

 

 

 

 

 

 

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 111
v8 100 _ '

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

200
J!)
E _.
4o . . . T ., .. .. 'V " _ ' 0 _:
<va) v8 20 [ ’ [ m‘h'l‘fl j J ".11 _;
T2173- -TITJ‘IITHI.I.*f}**I-IT. . ”31211
... 1 .II:. 1.1.11» - -....11 "'1 .1 . HT
40:— “ h J - ‘ J .. l
.m: u . .
-100 t=0 100 200 t=300 400
(Start) Normalized event time (end)
Legend: R9=73o ——Re=1400 —- Re=2380 —-- R9=3120

 

Figure 3.5.33 Mixed-sealed TERA sweep ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

<uv>

<0) >V

_Z_

189

 

 

-1(X) t=0 100 200 t=300 400
(Start) Normalized event time (end)
Legend: Ro=730 — — Re=1400 —- Re=2380 —-- R9=3120

Figure 3.5.34 Inner-scaled TERA sweep ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4m :
.m- .2
U00 w%n . _.:
4m:— _:
4m: :
mo
".11 __
52 ’ .
U“, .. 1T
<uv> ‘
_ .u' . '
1 l
m- H.- l 1.
a ._ ._. q. _ 1 1.1.1.1
<coz>5 -02 T T ' h] ' J ”fl I T L ll
1 u I r . 1 I 11
[I]9° .114 4 J J . . h .. . lint-J" . .. .. I. .

'05 .. - -

fl .. --

-m ' . " -- -- .

0.02 2'
<vu) 5 . '
—Uz‘:— 41.02 1.1 .L 1 1 E

w -I

-100 t=0 100 200 t=300 400
(start) Normalized event time (end)
Legend: Re=730 - — Ro=1400 - - R9=2380 —- - Re=3120

Figure 3.5.35 Outer-scaled TERA ejection ensembles. Error bars indicate
25% of an ensemble‘s standard deviation about each point in time

191

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

=III HH Ill

 

 

 

 

 

 

 

 

 

 

 

 

at
J—«
I

 

 

 

 

“r— ,w
-l :Hr-Lq

l—‘I—'—t

I—L-L;

 

 

 

 

 

 

 

 

 

4110

 

g
l I Illllll Ill [1" illiil ll
' l‘
a

 

 

 

3
E v
dc:

<

00
§ .9
i In I
_ t
L'. “«
i=1 i
‘=:‘

 

 

 

 

 

 

 

 

 

 

. :. “L4.
.' " '5
m 5'34.
e' :' I
. 'ic.

LL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

lllllll

   

 

 

400 t=0 160 260 t=300 400
(Start) Normalized event time (end)
Legend: R0=730 — — Re=l400 — - R9=2380 — - - R6=3120

Figure 3.5.36 Mixed-scaled TERA ejection ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

192

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.
(Q) fi'fi’%
UT _:
j
3
<v> L" .
‘I‘L'r Io
U1 .TI
1 ll- .. ..- -
2.4T, r. 1‘? 17
l i-r-L “A. Q
2
U1

 

L1
.4
.h

 

ll
+5

1

L.
H

H

 

 

 

 

 

l-i
l
I
+—\J—'

I
J|_'._*
p—‘z—a—"

I
f‘—r—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.1

L4?
~1-

: 5‘_':
'—i=“r‘
._er
lllll - l

 

 

 

 

 

4:105 . .
-100 t=O 100 200 t=300 400
(Start) Normalized event time (end)
Legend: R9=730 — — R9=1400 —- Re=2380 —-- Re=3120

Figure 3.5.37 Inner-scaled TERA ejection ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

193

 

 

 

 

 

 

Number
of Events
350 v I r I r I
V
, R9~720
300 b + + y" = 14.6, S q
0 : 1' y” = 14.6, E
250 _ . i A y+=15.0,S -
° 4‘ A y"’ = 15.0, E
200 o 4 + Cl y+ = 18.9, S
3 8 * + a y+ = 18.9, E
g ‘ , t + 0 y+=24.2,S
150» 5 ° + + o_y+=24.2,1=. ~
4 a 3 g a Z i +
100 * 5 A a E a! o + ° ‘
a 2 A g m a t +
A + .
50 _ A 2 2 E O t * 4
A is a g 9
‘ t E a ’ t
O A LLLi—i—l—e—HE
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.1
Number of u-level Events
vs. Threshold (Inner-region data)

194

 

 

 

 

 

 

Number
of Events

250 l. I I I r
Ring-Like
motions
200 ~ 3 x R9: 730,3
it 3‘ R9: 730,E
a V R9=1400,S
150— *2 v R9=1400,E
+ a o R9=2380,S
*‘ g x e Re=2380,E
_ 3 a x ° R9=3120,S
100 . ° .. ‘ é - R9=3120,E

t o e a 8 '
V X
s s v ‘ ‘ 2 a a g
50 L v 3 v ‘ t é Q 5 ‘
V 3 v ' ° 3 o ' Q 9
V V ' ’ I * 3 * a é a
v V v 8 g x , i é § 3 a‘
O " i 9 6 ; a T ‘ x i i
0.0 0.5 1.0 1.5 2.0 2.5

u-level thresholding constant

Figure 3.6.2
Number of u-level Events
vs. Threshold (RLM data set)

195

 

 

 

 

 

 

Number
of Events
1200 I I I I I I
0 Large-scale
1000 _ motions i
0 Re: 730,8
. a R9= 730,E
800 _ T B 2 “ R9 = 1400, S _.
o . # Re=1400,E
a a . «2 R9=2380,S
600 _ a 3 ; . R9=2380,E -
e a i a R9=3120, S
g g e R9=3120,E
40° ” 3 2 . g - ‘
E
8 g S 8 a 6 S 2 a
200 ~ ° 9 a o . e 2 . ~
8 e .
0 ° ‘ I
0 * * * a E a a g . o g 2
O a a u .. . * a if g g Q o e e e e g g g 8 8
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.3
Number of u-level Events
vs. Threshold level (LSM data set)

196

 

 

 

 

Total U1?
Event x—
Time
10000 41 «t 4 l 1 I 1 1 1
2 o o o : + * t
O . o . o o 0 I +
E 0 ° 0 o o g +
E m a g g g S O . Q + +
+
a 6 Q a o I . +
1000 r E a . ° +
‘ 2 a ° . +
D o
Re~720 A S E +
+ y+ 14.6.8 0 6 E, .
+ y+=14.6,E A E ’
A y+=15.o,s . U .
... +=15.0 E ’3 i
1 _ y 9 A
00 1:1 y+=18.9,s . 3
E3 y+=18.9,E E ‘ A m
0 y+=24.2,S [:1 A o
o y+=24.2,E
O
10 1 1 1 1 1 L
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.4

Inner-Scaled Total u-level Event
Time vs. Threshold

(Inner-region data)

 

197

 

 

 

 

 

Total U2
Event 1:—
Time
10” l 1 1 1 1
o
:gggg O o
'3 5 3; x e ‘9 2 o
It i " 311:; x 9 g 8
7 . . t X g 2 x e e
low—i'izsz‘tig 6e
v v ' 3 V ‘ i i o e
V 3 ¢ i e
3 8 V : x I: 3 : I): e
Ring-Like a ' , : ... g
motions V V ¥ 0 O ‘ x
xR9=730,S " va ta.
*‘ R =730E ' t a I O v v g "E
— 0 ’ e
100 v Ro=l400,S 3
v Re=l400,E X o
e Re=2380,E
a R9=3120,S 0
‘.R9=3120,E
10 1 1 1 1 1
0.0 0.5 1.0 1.5 2.0 2.5

u-level thresholding constant

Figure 3.6.5
Inner-Scaled Total u-level Event
Time vs. Threshold

(RLM data set)

Total U12
Event x—
Time V
100000 T F l 1 l 1
Large-scale
.. . .. motions
low-Egg::;;:= .
e 6 9 8 I I § 2 . a .
e 8 e 3 ' B u . : “
g 8 a - . . . .
1i ” * +1 a 8 e e ' I . .
$3 at “ 1 * ” +1 3 O 9 § . .
1000"- : *t a “ 8 e g . .
a a a a ‘ e ' a ‘
# at ‘t a O a e e
9 Re=730,S ** .. : t , g 0 ° . 3
a R9= 730,E “ . e
1 Re=l400,S “ * 6 ,
100— 1: R9=1400,E a o « “ -
. R9=2380,S ... .
. Re=2380,E ” a a a
a R9=3120,S
91R9=3120,E o
10 1 1 1 1 1 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

198

 

 

 

 

 

u-level thresholding constant

Figure 3.6.6

Inner-Scaled Total u-level
Event Time vs. Threshold
(LSM data set)

 

199

 

 

 

 

 

Event x 2122
Time V 5
10m 1 1 1 I 1 1
Re~720
+ y+=14.6,S
+ y+=14.6,E
‘1 J. * -¢- A y+=15.0,s
22°ol* 1. Ay+=15.0.E
..9:°o*++ Dy+=18.9,S
lwpgggguu 0 ..Zé‘ ++ EB y+=18.9,E_
‘ A E i c] 8 + 0 +=24.28
} 9 + y .
2%! a 8‘0 : . + o y+=24.2,E
A 2 E a + O +
O
. 2 a . +
A Q T o
6 EB +
100* ‘ D 3 a Hi 0 T
D e T
A g B Q +
a , o
D E
A O
10 1 1 1 1 “ 1 Y
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.7
Total u-level Event Time
(Mixed Scaling) vs. Threshold
(Inner-region data)

200

Total U U9.

 

 

 

 

Event x —
Time V 5
1000 i . 1 1 , . 1
5 e
t 6 as
3 3 a: 9 o
I! g 0 X 2 5 O
3 x 5 0
it ° a o 3‘ 3 2 o
11" 3 g s a * j e
' v , f . 9: x . S i
v v: . # X x 0 § "‘
3 t x e ”E
100 " Ring-Like 3 v a . e *‘
motions ... z , a . ‘9 x
x R9=730’S v V x ‘ at
at R9=730,E V v i l. e
v R9=l400,S o v v *
V R9=1400,E ° 3 t a
O Re=2380,3 t V v x
9 Ro=2380,E ° 0 .
° R9=3120,S a x e ‘
*_R0=3120,E
10 1 1 1 1 1 V 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.8
Total u-level Event Time
(Mixed Scaling)vs. Threshold
(RLM data set)

 

201

 

 

 

 

 

Total U U”

Event x '71-?-

Time

10000 1 1 1 T T 1
a Ro=730,S
a Ro=730,E
;. a . +1 R9=1400,s
. ' . I I 3 R0=14ng
l... ‘ I :3 . R9=2380,S
1. e ” a a a in . Re=2380,E
1000- “sagas 3:. eRe=3120,S‘
“638 o‘:-. 9R9=3120,E
{I .... * # g 8 : a . I '
0 ‘t at ‘1: ” El 8 e a . I
w “ a 0 2 2
it a 9 e g
3 it a a e e I
1m_ * . D a 8 .1
* * at . e e
a a
Large-scale ” +1 9 °
motions ' .t
a a “ a
10 1 1 1 1 1 1

0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.9
Total u-level Event Time
(Mixed Scaling)vs. Threshold
(LSM data set)

Total

202

 

 

 

 

Event x29-
Time
1 (m ¢ I I I I 1 1
0 it It * +
0 O o o + t +
o o o l + +
. O . 0 0 I +
C3 1:1 D D o . o t +
£9 a B m D D O 2 1 +
a! 8 1:1 3 +
9
fl ‘ ‘ a ‘ ‘ 111 g I o o +
A S A Q B i . +
100 b R 720 9 a E E ’ +
e~ . A .
+ y‘l' = 14.6, S g D Q
+ y+ = 14.6, E A D 1; °
A Y... = 15.0, S ‘ i A o E
‘ y+ = 15.0, E E 8
1:1 y‘l' = 18.9, S . i
53 y+ = 18.9, E 1!
0 y+ = 24.2, S D .
o y+ = 24.2, E A +
10 1 1 1 1 1 9 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.10
Outer-Scaled Total u-level
Event Time vs. Threshold
(Inner-region data)

 

203

 

 

 

 

Total
Event x-Ji
me
1“» I 1 1 I 1 r
Ring-Like
motions
x R9=730,S
*6 Re-730,E
v R0=1400,S
x x v R9=1400,E
1. x x x o Ro=2380,S
" x x x x e R9=2380,E
0 o o * x ,K x a Re=3120,S
IOO'EB e e 2 o 0 at: . R9=3120’E
1, a e a 2 0 § *
° 0 a O as Z 0 0 § 3‘
fizz ; v v a a 9 e: 3“ 11s a;
’ V Q x at
. O V a a;
3: Ill ‘ 0 x y‘
3 v . 0 X
¢ v ‘ 9 x
v v t
a v ' 3 3‘. ,
10 1 1 1 1 1 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.11

Outer-Scaled Total u-level
Event Time vs. Threshold

(RLM data set)

 

204

 

 

 

 

Total
Event x—33-
Time
I“ O 1 r I 1 I I
' . 0 ° 0 Large-scale 0 R9: 8
.1 . ' - ° 0 Motions ' R9 = 5
db . . a - 3 o ' Re: S
e . ' . o 8 Roil400E
. - I 0 Re- 2
a a e 2 , 3. a lrig-43120.5
a a ‘ g ' . e R083120,E
0 e e e 81 a . O ‘
e 9 8 a 8 g g - I
e . a
8 a .
100 -11 * 8 e 9 . a
1' at “ * +1 * a 8 e e a .
‘t at a fi 11 a 8 8 a .
at 8 fl 8 9 . .
* it a O 8
a * 3 a a .
z 9
g at a e ‘
+1 at *t .
* * a “ at a
0 8
10 I 1 1 J L 1 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.12
Outer-Scaled Total u-level
Event Time vs. Threshold

(LSM data set)

 

205

 

 

 

 

 

 

Number
films. x_V_
Total Sample [112
Time
.m3o i l l l l T l
R0~720
.0025 - g + y*=14.6,S —
B 1 y+=14.6,E
:1 A y+=15.0,S
0020*? a D D A y+=15.0,E ‘
3 A 111 m D y+=l8.9,S
9 83 *= 189 E
a . y . . _
‘0015 2 A a 3 a o y+=24.2.s
$ t i ‘ A a; 9. y*=24.2,E
.0010 P o * + ‘ 2 D D E! d
3 o + f + 2 A 0 111
O + E
8 . 1’ A
.0005 - . ° 2 . f I E a -
° 3 0 t 6 a
o o E : Q a I
o o 3 ° Lit—M
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.13
Inner-scaled u-level Event
frequency vs. Threshold level

(Inner-region data)

206

 

 

 

 

 

 

Number
of Events x L _5
Total .Sample U: U..
Time
9 i I I I 1 1 I
_ R ~720 a
9
8 g + y+ = 14.6, S
7 1.. a + y+ = 14.6, E -1
0 A y+ = 15.0, S
6 ~ 113 D 1:) ‘ y+ = 15.0, E —
x10-4 8’ .. B y“ =18-9.S
5 " 9 33 y" = 18.9, E -
E
1} a 0 y+ = 24.2, S
4- 39. D “3 m o.y"’=24.2,E —
3 T 0 4 g a A D D a ‘
8 . + t D B
. a . 2 t a -
2 3 z o . i X E 53
_ ° ° 3 1 ’3 w e _
1 o f; t t . 1a a
0 3 t ‘ B
0 MFG—0+.—
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.14
u-level Event frequency
(Mixed-scaling) vs. Threshold
level (Inner-region data)

 

 

Number
m x_5_
Total Sample Um
Time
30 I I I I I I
E R ~720
25 ’ + y+ =14.6,S ‘
B + y+ = 14.6, E
20 _ E a A y“ = 15.0, S d
m D C] ‘ y+ = 15.0, E
x10-5 8 a 13 y+ =18.9,S
15 — B a a y+=18.9,1—: -
v a! 0 y+ = 24.2, s
1, U B +
A l 1 a 0 . y = 24.2, E
10 — A ‘ + ‘3 c1 61 a
0 8 . ‘ ‘ fl ... X B B
o 3 T m
8 3 : a t + D
5 P ° ° 9 I; * + E 4
0 0 e t ‘ a B
0 E
0 8 g g 2 W

 

 

 

0.0 0.5 1.0 1.5 2.0
u-level thresholding constant

Figure 3.6.15
Outer-scaled u-level Event
frequency vs. Threshold level

(Inner-region data)

2.5

3.0

 

208

 

 

 

 

 

 

 

Number
Qvaents xi
Total Sample U?
Time
16 I I I I I I
14 - 0 Outer-Region 1
motions
12 a . 0 R9= 730,8 -
a Re: 730,E
3 1+ R9=1400,S -
1° ' u Re=1400,E
x104 : . e Re=2380,S
8 _ t r - . R9=2380,E -
3 g = .. a Re=3120,S
6 - 8 a 3 - e R =3120,E ~
6 a a a . 0
0 g 8 ‘ 3 :
4 T 8 g a : . : o "
Q a
o g a
a o I i .
2 -— a 8 0 a ' . ’ d
I g I : § 8 z a a
o “aflfiaa.:::::
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.16
Inner-scaled u-level Event
frequency vs. Threshold level

(LSM data set)

Number
_Q£_Exema_ x .2. _5_
Total Sample 11% U...

 

 

 

 

 

 

Time
30 I I I I I
Outer-Region
25 _ motions
; a Re: 730,3
8 B = 730,E
20 ._ 2 * R0 = 1400, S
a 0 =
x10‘5 0 I o * R9 1400’E
3 1 . a e =2380,S
15 _ +1 ; . I i . Ro=2380,E
. * ; . . B =3120,S
i 2 ° - e R9=3120,E
10 _ 8 * a O -
8 8 3 . a .
e a a " 9 . I
9 e a g,- 9 a a I
5 __ a O 8 a E o * - I -
a Z 8 a . 3 2 ' I
a E ’ g 2 2 . ' I
a D a E a 8 9 a ‘ = :
0 “J—LI—l—I—u—i—L
0.0 0.5 1.0 1.5 2.0 2.5

u-level thresholding constant

Figure 3.6.17
u-level Event frequency
(Mixed-scaling) vs. Threshold
level (LSM data set)

210

 

 

 

 

 

Number
QEEXQDIS x 8
Total Sample U“,
Time
10 I I I T I I
Outer-Region
8 _ motions
0 R0: 730,8
1: Re= 730,E
i I =1400,s
6 " a o 41 R0=1400,E
-5 u o a =2380,S
"10 ' 2 a . =2380,E
4 q, " a a R9=3120,S
0 it 3 3 a e R0=3120’E
‘ ii 0 u ‘
_ an # a a .
2 'f a . ‘ 2 * ° ' '-
8 B a a a g : i a 9 at ‘t . . g
. . . g g 2 a g Q . . .
B 8 a G 3 = * ‘t * - ' ' I
0 a ”Law—SM;—
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6. 18
Outer-scaled u-level Event

frequency vs. Threshold level
(LSM data set)

 

211

Total
.Exentlimz XPLUJ
Number of V

 

 

 

 

 

 

Events
9m I fl I I ‘
+ y+=l4.6.S Re~720
+ y+=l4.6.E
_ A y+=15.0.S
8w A y+=15.0.B
c1 y+=18.9.S
ea y+=18.9.E .
700” o y+=24.2,S + o
oty+=24.2.B + + +
A
600— + + ‘ e 0 0
i + 1 Z * s 3 § + A E D
‘ 1 g 8 0 ‘ A 2 1) . A a a g
b ‘ 0
500—1 3 a g A A 1 . ..
1t 0 A [:1 o i . <>
0 D C] D A
D D a D :1 11: 113 i +
_ o o ’ o 0
4m 3 a a . O . O B a
a: 9' m in a as . o . . o X
o
300~
200—
1m 1 1 L L
0.0 0.5 1.0 1.5 2.0

u-level thresholding constant

Figure 3.6.19
Inner-Scaled Average u-level
Event Length vs. Threshold
(Inner-region data set)

212

 

 

 

 

 

 

 

Total 2
W x M
Number of 6 v
Events
50 r l l l o T l
+ t +
+ o
+ E o
40 - 1 ‘t 2 Q 3 a 9 g 3 1) ¢ + D a U a D a: a ‘
1 O o I 9 ° '3 0
<5 C] 3 § z 0
a 1
30 1- D . I: E] D 2 D : é a A A g Q 1 § . _
2 x a . g 3 a . . A .
i B m a E E B E E . . . 8 ‘
O 2 B O
20 — A _
Re ~ 720 * A
+ y+ - 14.6, S
10 ~ 1 y+ = 14.6, E D d
A y+ = 15.0, S
A y+ = 15.0, E
0 _—0 1+=18'9’S =a—I—r—o—o—
93 y"' = 18.9, E
<> y"' = 24.2, S
O . y+ = 2142’ B 1 1 1 1 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.20
Average u-level Event Length
(Mixed Scaling) vs. Threshold

(Inner-region data)

213

 

 

 

 

 

 

 

Total
EventTime x203
Numberof 8
Events
4.0 I I 1 I r r
3.5 h- + 0 + . _.
+ + + + o
3.0 L‘ + E] o ‘
o + D a a;
..t‘:”’ *f‘ffW .82?
2.5 L l; o ? 4, o o ‘
C] D [3 D D 0 ¢ +
[2 . Q . D D 9 D a B 1 i O
2'0 “£5 a a I; g o . ‘ a; o '1
B B B m g B ‘ . 8 . Q . ‘
1.5Li““83 3‘ A Aaoa' -
+ y"’=14.6,S A 1
1.0- + y+=14.6,E A A A _
A y+=15.0,S D
+
0.5 _ ‘ y =15.0,E q
a y+=18.9,s
0 T“ a Y+=18'9JE R0 720 : I—H—I—I—
0 y+-24.2,S
. y+-241'2’E 1 1 1 1 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholdin g constant

Figure 3.6.21
Outer-Scaled Average u-level
Event Length vs. Threshold
(Inner-region data)

214

Total
Event Time $.va
Number of V

 

 

 

 

 

 

Events
9m 1 l I 1
‘3 =730,S
n :g=730,a ° ...
* Re=l4m,s b °
* Re=l4m.8 0
a Re=2380.S a a
- Re=2380.E .. a e c a
Ro=3120.S a .
eRe=3120.B a a a .
am— . ° a . . . . . . : a a
a '3' ' E Q a ; a 8 a a
500 o ‘ . . a a * e e 9 2
b ” 1+ 1+ 8 “ *
éqoégeeeeée"
400— a
89.35360333036”
300— * a o o
A . I ' C I I I . I g C U - 3 ' a a
200—
Outer-Region Motions *
a
1m 1 1 1 1 1
0.0 0.5 1.0 1.5 2.0 .5

u-level thresholding constant

Figure 3.6.22
Inner-Scaled Average u-level
Event Length vs. Threshold
(LSM data set)

215

 

 

 

 

 

 

 

Total 2
EVQH! TEE X Uoo U1
Numberof 8v
Events
30 I I I I 1 r
25* 3 -
a a O a a a if a a
a O ” ii if . .
20-2392333.f28323‘a-.I. ..-
a d f ‘ E I a g a a a a 3 ° 0 a o . :
3 ; . I I g ‘ . I . 8 9 8 a 9
15'- 2.93333893285’...:ggo::a~
* .1. . g; a
Outer-Region a 8
10’ motions ‘
a R9=730,S o
* O
5 a Ro=73o,E ” ‘5 4+ 4}
" 1+ R9=1400,S a 11 a d
11 =1400,E a
e RL=2380,S 1
0 I R6=2380,E " F
a R0=3120,S
__91K9=311201E 1 1 1 1 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3..6.23
Average u-level Event

Length (Mixed Scaling)
vs. Threshold (LSM data set)

216

 

 

 

 

 

 

 

Total
Evn irn x23
Numberof 5
Events
1.6 I I I I
1.4 -
o
a o 0 o a o ° 0 o o o o 9
1.2 P u; a
it o O
I * 1.
10 — I B I I Q . . . . . . 1.
1+ ” 1+ “ fi * ti “ e a 2
0'8 F— 4* * . ‘ a a a a 2
3°"::;z*“ 3‘;:*
0.6 e I 6 ii E E I 3 ‘ a ' 3 3 6 a 9 ‘
a . . D D a 8 e 8 e e
1) e 9 e e e o e e 9 e 9 e a
0.4 - 0 a 9
a =730,S
9 @usqa _
* R9=l4m.S . o
1. R9=1400.E Outer-Region motions
a Re=2380.S
- Ro=2380.B
Re=3120.8
8 Re=3120.B 1 1 1 1
0.0 0.5 1.0 1.5 2.0

u-level thresholding constant

Figure 3..6.24
Outer-Scaled Average u-level
Event Length vs. Threshold
(LSM data set)

Total
W x_JU°°U
Number of v y+

Events

217

 

 

 

 

 

60 I I I I I I
A
50 _ + a
A +
+ +
+
A
40 ~ + + ‘ t + -
‘9 4 ‘i + +
0 fi A ‘ ‘ A A 3 1 A
3 A A [5 1 A
- 81
30 D D g Q g o 4
A
:1 1
D D g g! S] 5 g a In 0
A
20 ’ E9 :3 g a; 93 B as m g 5 o o o ‘
Q o o 0 o . o . . o D
o o . . o 9 o
+ y+=14.6.s ‘
10 e + y+=l4.6.B a
A y+=15.0,S
A y+=lS.0.B R9 ~ 720
0 __EI y+=18.9.S I I - I I
B y+=18.9,E
<> y+=24.2.s
o y+=24.2,E
‘ 1 1 1 1 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.25
Inner-Scaled Average u-level
Event Length / y+ vs. Threshold

(Inner-region data)

 

218

 

 

 

 

 

 

 

juv<0ljuv<0
m Intimes

1m% T I I T I I

Re~720

+=14.68
80%- + y . -

1 y+=14.6,E

A y“'=lS.O,S

‘1 y+=15.0,E
60%—0 + + + + :1 y+=18.9,s ‘

"09é*+++ EBy“=18.9,E

111mm“.
40%~ *1 . a 3 ° s 1. + o y+=24.2,1~: -

1 § 3 + '
1 Q :1 0
1 . . +
1 c1
1 o '3 Q Z
20%_ A D . + "‘
1 2 E g +
i o s g
9 2 9 E Q

0% ‘ 1' La—g—é—z—w—
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.26
Percent Reynolds Stress ”captured" during
u-level events vs. Threshold
(Inner-region data)

219

 

 

 

 

 

 

 

juv<0ljuv<0
during liltimel
emu
lm% T I T I I l
Outer-Region
motions
80% ~ 0 Re: 730, S
a Re: 730,E
++ R9=1400,S
60% ' . a R9=1400,E
I ,. a R9=2380,S
o t g C R0=2380’E
. f 3 a R9=3120,S
40% . 9 . e R9=3120,E
é . . I
. 2 .
2096* ' ° . . ' a . “
o . . . a
a a . . . ' 8
“95a ““5593?“
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.27
Percent Reynolds Stress "captured" during
u-level events vs. Threshold
(LSM data set)

2.0
1.8

1.6

1.4

1.2

0.8

0.6

0.4

0.2

0.0

220

 

 

 

 

j I I I I T
_ + y+=14.6,s
* y+zl4.6,E
_ A y+=15.0,S
‘ y+=15.o,E
'3 y+=18.9,S A
r a! y+=318.9,E
° y+=24.2,S
_ . y+=24'2’E A g
A A A + +
J“““"f::?e‘éstifii++.
! a l a fi 3 a - B a O . ' t . . + +
o O 0 § Q a ‘ Q g 8 g 9 5 a a . O
b“ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ A A 2 8 3 a; g f g a; m o
o . o o ‘3 o
.— D D
b O
L l l l l 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholdin g constant

RMSFigure 3.6.28
Sufi During u-level
Evemts ormalized by (0’
vs. Threshold (Inner-region data)

 

to’l .
2 2%

3.0

2.5

2.0

1.5

1.0

0.5

221

 

 

 

 

 

I I I I I . ‘
a 3730.3
. 23.7....
it R9=l4oo.s a
_ fl Ro=lmB a a a . .
a Re=2380,8 .
- =2380,S 0
Re a
B Re=3120.S .
’ e R0=3120,E a a . .
a 5 2 e
E o
_ . a a
n 2 3 at " at a a I I
at * l ; a a . t
a : . 3 g I a o I 2 fi 3 5 , a
I .
>— 9 . o o
e a o a z 4} a 9 a O
3 d a e 3 3 o 8 g 3 a 6
e 3 3 § g 3 e
H» e e e e e e e e e e e Z 2 e a a
a
Outer-Region Motions
0.0 0.5 1.0 1.5 2.0 2.5 3,0

u-level thresholding constant

Figure 3.6.29
RMS 0) During u-level
Events fiormalized by (0’

2

vs. Threshold (LSM data set)

 

222

 

 

 

 

<u2+v2>lm
___m_
(u2+v2)’
6 I I I I I I
R9~720 ,
_ + y+=14.6,S
5 + y+=14.6,E .
A y"’=15.0,S
A y+=15.0,E ,
4 _ El y+=18.9,S Q m
m y+=18.9,E . a A A
<> y+=24.2,S ‘
3 _ ..y+=24.2,1~: . t m a A
m + + +
e B a 5’
£2 A i + G
2 -- g .1. t ‘ U 0 0 0
e ' a 0 t + ° ‘ .
Q 6 $2 0 g 9
39 t H a D 3 °
1~ i S g g ‘3 3 ° °
9 9 9 9 9
0 1 1 l A 1 l
0.0 0.5 1.0 1.5 2.0 2.5 3.0

u-level thresholding constant

Figure 3.6.30
Average TKE During u-level
Events Normalized by TKE’
vs. Threshold (Inner-region data)

 

<u2+v2>| .

223

 

 

 

 

dim:
___£¥m
(u2+v2)’
6 l I T I I
Outer-Region
motions
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Average TKE During u-level
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224

 

 

-100 t=0 100 200 t=300 400
(Start) Normalized event time (end)
Legend: R0=730 — - Re=1400 — - Re=2380 — - - Re=3120

Figure 3.6.32 Outer-scaled u-level sweep ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

 

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Figure 3.6.33 Mixed-scaled u-level sweep ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

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Figure 3.6.34 Inner-scaled u-level sweep ensembles. Error bars indicate

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Figure 3.6.35 Outer-scaled u-level ejection ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

228

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 3.6.36 Mixed-scaled u-level ejection ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

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Figure 3.6.37 Inner-scaled u-level ejection ensembles. Error bars indicate
25% of an ensemble’s standard deviation about each point in time

230

 

 

 

 

 

 

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P(D)

100%

80%

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231

 

 

 

 

 

 

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vs. Threshold

232

 

 

 

 

 

 

 

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P(D): Probability of an LSM Detection
Occurring During a u-level Detection

vs. Threshold

P(E)

100%

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Occurring During an LSM Detection
vs. Threshold

234

 

 

 

 

 

 

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vs. Threshold

235

 

 

 

 

 

 

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P(E): Probability of a u-level Detection
Occurring During an LSM Detection
vs. Threshold

236

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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237

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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238

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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239

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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243

 

 

 

 

 

 

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P(D): Probability of an RLM Detection
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P(D): Probability of an RLM Detection
Occurring During a u-level Detection
vs. Threshold

 

 

 

 

 

 

245

 

 

 

 

Ring-Like
1m%_ wtions _
x R9=730,S
*6 R9=730,E
80%” V R9=14OO,S 0
v R0=1400,E
P(E) o R9=2380,S
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z ¢ R9=3120,S
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0 g 0 ‘-
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0.0 1.0 2.0 3.0 4.0 5.0

6.0

uv—quadrant technique threshold level

Figure 4.2.4

P(E): Probability of a uv-quadrant Detection

Occurring During an RLM Detection
vs. Threshold

7.0

P(E)

100%

80%

60%

40%

20%

0%

 

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R9 = 1400, E
R9 = 2380, S
R9 = 2380, E

 

 

0.0

1.0

2.0

3.0 4.0

TERA threshold level

Fi

gure 4.2.5
P(E): Probability of a TERA Detection
Occurring During an RLM Detection

vs. Threshold

5.0

P(E)

100%

80%

40%

20%

0%

247

 

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u-level thresholdin g constant

Figure 4.2.6

P(E): Probability of a u-level Detection
Occurring During an RLM Detection

vs. Threshold

 

base

has

248

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

prob hi“ I I T T r I I
of a gmb? Thresth Figure 4.2.7a
based sweep . + 0.00 P(T): Probability of a uv-quadrant ejection 4
detection ' 0-35 vs.
75% A (133 Phase of an RLM smoke ejection 4
_ ‘ . _
01.40 (Re-730)
_ 01.75 _
50% o 2.10
0 2.45
25% - ’ -
0% on 8 a
a i Q! 3000 ’ 00 0"Qn 00
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+ ++ 800§0+§0§+. ??AAAA ‘ ++++
++++++++0+4,+ ’* **;+*+ ++
50% r +++++*++++ 1
75% - _
Probability
ofaprobe- L 0
based ejection
detection 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
Probability ' ' ‘ ' ' I I
ofaprobe-
based sweep ~ _
detection
75% “ d
50%»— +IL++++++++++t+++++++++++++++++ ++ +
+++++ I IIIII+++++ **+0+‘+** ‘§* ++ +++
25% “.“.§ AAAAAAAAAAAAA AA I ‘I *i ‘*O_
.“A222§¥§AAAAAAAAAA 22 2 222
0% n99!!!! ""!!!ifiunfifi
Threshold -
25% ” + 0.00
v 0.35
50% - A 0.70 Figure 4.2.7!) 0
Q :23 P(T): Probability of a uv-quadrant sweep
75% - ' vs. -
Probability : :13 Phase of an RLM smoke sweep
ofa probc. F ._2,45 (R9 = 730) 1
based ejection
detection 1 1 1 1 1 1
-100 t=0 100 200 =300 400
(start) Phase of a smoke event (end)

(Normalized event time)

249

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili T ' I I I I I
of a pmbtey. Threshold Figure 4.2.8a
based sweep r + 0.00 P(T): Probability of a uv-quadrant ejection 0
detection ' 035 vs.
75% _ 2 (:3 Phase ofanRLMsmoke ejection _
01:40 (R0=14m)
_ 01.75 a
50% . 210
25% 0.2.45
0% 00 8 t a
H M I 0 ° Illa ...
25.. -3!;59399.301.1§111I21;1ge§23;.3..~g;
+ +++ 700.......*..§0??A * ++++++
++++++++++++ oti++
50% .— +++++++4>+ ..
75% ~ .
Probability
ofaprobe- F _
based ejection
dcmfion 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
Probability ‘ ' ' ' ' I I
ofaprobe-
based sweep - .
detection
75% _ .
50%- +++++++++++++t++++++++++++++++++++++ —
+++++ .0 OOIIIOIOIO **§§*.*§. ‘.* ++
25%-I..“. AAAAAAAAAA * "¢*‘.. ..
eeezzaezgeiiii...... 22 A AA LL;
0% .iaetti- ----::eti..== .3: .9 ::2
Threshold 1
25% ” + 0.00
1 0.35
50% - A 0.70 Figure 4.2.8b ~
g :23 P(T): Probability of a uv-quadrant sweep
75% " 91.75 VS. _
Probability o 2:10 Phase of an RLM smoke sweep
of a probe- .. 02.45 (Re =1400) _
based ejection
dCtOCtion 1 1 1 1 1 1 1
—100 t=0 100 200 =300 400
(Start) Phase of a smoke event (end)

(Normalized event time)

 

 

 

 

 

 

250

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Prob bili ' I I I I I I
of .1;me Threshold Figure 4.2.9a
based sweep - + 0 00 P(T): Probability of a uv-quadrant ejection 0
detection ‘ 0 35 vs.
% _ ‘ 0-70 Phase of an RLM smoke ejection _
II 0:2: mm»
_ 0 1.75 ..
50% . 2.10
25% 0 . 2 .45
0%
filiiill
25%L-1 + + + + ... + + ’
50% ~
75% - .
Probability
of a probe- - -
based ejection
dCtOCfiOn 1 1 1 1 1 1 1
-100 t=0 100 200 t= 400
Probability T ' I I I I I
of a probe-
based sweep - _
detection
75% I A
50%_+ +++"++++++++++I+++++++++++++++I+ ++ ‘
++++ 11*I111111 11111 1 ++ +
0 0 * O I 6 . A . I I I * I ‘ O 0 O 0 + +
25%_ AAA AAAAAA A AA 1 11 ***~
A A A A A A A A A A A A A
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0%
Threshold 1
25% +0.0
1 0.35
50% — A 0.70 Figure 4.2.9b 4
75% g :23 P(T): Probability of a uv-quadrant sweep
- vs. -
Probability : {:3 Phase of an RLM smoke sweep
of a probe- - 0 . 2.45 (R9 = 2380) _
based ejection
detection 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

 

 

"‘ .i"fl‘*’,fin~"u"‘ef ‘r' {Us-V ' w“... .

 

251

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

Probabili 1 r 1 l I 1 1
of a Wolfe”. Threshold Figure 4.2.1011
based sweep _ + 0.00 P(T): Probability of a uv-quadrant ejection _
detection ‘ 0-35 vs. . .
75% _ : (133 Phase of an RLM smoke ejection _
.1240 <Ro=3120>
_ a 1.75 q
50% o 2.10
25% e 12.45
0% e e s I
isgil3ii
25% —++++++++'
50% -
75% - *
Probability
of a probe- - ~
based ejection
dCtCCfion 1 1 1 '1 1 1 1
-100 t=0 100 200 t=300 400
Probability l I I I I V l
of a probe-
based sweep * .
detection
75% ’ ‘
50%—+++++ +JI++1i++++++1~++++++++<1~+++++++++++++ «
0 O9 1o+++o 1+++o*+*‘ ‘*‘ ++
25% 1111.11... . ‘ ‘ . * I I I .—
0% .992???‘ iiiiiiiiiiiaagfi“iffff‘ A Aid???
Threshold q
25% ’ + 0.00
1 0.35
50% - A 0.70 Figure 4.2.10b ‘
‘ {250 P(T): Probability of a uv-quadrant sweep
75% r 2 1'75 vs. -
Probability o 2.10 Phase of an RLM smoke sweep
of a probe- - ° , 2.45 (R9 = 3120) .
based ejection
dCtOCtiOll 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

252

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili I I I I I I I
ofapmbtz. mad Figure 4.2.118 . .
based sweep - + 8(3) P(T): Probability of a TERA ejection -
detection ‘ - vs. .
75% F ‘8-8 PhaseofanRLM smoke ejection .
131.2 (R9=730)
_ 915 _
50% :13
25% 02.1 _.
0% i
33......‘383°§380000g0 8! . 03§.5§
O a I!
25%Mififiiiigfizaiiizinaziéiémgiiig; Earnhu
ii+++:.. 9.?.A?AAAAAAAAAAAAAAA AAA ‘¢.*v::1¥-
50%_ ++.1++ o 00...,o¢¢.,*,,too+0:+++++ z
*++++++++++++++++++++++
7596- —
Probability
ofaprobe- r- _
based ejection
dCtOCtion 1 1 i 1 m 1 1
-100 t=0 100 200 = 400
Probability l l I r l T 1
ofaprobe-
based sweep - «
detection
75%_ + +++++++++++++++++++++*++++ ‘
+++++ ++1I++++ .0*H‘*.+9v§. ++oo+oiosooi+ *
mporiooooi oooo‘iAAeAAAAAAAA
AAAAAAA AA
u%-I....:::::‘;ssa°2 2:::"-;;;‘
0%jigge-“liiizgfzzssszifgggg
25%-Threshold -
+0.0
50% 10.3 F' -
” A 0.5 Igure 4.2.llb
b 0.9 P(T): Probability of a TERA sweep
7596- I312 vs. 1
Probability In :3 Phase of an RLM smoke sweep
b of aprobe- r :2:l (R9=730) -
asedejection '
dCtOCdOn l J 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

253

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili 1 l l. I 1 1 1
of a prob?- Threshold Figure 4.2.12a . .
based sweep - + 8.3 P(T): Probability of a TERA ejection -
detection * . vs.
75% _ A 33 Phase of an RLM smoke ejection _
.12 (Ro=1400>
__ 81.5 _
50% 01.8
02.1
2596- -I
0%
sOOOOOOOI.8QQQOs. .. . .égs
use as ° 3683 3’ gang 8 s o 0 53359 a;
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ii+++*" *A? AAAazAAAAAAAAAAAAAAAAA totiii:i
50%_ +++o+:'1*+6,*.,906,,§,,*+0060*++++ ‘
++++++ ++++++++++++++++
7596- I
Probability
ofaprobe— - -
based ejection
dCtCCtiOn 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
Probability ' ‘ ' ' ' r '
ofaprobe-
based sweep I -
detection
75%- + +++++*+++++++++++++++4++++ ‘
+++++ ++<>++++ *§**.'**+++§. vooooodrioivts» +
50%-+ooioooo 01+9'LAegAAAAAAAA
ifififififiafi DIIIII 2
25% bAAAggifiil 00.0 in 51111113Ill .330
III. .. a IIII se.
0% BEL! Ioggomm m
25%—Threshold I
+0.0
50% 90.3 . _
” A 0.6 Figure 4.2.12b
I 0.9 P(T): Probability of a TERA sweep
75%.. 131.2 vs. ~
Probability a 1.5 Phase of an RLM smoke sweep
of a probe- — :3 (R0 =14OO) _
based ejection '
deteCtion i 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

254

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili T l I 1 1 1 1
based sweep ~ + 0.0 P(T): Probability of a TERA ejection _
detection *0-3 vs.
75% _ ‘ 83 Phase of an RLM smoke ejection _
m mo=2380>
_ 1111.5 —4
02.1
25% - I
0% an 8 g ‘
r 1: iii? iiiia .. a o-sia359553%!?
2.. “2:1... .iIIngégrllilliélggggeem5.:II3._
+++ *‘o.."*+o"o?A§¢ ++ ++
+++++++++++ 1 +4
75% ~ «
Probability
ofaprobe- ~ _
based ejection
detection 1 1 1 1 1 1 1
-100 t=0 100 200 t= 400
Probability I I I I I I I
ofaprobe-
based sweep r .
detection
75%_ + +++++++++++++++++++++4++++ _
+++++ ++fl++++ 0......§v§** +II+III¢¢I+I *
50% "+1++1+oo
25% I-AAAAAAAA
.....
iiél’lln?
0%
25% ~Threshold -
+0.0
90.3 . _
50% ” a 0.5 Figure 4.2.13b
. 0.9 P(T): Probability of a TERA sweep
75% - '31.2 vs. _
Probability : :3 Phase of a(ili‘ RI_.I\2Il3gsi(i)i)oke sweep
Ofapmbc' b 02.1 o.- I
based ejection '
detOCtion 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

255

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili I I 1. I I 1 I
of a pmbtey: Threshold Figure 4.2.14a
based sweep _ + 0.0 Probability of a TERA ejection
detection '0-3 vs.
75% _ ‘ 33 Phase of an RLM smoke ejection
.12 IRe=3120>
_ 815
50% 01.8
02J
25%-
0%
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+++++++ ++ +++++++++++++
+ +
75%-
Probability
ofaprobe-~
based ejection
detection 1 L 1 ¥ 1 1 1
-100 t=0 100 200 t=300
Probability ' ' ' I I I I
ofaprobe-
based sweep -
detection
75%_ + +++++++++++++++++++++*++++
+++++ ++II++++ 0*..‘.‘§v+** ++rotooo+so¢++
50%b+1+¢1+oo IIIII
25% -.MMMMI’I‘I‘I‘B
.......fi‘ [3
I II
0% Bi? 3 !
25%»Threshold
+0.0
50% ~ 3.3% Figure 4.2.14b
I 0.9 Probability of a TERA sweep
75%- 01.2 vs.
Probability In 1.5 Phase of an RLM smoke sweep
ofaprobe- ' :3 (Re=3120)
based ejection '
dCtOCtiOll 1 1 1 1 1 1 1
-100 t=0 100 200 t=300
(start) Phase of a smoke event (end)

(Normalized event time)

 

 

256

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili l I I I I I I
of a prob?- Threshold Figure 4.2.15a
based sweep _ :33 P(T): Probability of a u-level ejection -
detection V8.
75% _ ‘ 323 Phase of an RLM smoke ejection _
‘ (R =7301
00.92 9
50%- 81.15 _
01.38
01.61
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-100 t=0 100 200 t=300 400
Hobability l I l l l l l
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based sweep - -
detection
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‘ 3:; P(T): Probability of a u-level sweep
75%r ‘3 - vs. i
.. ‘1-15 Phase ofanRLMsmoke sweep
Probability 01.38 -
0 01000000-- .151 (Re-73°) -
asedejection
dCtOCtion 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

257

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili I I I. I I ' '
of a prob? Mom Figure 4.2.16a
based sweep _ + 0.00 P(T): Probability of a u-level ejection _
detecfion '033 vs.
75% _ A 046 Phase of an RLM smoke ejection -
0333 (110:1400)
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50% 0138
25% :151 _
0%
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25%r0.§§“g; 3303;232:2325:3005250035. igéisgga
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50%— *‘t’i‘iitotA g“888233A3AAAAAA #444 ..
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75%- ‘
Probability
ofaprobe— — —
based ejection
deteCtion 1 1 1 1 1 1 1
—100 t=0 100 200 = 400
Probability I l T T I l l
ofaprobe-
based sweep - I
detection
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25% +0.00
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‘ 0-69 P(T): Probability of a u-level sweep
75%- 0092 vs. .
P l lility 2%: Phase ofanRLMsmokesweep
of aprobe- r 91:61 (Ro=1400) -
based ejection ‘
detOCtion ; 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

258

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili r I r. I I I I
of a prob?- Threshold FIgure 4.2.17a
based sweep - + 0.00 P(T): Probability of a u-level ejection .
dtectio *023 vs.
e n _ A 0-46 Phase of an RLM smoke ejection _
75% ; 3-33 (110 = 2330)
_ 91.15 _
50% 01.38
001.61
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Probability
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based ejection
detection 4 1 . . 1 1 1
-100 t=0 100 200 t=300 400
Probability I I f I I I I
ofaprobe-
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detection
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‘ 01;; P(T): Probability of a u-level sweep
.. 00. vs. ‘
7.5% “I 1-15 Phase of an RLM smoke sweep
Probability o 1.38 (R _ 2380)
b ofaprobe- - 01.61 0' I
asedejection
detection 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(Start) Phase of a smoke event (end)

(Normalized event time)

259

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili I I T. I I I I
of a mg; Threshold Figure 4.2.18a
based sweep _ + 3.230 P(T): Probability of a u—level ejection —
detection I VS~
75% _ A 823 Phase of an RLM smoke ejection _
130.92 (R9=3120)
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01.61
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Probability
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based ejection
dCIWtiOn 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
PfObability I I I I I I l
ofaprobe-
based sweep - ‘
detection
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‘ 3:: P(T): Probability of a u-level sweep
75%— a - vs. _
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Probability 0 1.38 Phase of an REL; 2sr(r)Ioke sweep
ofaprobe- - 9.1.61 (Re- ) _
based ejection
dCtOCtiOll 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

260

 

 

 

 

 

 

1M" UIAAIIDAAIIIIAA—I
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P(D) a a A , 0 ' . 0
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I ‘ A A 5 B B
40%H
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A y"'=15.0,S
A y*=15.0.E R9~7zo
0%__Dl"’=18.9,8 ::..____._._
“3 y+=18.9,E
° y"'=24.2,S
°.y"'=24.2,B
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

uv-quadrant technique threshold level

Figure 4.3.1
P(D): Probability of an Inner-Region Visual Detection
Occurring During a uv-quadrant Detection
vs. Threshold

P(D)

1(X)%

80%

40%

20%

0%

261

 

 

 

 

 

 

— + D D I I I I I I A A A A -!
+ . I I I I t 3 ° °
+ 3 g 9 0 i i g 2 2 0 ‘
j 5 0 Cl . a U m A 8
g 6 D D A A X D I ‘ _.
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A i A
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A y+=15.0,S
A y+=15.0,E
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‘9 y+=18.9,E
° y+=24.2,S
0 y+=24.2,E
0.5 1.0 1.5 2.0 2.5 3.0

u—level thresholding constant
Figure 4.3.2

P(D): Probability of an Inner-Region Visual
Detection Occurring During a u-level

Detection vs. Threshold

262

 

 

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+§AUOO$ A

 

 

SESESESE
6.6..00009090202.

 

 

 

 

+IDAS¢ 44550000441
11111122
+BA o o a A = = = = = = = =
+ + + +
+ m. on a Y+y Y+YY+YY+Y
+ 000A A3 + t A A D m o O.
I _
_ 1. _ _ _ H
0
m 000 2 W
l

Pm)

2.0 3.0 4.0 5.0 6.0
TERA threshold level

1.0

0.0

Figure 4.3.3
P(D): Probability of an Inner-Region Visual

Detection Occurring During a TERA Detection
vs. Threshold

P(E)

100%

80%

60%

40%

20%

0%

263

 

:55

I A A-
v “r

I

I

OOPS-ED

DD

00» D!
MODDB
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90+»!
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‘43» I
6 O B D b D + +
‘<

+IJO- DE
‘DODB

 

 

 

 

l

 

0.0

1.0 2.0 3.0 4.0 5.0 6.0 7.0
uv-quadrant technique threshold level

Figure 4.3.4
P(E): Probability of a uv-quadrant Detection
Occurring During an Inner-Region Visual Detection
vs. Threshold

 

 

264

 

 

 

 

 

 

 

R9 ~ 720
100% — + y+ = 14.6, S _
+ y+ = 14.6, E
g a A y+ = 15.0, S
30% 9. A y+=15.o,E «
P(E) " 9 g g a y+ =18.9,S
9 ‘ . A E y+ = 18.9, E
60% — ° 9 ‘ a; a 0 y+ = 24.2, S d
0 + ° 9 _ y+ = 24.2, E
[S 1 c Q .
40% *' 0 [a + E . ‘
9 + i? . . .
20% — g + 9 g ‘9 c o _
Q q, A g ° 0 .
‘ 9 a 3 Q a Q . . ° 0 o
. O
0% 2 ‘ WM
0.0 1.0 2.0 3.0 4.0 5.0 6.0

TERA threshold level

Figure 4.3.5
P(E): Probability of a TERA Detection
Occurring During an Inner-Region Visual
Detection vs. Threshold

 

 

 

 

 

 

 

 

 

265
R ~720
100% ~ + y"' = 14.6, S - in
+ y+ = 14.6, E i
g 6 a A y+=15.0, S
8096* I & g g A A y+=15.0,E * _

0 o A += . ,

P(E) Wag“ 2y._1898

9 3 § 8 E y —18.9,E
60% '- 9 m a 0 y+ = 24.2, S d

° 2 5 . l: o y+=24.2,E

5
40% ~ é .. a —
3 z . e
A + o
20% r o e a g a q
o a 0 + 3: ’
A $ 0
A a, . .
0% R Lg—I—i—o—t—o—a—
0.0 0.5 1.0 1.5 2.0 2.5 3.0
u-level thresholding constant
Figure 4.3.6
P(E): Probability of a u-level Detection
Occurring During an Inner-Region

Visual Detection vs. Threshold

266

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili T I T I I I I
of a pmbtcy. ThreshOld Figure 4.3.7a
based sweep _ t 3.1;? P(T): Probability of a uv-quadrant ejection -
detection - vs.
‘ 0-70 Phase of an inner-region smoke ejection
75% ” . 1.05 + _ _
(y - 14 6)
c: 1.40 '
_ a 1.75 A
50% o 2.10
o 2.45
25% - ‘ -
0% no a ‘ ifllll!!!
. A
aggitilfiiififiilggtegaiggoa; gaggsfififl .AA?.+..
25% b++++++++jr+§’9.:.gl t.A EA AzA.‘AA? .“ ++..
+ A A + + + +
++++++::++::::oo:‘¢+,¢o+ ++
50% ” + + + + + + + + r
75% - -
Probability
of a probe- - -
based ejection
dCtCCtion 1 1 1 1 1 1 1
-100 t=0 100 200 =300 400
Probability I I I I l I l
of a probe-
based sweep - —
detection
75% r -
50%— + <1~+++++++++t+++++++++++++++«1+ ++ —
+++++ 09H++9+++ §§§{§.§*’ **‘ ++ +++
25"" .. L...;‘1”“
0% .nniiii‘ ====ii§fifi::==i ‘fia. .. 2:?
Threshold
25% ” + 0.00 ‘
v 0.35
50% ~ : (Ii-07g Figure 4.3.7b ~
75% a 1:40 P(T): Probability of a uv-quadrant sweep
” 1.7 . VS‘ . ‘
Probability : 2.1: Phase of an inner-region smoke sweep
of a probe- ~ 0 (2.45 (Y = 14-5) _
based ejection
detection 1 1 ‘ 1 1 1 1 1
-100 t=0 100 200 =300 400
(start) Phase of a smoke event (end)

(Normalized event time)

267

 

 

 

 

 

 

 

 

 

 

 

  
       
  

    
 

 

 

 

 

 

 

$333le Threshold Figure 4.3.8a
based sweep r : 81315) P(T): Probability of a uv-quadrant ejection _
detection - vs.
‘ 0-70 Phase of an inner-region smoke ejection
75% ' ‘ 1.05 0+=150) 4
I3 1.40 '
_ $1.75 A
50% . 2.10
o 2.45
25% - ' 1
0% II 8 ‘
1 11 r . - a: ...A !
.....Shffif!.9n?ziiriiiiiiiiiieaieiz. t~*”::-
+ +++ *OO,*§‘,“*“????A4.OQ +++++
++++++++++++ + + It +4: J
50%- ++ + ++++
75% r ~
Probability
ofaprobe- e 1
based ejection
detCCtion l l J J J l l
-100 t=0 100 *200 =300 400
Probability I I I I I 1 I
ofaprobe-
based sweep - J
detection
75% r a
m— 4...... +++ ++t ++++++++ ++++~1 ++ ~
+++++++ otttiootrot++1i‘+*0+:** +++ +++
25% ~*§*‘*‘ AAAAAAAAAAAAAAAAAA ‘ ‘* "§¢.*..e
“‘2:222#£AAAAAAAAAA ““‘222AAA AA AAA
0% .9992!" ""3!§Wn36 -- -“‘ “m
Threshold
25% I. + 01x) "
o 0.35
50% - 2070 Figure 4.3.8b —
a :23 P(T): Probability of a uv-quadrant sweep
75% r- . VS. ~
Probability : é}; Phase of an inner-region smoke sweep
of a probe- - o 2.45 (y =15.0) -
based ejection
dCtCCfion 1 1 i 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

268

 

 

 

 

 

 

 

 

 

 

 

    
  

     

 

 

 

      

 

  

 

 

Probabili r ' ' r T r '
of a pmbtcy Threshold Figure 4.3.9a
based sweep _ + 0.00 P(T): Probability of a uv-quadrant ejection 4
detection ' 33(5) vs.
A . . _ . . .
75% _ ‘ 1.05 Phase of an rage: :glrsogfmoke ejection -
a 1.40 '
__ In 1.75 A
50% o 2.10
o ‘ 2.45
25% - a
0% nose. 3 ° is int 553335“
élfigogas szzoooagagaééggéséén g Q g 99
2 _Gaogg Baum!“ 0000 DDDUAQ‘RR g A82322AA
5% “‘ 020 0.0000000 .....A‘A‘ AAAAA ..iotottd
AAA‘A‘ A A“ ‘AAA‘ AAAAA ....Ofl
AAAAA AaazzaAAAAAQA?A*.,*** +++++++++++++
50%'}.***+60 ,,,++**’* ’ :+:+++++++ 4
+++++++ ++++++++++
+ ++
75% - ‘
Probability
of a probe- — -
based ejection
dCtCCtlon 1 1 1 4 1 1 1
-100 t=0 100 200 t=300 400
Probability f l T I I f r
of a probe-
based sweep - —
detection
75% - -
50%-+++++ +~++++++++++t+++++++++++++++++ ++ —
*0 Ot‘*i+v§§§ +§6§§*§‘* *§* +++
I O i t t
25% hAAAAAAAA AAAAAAAAAAAAAAAAAAAA;AAA;‘fl. ‘*‘*‘*_
0% .iiiiiiii====iiifii::aaifi;;;tfftee:$‘ AAA???
Threshold
25% ’ + 0.00 ‘
i 0.35
50% — A 0.70 Figure 4.3.9b ..
g 1250 P(T): Probability of a uv-quadrant sweep
75% ' e 175 vs' ‘
- Ph ' - '
Probability o 2.10 ase of an mner—refgéon smoke sweep
of a probe- _ ° .2-45 (y - '9) -
based ejection
detwtion - 1 1 1 1 4 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

 

 

 

269

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

(Normalized event time)

Probabili I I I I I I I
ofaprobtz. Threshold Figure 4.3.10a
based sweep + 83(5) P(T): Probability of a uv-quadrant ejection .
detection ‘ vs.
75% ‘ 0-70 Phase of an inner-region smoke ejection .
0:33 (Y'=2M2)
al.75 -
50% o 2.10
25% 0.2.45
0% a
“aagzgfifiifiiflfll OI ‘ i B 33339 AaAAf
‘AAA .0 f i
25% -+!++++++ :ifsggg?atfégaiaggngZA¢A§ i++++++..
+++++ :+++‘.*"***ti+* +
++ + + 4.
50% +++++++++ -1
75% .
Probability
ofaprobe- _
based ejection
dCtOCdon 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
Probability ' ' ' ' ' r '
ofaprobe-
based sweep «
detection
75% ~
50% +>+++++ ++++t++++++++++ +++++ +++++ -
+++++ §i+‘666§§§ i666+*+§. ... ++
25% ”
0% Ign§§§§=*===a .iiéfifi::ll!§;;;:t:: A::€
Threshold q
25% ” + 0.00
i 0.35
50% A 0.70 Figure 4.3.10b ‘
g 1.23 P(T): Probability of a uv-quadrant sweep
75% vs. .
Probability : :33 Phase of an inner-region smoke sweep
of a probe. . 2.45 (y” = 24.2) -
based ejection
dCICCtion 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

270

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili I I I I r I r
of a probtey- Threshold Figrre 4.3.111!
based sweep — + 0.0 P(T): Probability of a TERA ejection .
detection *3: vs.
A Phase of an inner-region smoke ejection
75% ‘09 + *
F 012 (y =14.6)
__ 1111.5 _
50% 01.8
02.1
25% - ' ~
0%
330000000383..38... . 9083
as the 83 . Ines
”khan?” Siioiiiiafisiifiiig ...éiiiiiagigiiifigi
gets o “ AAAA A A AA
++++++:: 'iio :‘AAAAAAAA‘A‘AA AAA I**I':1:l
50““ "“+++:.:i'::*:::::::::::tivw‘ -
+ + "'
75% - 1
Probability
ofaprobe- — -
based ejection
dCtCCtion 1 1 1 1 1 4 1
-100 t=0 100 200 t=300 400
Probability I I I I I I I
ofaprobe—
based sweep r -
detection
75%P + +++++++++++++++++++++4++++ d
+++++ ++jt++++ *o*'*'*'+oo.* vvtt¢0009vet+++
50%POOIIOGOOOIOIOI‘LAAAA AAAA ‘ ‘
leieiiaa‘S.....“°“2iiiA..22 ....
25% "AAAggififna 000 a mass .330 ‘ AA“‘ ‘
0%Egg-“39:323.:222228332
25% -1‘hreshold _
+0.0
i0.3
50% - . 0.5 Figure 4.3.llb ~
e 0.9 P(T): Probability of a TERA sweep
75% r 91.2 vs. _
Probability 9 1-5 Phase of an inner-region smoke sweep
of a prObe- . 2;? 0+ =14.6> _
based ejection '
W600 1 1 1 1 1 1 1
-100 t=0 100 200 =300 400
(Start) Phase of a smoke event (end)

(Normalized event time)

271

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Whirl I I I . I I r I
of a p103. Threshold Figure 4.3.12a
based sweep ~ + 0-0 P(T): Probability of a TERA ejection .1
detection ‘ 0'3 , V32 . .
75% _ :8-3 Phase of an inner-region smoke ejection -
131.2 (y =15.0)
_ 131.5 d
50% 01.8
25% 911
0% L
8.0.0...‘.8..998. . O. 8
8‘9 :6 ° °ss§ "iéai 3 8 ° . ééaéefiég
_ fl 3 m o I Q A
25% E11???“.igigseeieieiaiiiééiiiiirigggrgiii“
:+++++:: *i?IAtAAAAAAAAAAAAAAAAAAAAI6vitiiii
5@%_. “+ i *‘§*O.OOO**§*§§OOI50+++++ j
+++++++ +++++++++++++++++
75% ” .1
Probability
ofaprobe- »- _
based ejection
dCtCCfion 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
Probability ‘ ' I ' I . r
ofaprobe-
based sweep — .
detection
75%_ ++++++++++++++++++ 4
++++ + +I+ioi +++‘“+"’+++
++++ «-++++ *s 909*. §++v§§i§§6+§+++
50%—Wiriiioi IIII'LAAAAAAAA ‘ AA i
25% A “Amer:33‘3"...““223’3ufi4MM...
_ AAgg“‘n 0000 $8533 "‘ ‘ AAA AA"
9“ ENE amamo ooozgglooa ‘g‘fififi
mg -E§:"' ’°22°°2°°'° ..iiiiigeeiii iiieie..
25% — Threshold 1
+00
10.3
50% - . 0.6 Figure 4.3.121» .
75% g (1).; P(T): Probability of a TERA sweep
— - vs. -
Probability S :3 Phase of an inner-region smoke sweep
ofaprom_ _ .2'1 (y+=15.0) .4
based ejection '
dCtCCtion 1 1 1 1 1 1 1
~100 t=0 100 200 =300 400
(Start) Phase of a smoke event (end)

(Normalized event time)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

272
Probabili I I I I I I fl
of a prob?- Threshold Figure 4.3.13a
based sweep e + 0-0 P(T): Probability of a TERA ejection 7
detection ‘0-3 vs.
‘ 015 Phase of an inner-region smoke ejection
75%“ ‘09 ‘
(y+=18.9)
01.2
__ ILS A
50% 013
0.2.1
25%- -
0%
8:°°°°°°":::"38~o01° a at East
.38 “a a 8 0 Q
mi-iaiiaiguruin”211111quseizures.-
11::+:’. 't?IA‘AAzb‘A‘A‘AAA“AAAAAAAtIt‘iiix
50%— ++.I+ q906,.**99§‘....6§§§6§j++++ q
+++++++++++++++++++++++++
75%~ ~
Probability
ofaprobe-- .
based ejection
dCtOCtion 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
Probability I I I I I I I
ofaprobe-
based sweep - .
detection
75%_ + ++++++++++++++++++++++‘++++ q
+++++ ++0++++ .Iii"’.i++* OOOOOOvvvvit+
”FOOIIIIOO 0&00‘;A2AAAAAAAAA
25% _A AAAs§222333 DIIIII.“2
22:2AAA“ 0:388 3 Emma can
Wjjg-rn “Wandering-gas
25%..Thresliold _
+0.0
50% _ 13:: Figure 4.3.13b ~
A 0.9 P(T); Probability of a TERA sweep
75% - 01-2 Ph f . VS“ . k ‘
I 1.5 ase 0 an Inner-region smo e sweep
mmp'r’fli‘l- 331: (W =13.» _
9 .
based ejection ‘
deteCtion — 1 1 4 1 1 1 1
~100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

273

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pmbabill I I I I I I I
of a pmbtz. Threshold Figure 4.3.14a
based sweep r- + 3g P(T): Probability of a TERA ejection .
detec' ' vs.
3:; F 2 35 Phase of an inner-region smoke ejection _
01°39 (y+=24.2)
P Il.5 _
50% 01.8
02.1
25%“ ~
0%
93°”“"*:s"°:so.ngo s 3 . . 533 gig”
25%*fimiiiiiirigiiiiiifieiiéiégééimi mirage
::::+::: 9f??A?AAAAA‘AAAAAAAAAAAAAA*O..‘i:il
50%” .L++ O it...*sse.‘§..tsoett4++++ —1
+++++++++++++++++++++
759b— _
Probability
ofaprobe-- ..
based ejection
detection 1 1 1 1 1 1 1
-100 t=0 100 200 =300 400
Probability ' ' ‘ ' ' ' '
ofaprobe-
based sweep - .
detection
75%~ +++++++ ++++++++++ ‘1
++++++++U++++ O **.‘**900 960:::::::::+
mbievbftiit Oiiv AA A
AAAA ‘
25% hAAAAAAAAx.“;
“42min”
0% iii.’ he
25%~Threshold .
+0.0
50%L- 00.3 ,
A 0.5 Figure 4.3.14b ~
A 0.9 P(T): Probability of a TERA sweep
75%- 01-2 vs. 1
Probability a 1.5 Phase of an inner-region smoke sweep
01.8 +=
basgd “£35; ' ° 42" (y 242) "
dCtOCtion 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(Start) Phase of a smoke event (end)

(Normalized event time)

274

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili I I I I I r I
of a probtey. Threshold Figure 4.3.158
based sweep _ + 0.00 P(T): Probability of a u-level ejection «
detection ‘023 vs.
75% _ 2 3-46 Phase of an inner-region smoke ejection -
00$ (y+=l4.6)
_ ll31.15 A
50% 01.38
01.61
25%- ~
0%
_;‘g °°.'”888333::0°30000 ... ,, . 000000d
25% Douéaggggsgggmmmmggnggg;gagggé88359 zésfiggga
tittgge >A.eesssog 0000000090292299 23.1321?
50%_ ¥¥11+i.*‘.53 gtfifiafiggb 2AAAAAA *44+ 1
+...1;****11111ii11:1*:*
75%r ‘
Probability
ofaprobe-A .
based ejection
dcmtion 1 1 1 1 1 1 1
JG) t=0 100 200 t=300 400
Probability f I I I f I I
ofaprobe-
based sweep - ~
detection
75%” + ++++++*+*::ttt+*++ZQ‘X*++++ d
++0 *AAAAAfiAAAAAAAfieaA AAAA +
...; x “‘11:: A AAA AA “:
50%1-f‘ii ... GDDDSDDDUDDESSDDDDDDDDDDD 000020;;
25% 888 in W” ””“sssasw“”33°3:338“
122%%%§§x??22322322322.." ””999‘
0%
(Threshold _
25% +0.“)
#023
50% " A 0.46 Figure 4.3.15b -
I: 3.3: P(T): Probability of a u-level sweep
7570A vs. -
Probability : :33 Phase of an inner-region smoke sweep
baggaprobe, _ ,m (y =14.6) _
ejection
detection 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(Start) Phase of a smoke event (end)

(Normalized event time)

 

 

275

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili I I I I I I I
1111111013. Threshold Wm 434“ . .
based sweep t + 3.23 P(T): Probability of a u-level ejectton q
detection ' VS-
‘ 0-46 Phase of an inner-region smoke ejection
75%’ ‘069 + ‘
00:92 (y =15.0)
_ 81.15 s
50% 01.38
25% 01.61
0%
:‘ ....”888.3..OO..000 . .. .0000.
Mugggg; :sséuzgztsnzgééaéiggmattagésssfigg‘
“A u an 36‘
i $1111‘f‘993133222333322Eziffifig $331
50%_ 3’ ***¢, AAA * * 11*!»4 .1
++++++:;;;111111111111+*
75%— ~
Probability
ofaprobe-~ —
based ejection
detection 1 1 1 1 1 1 1
—100 t=0 100 200 t=300 400
Probability I I I I I I I
ofaprobe-
based sweep — _
detection
75%” . 11+++++++111H++++AHN.... ‘
gt§§I.IIxxxxxxlé‘eeeeieseeeeefifie...aéé‘e‘z..
m-‘A DDDDUDDDDDDDDDDDUOUDUD DDUDDDDD
.000 BEBE E 888883 BEEEEEBE
25“'?§§?§%%§111332§2seeissiiiiiihmi“ 22222993“
0%
_Threshold s
25% +0.00
10.23
50% - 1 0.46 Figure 4.3.l6b «
75% g 33; P(T): Probability of a u-level sweep
_ . vs. ~
PrObability Z :3: Phase of an inner-region smoke sweep
1113 “F0!”- ’ .1151 (”‘15”) -
ejection
dCtCCtiOll 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

 

 

276

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

mbabm I I I. I f I I
of a probtz. Threshold Frgure 4.3.17a
based sweep 1 + 0.00 P(T): Probability of a u-level ejection 1
detection ‘81:: vs.
A - Phase of an inner-region smoke ejection
75%” ‘0.69 += ‘
G032 (y 18.9)
_ $1.15 1
50% 01.38
25% .1151
0%
’ o J)
_alg " ’ 888333330030... ... ..... onOOOd
25% Dong“ssgjggggmmmggga13mm. Sésmga
$§$23§e 4141.339290 01301300013 DDRDRRQ 834133;?
50%__ **”+11,11A8ggA933833‘932A2AAA $144 _‘
++++i:*111;iiii?:il::oit
75%~ -
Probability
ofaprobe—— 4
based ejection
dCtCCtiOD 1 4 1 1 1 1 1
-100 t=0 100 200 t=300 400
Probability I I I I I I T
ofaprobe-
based sweep ~ 1
detection
”“2 m1 -1111::122211221111wz111:. ‘
511,43th““3331111133310011.1336 11111335.
A 000 E
:0 EEBEEBBBBBB BBBEB: ESSSOBEE
myE§@@@%%11222222sezizeiwiwmi' ””‘933‘
O. 000
0%
_Threshold _
25% +0.00
0.23
50% - :1 046 Figure 4.3.17b _
. 0.69 P(T): Probability of a u-level sweep
75%_ [30.92 vs. 1
Probability 8' 11:; Phase of an inner-region smoke sweep
o . +3
basé’éarrope- ~ .111 ‘y ”'9’ 1
ejectron
dCIOCfiOI'I — 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

 

 

 

 

 

277

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Probabili f I I. I I I I
of a probtey. Threshold Figure 4.3.1811
based sweep 1 + 0.00 P(T): Probability of a u-level ejection 1
deteCti 10.23 vs.
on _ ‘ 0-46 Phase of an inner-region smoke ejection q
75% g 3.3; (yt- = 24.2)
1 81.15 1
50% 01.38
25% 0.1.61 _
0% 1
3‘ ”°°‘888;°°°009300oo e , . onOOOfi
25%”00593313111112.3322:2.2.2131;mam. 31311116
§§§3321* Aasafiiggggo000000092292299 gAaAgfig
50% — (won. “Muzgawmumuu 1
++++;:0111ixi11+1:ii:11¥
75% - -
Probability
ofaprobe- - —
based ejection
detection 1 1 1 1 1 1 1
-100 t=0 100 200 t=300 400
Probability I I I I I I I
ofaprobe-
based sweep - ~
detection
75%” 111*”litiiwllliwmzzzu 1
+1 I ‘LIXXXAAA ““A2g““““AAA AA
mbiA§§ ...T DUDUDBDUDDDUDDDDDDDDDD 000020;;
0000 E838 $88883 $388 $88
25%1aasgggggggggggggw 2.2 gzsgggeee....22 222223221
2.20.. O
0%
1 Threshold 1
25% +0.“)
10.23 .
50% r A 0.45 thure 4.3.18b ‘
‘ 33: P(T): Probability of a u-level sweep
75% ~ ‘3 - vs. 1
Probability :‘ :3: Phase of an inner-region smoke sweep
baseodapmbc- ” 011.61 (”=2”) 1
ejection
dCtOCtiOl‘l 1 1 1 1 1 1 4
~100 t=0 100 200 t=300 400
(start) Phase of a smoke event (end)

(Normalized event time)

REFERENCES

Alfredsson, P. H. and Johansson, A. V. 1984 On the Detection of Turbulence-
Generating Events. J. Fluid Mech 139, 325.

Blackwelder, R. F. and Haritonidis, J. H. 1983 Scaling of the Bursting Frequency in
Turbulent Boundary Layers. J. Fluid Mech 132, 87.

Blackwelder, R. F. and Kaplan, R. E. 1972 Intermittent Structures in Turbulent
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