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This is to certify that the

thesis entitled

Velocity and Vorticity Measurements in an
Atmospheric Boundary Layer

presented by
Matthew C. Maher

has been accepted towards fulfillment
of the requirements for

MS degree in Mechanical Engineering

 

 

gm m

ajor professor

Date August 19, 2002

 

0.7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

LIBRARY
Michigan State
Univers:ty

 

 

 

PLACE IN RETURN Box to remove this checkout from your record.
To AVOID FINES return on or before date due.
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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8/01 c:/ClRC/DateDue.p65-p. 15

VELOCITY AND VORTICITY MEASUREMENTS IN THE

ATMOSPHERIC BOUNDARY LAYER
By

Matthew C. Maher

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

2002

ABSTRACT

VELOCITY AND VORTICITY MEASUREMENTS IN THE
ATMOSPHERIC BOUNDARY LAYER

By

Matthew C. Maher

Velocity and vorticity time series were measured in the near wall region of an
atmospheric boundary layer. The measurements were acquired at the SLTEST site
located in western Utah under thermally unstable, thermally stable, and thermally neutral
ambient conditions. The surface was nearly flat and free of vegetation with a small scale

surface roughness of approximately 2mm. The measurements were acquired at locations
of 20cm and 40cm from the wall (y+ = 3800 and W = 10, 300 respectively). The Rey-

. . 6 .
nolds number based on momentum thickness was approxrmately Reez 5x10 With a

boundary layer thickness of approximately 200m.

The vorticity measurements indicated an extremely long correlation time of the
near wall vorticity field. For example, the first zero of the autocorrelation of the spanwise
vorticity component was found to be as large as 40m. The first zero of the wall normal
vorticity autocorrelation was found to be as large as 220m. The gradient of the Reynolds

shear stress was also investigated by measurement of the two contributing velocity-vortic-
ity products (v'mz' and w'w‘f). The W'(1)\,' product appeared to produce the dominant
contribution to this gradient. Coherence spectral observations show that the relatively

high wavenumber components produce the relatively large correlation (== 0.2) between

the lateral velocity fluctuations and the wall normal vorticity fluctuations.

ACKNOWLEDGEMENTS

I would like to thank my advisor, John Foss, for his support and assistance over the
past few years. My experiences at the Turbulent Shear Flows Laboratory are something I
will never forget. The assistance of my colleagues. who have contributed their time and
efforts, is greatly appreciated. I would like to thank Scott Morris, Al Lawrenz, Rich Pre-
vost, Mike Dusel, Doug Neal and Scott Treat for their individual efforts.

I would like to thank my committee members, Ahmed Naguib and Charles Petty,
for their contributions. The financial assistance of the Office of Naval Research (ONR) is
also greatly appreciated.

Lastly, I would like to thank my family. who have been patient and supportive

throughout this endeavor.

iii

TABLE OF CONTENTS

List of Tables .................................................................................................................... vii
List of Figures ................................................................................................................. viii
Nomenclature ............................................................................................................... xviii
1.0 Introduction ........................................................................................................... 1
1.] Boundary Layer Overview ........................................................................... 3

1.2 Literature review .......................................................................................... 5

2.0 Experimental Facility and Conditions .............................................................. 11
2.1 Test Site Overview .................................................................................... l l

2.2 Test Site Capabilities .................................................................................. 12

22.] Wind Monitoring ............................................................................ 12

2.2.2 Thermal Effects ............................................................................. 13

2.2.3 Shear Stress Measurements ............................................................ l6

3.0 Experimental Equipment ................................................................................... 21
3.1 Mobile Data Cart ....................................................................................... 22

3. l .1 Cooling System .............................................................................. 22

3.1.2 On-board Equipment ...................................................................... 23

3.2 Calibration Facility .................................................................................... 25

3.3 Three-Cup Anemometer ............................................................................ 27

4.0

5.0

3.4 Wind Vane .................................................................................................. 28

 

3.5 Thermistor .................................................................................................. 28
Hot Wire Techniques .......................................................................................... 37
4.1 Single wire calibration and uncertainty ..................................................... 37
4.2 X-wire calibration, processing and uncertainty ......................................... 41
4.2.1 X-wire processing algorithm ......................................................... 42

4.2.2 X-wire uncertainties ....................................................................... 43

4.3 Vorticity Probe ........................................................................................... 44
4.3.1 Vorticity Algorithm ........................................................................ 46

4.3.2 Vorticity probe uncertainties .......................................................... 49
Results and Discussion ....................................................... -- 60
5.1 Daily Specifics ........................................................................................... 60
5.1.1 18-July, 2001 .................................................................................. 61

5.1.2 19-July, 2001 .................................................................................. 63

5.1.3 25-July, 2001 .................................................................................. 65

5.2 Mean flow statistics ................................................................................... 67
5.2.1 Taylor microscale ........................................................................... 69

5.2.2 Dissipation Measurement .............................................................. 70

5.2.3 Flow length and velocity scales ..................................................... 74

5.3 Spectral Properties ..................................................................................... 77
5.3.1 Spectral representation of the velocity field .................................. 77

5.3.1.1 u-component spectra .......................................................... 81

5.3.1.2 v-Component Spectra ........................................................ 83

5.3.1.3 w-Component Spectra ........................................................ 84

5.3.2 Spectral representation of the vorticity field .................................. 84

5.3.2.1 <wz> Spectra ..................................................................... 87

5.3.2.2 <30y> spectra ...................................................................... 89

5.3.3 Velocity-vorticity products ............................................................ 90

5.3.3.1 u'v' product ....................................................................... 92

5.3.3.2 u'w' product ...................................................................... 94

5.3.3.3 v'<a)l'> product ................................................................ 95

5.3.3.4 w'<(x)y'> product ............................................................... 97

5.4 Vorticity Probability Density Functions ..................................................... 99

6.0 Conclusions ........................................................................................................ 149
Appendix A: Pre-Post Comparison ............................................................................ 154
Appendix B: Combined Calibration Plots ................................................................. 162
References ...................................................................................................................... 172

vi

LIST OF TABLES

Table 5.1 Data Set Properties ......................................................................................... 101
Table 5.2 Mean Dimensional Flow Parameters .............................................................. 108
Table 5.3 Mean Flow Properties ................................................................................... 109
Table 5.4 Dissipation Estimates ...................................................................................... 109
Table 5.5 Normalized Flow Parameters ....................................................................... l 10
Table 5.6 Taylor Microscale Parameters ....................................................................... l 1 1
Table 5.7 Dimensional Flow Statistics ........................................................................... 127
Table 5.8 Normalized Flow Statistics ............................................................................. 128
Table 5.9 col PDF Statistics ............................................................................................ 148
Table 5.10 coy PDF Statistics .......................................................................................... 148

vii

LIST OF FIGURES

Figure 1.1 The breakdown of a turbulent boundary layer [24]. ........................................... 8
Figure 1.2 Scaling collapse on the inner region of a turbulent boundary layer [24]. .......... 9
Figure 1.3 The Reynolds number dependence on the size of the overlap region [23]. 10
Figure 2.1 Topographic map of the Dugway area. ............................................................ 18
Figure 2.2 Sensing capabilities of the SLTEST site [30]. ................................................. 19
Figure 2.3 Typical boundary layer profile at the SLTEST site [30]. ................................. 19

Figure 2.4 A 2.4 meter drag plate was used to gather accurate values for the

wall shear stress [30] ......................................................................................... 20
Figure 3.1 Schematic of Mobile Data Cart. ....................................................................... 30
Figure 3.2 Interior view of Mobile Data Cart. ................................................................... 31
Figure 3.3 The Data Cart’s portable calibration unit. ........................................................ 32
Figure 3.4 Top view of the calibration facility showing the flow conditioning. ............... 32
Figure 3.5 Wiring diagram for the calibration unit ............................................................ 33
Figure 3.6 Total pressure vs. the static tap reading for the calibration unit ....................... 33
Figure 3.7 Three cup anemometer calibration ................................................................... 34

Figure 3.8 Tripod used to mount the three cup anemometer, wind vane and

hot wire probes. ................................................................................................ 35

viii

Figure 3.9 Thermistor re-calibration due to large ambient temperatures. ......................... 36

Figure 4.1 Geometry of spanwise vorticity probe. ............................................................ 51
Figure 4.2 Perspective view of spanwise vorticity probe. ................................................. 51
Figure 4.3 Geometry of a single hot-wire probe. ............................................................... 52
Figure 4.4 Sample calibration and fit ................................................................................. 52
Figure 4.5 Normalized histogram of observed velocities from 25-July, 2001. ................ 53
Figure 4.6 Example drift determination comparison taken on 19-July. ............................ 53

Figure 4.7 Pre-calibration data, post-calibration data. and the combined

trend-line for 19-July. ....................................................................................... 54
Figure 4.8 Geometry of the X-wire probe. ........................................................................ 54
Figure 4.9 Sample data demonstrating the angle locating algorithm for

X-wire processing. ........................................................................................... 55
Figure 4.10 Example drift determination comparison for an X-wire taken on 19-July ..... 55
Figure 4.1 1 Mean vertical angle measured over the evening of 18-July, 2001. ................ 56
Figure 4.12 Schematic of the micro-circulation domain used in the vorticity algorithm. .56
Figure 4.13 Velocity of each straight wire on the Mitchel Probe as it was

traversed through the shear layer. ..................................................................... 57
Figure 4.14 Collapse of shear layer traverse data used to compute (Ay). ........................ 57

Figure 4.15 Vorticity probe and processing algorithm verification in a free stream of the

calibration unit. ................................................................................................. 58

Figure 4.16 Vorticity probe and processing algorithm verification in a free stream. ........ 58
Figure 4.17 Sample vorticity time series from 25—July, 2001. .......................................... 59
Figure 5.1 Mean wind speed for l8-Ju1y, 2001. .............................................................. 102
Figure 5.2 Mean wind direction for 18-July, 2001. ......................................................... 102
Figure 5.3 Thermal stability parameter for l8-Ju1y. 2001. .............................................. 103
Figure 5.4 Friction velocity as a function of time for 18-Ju1y, 2001. .............................. 103
Figure 5.5 Mean wind speed for 19-Ju1y, 2001. .............................................................. 104
Figure 5.6 Mean wind direction for 19-Ju1y, 2001. ......................................................... 104
Figure 5.7 Thermal stability parameter for l9-July. 2001. ............................................. 105
Figure 5.8 Friction velocity as a function of time for l9-July, 2001. .............................. 105
Figure 5.9 Mean wind speed for 25-July, 2001. .............................................................. 106
Figure 5.10 Mean wind direction for 25-July, 2001. ....................................................... 106
Figure 5.1 1 Thermal stability parameter for 25-July. 2001. ............................................ 107
Figure 5.12 Friction velocity as a function of time for 25-July. 2001. ............................ 107

Figure 5.13 Normalized autospectral density of the u—velocity fluctuation (25-July). ....1 12
Figure 5.14 Compensated autospectral density of the u-velocity fluctuation (25-July). . l 12
Figure 5.15 Normalized autospectral density of the u-velocity fluctuation (18-July). ....1 13

Figure 5.16 Compensated autospectral density of the u-velocity fluctuation (l8-Ju1y). .1 l3

Figure 5.17 Normalized autospectral density of the u-velocity fluctuation (l9-Ju1y). ....1 14
Figure 5.18 Compensated autospectral density of the u-velocity fluctuation (19-Ju1y). . l 14
Figure 5.19 Normalized autospectral density of the v-velocity fluctuation (25-July).....1 15
Figure 5.20 Compensated autospectral density of the v-velocity fluctuation (25-July). .1 15
Figure 5.21 Normalized autospectral density of the v-vclocity fluctuation (18-Ju1y).....1 16
Figure 5.22 Compensated autospectral density of the v-velocity fluctuation (18-Ju1y). .1 16
Figure 5.23 Normalized autospectral density of the v-velocity fluctuation (19-Ju1y).....1 17
Figure 5.24 Compensated autospectral density of the v-velocity fluctuation (19-July). . 1 17
Figure 5.25 Normalized autospectral density of the w-velocity fluctuation (18-Ju1y). ...1 18
Figure 5.26 Compensated autospectral density of the w-velocity fluctuation (l8-Ju1y). 1 18
Figure 5.27 Normalized autospectral density of the w-velocity fluctuation (l9-Ju1y). ...1 19

Figure 5.28 Compensated autospectral density of the w-velocity fluctuation (l9-Ju1y). l 19

Figure 5.29 Normalized autospectral density of the <;el> vorticity (25-July) ................ 120
Figure 5.30 Compensated autospectral density of the <-:cz> vorticity (25-July). ............ 120
Figure 5.31 Normalized autospectral density of the <;c,> vorticity (18-July) ................ 121
Figure 5.32 Compensated autospectral density of the <xz> vorticity (l8-Ju1y). ............ 121
Figure 5.33 Normalized autospectral density of the <;c.,_> vorticity (l9-July) ................ 122
Figure 5.34 Compensated autospectral density of the <ch> vorticity (19-Ju1y). ............ 122
Figure 5.35 Autocorrelation of the <ccz> vorticity for each day. .................................... 123

xi

Figure 5.36 Autocorrelation of the <30]? vorticity in semilog format. ........................... 123

Figure 5.37 Normalized autospectral density of the <»:ay> vorticity (18-Ju1y). .............. 124
Figure 5.38 Compensated autospectral density of the <:.)y> vorticity (18-Ju1y) ............. 124
Figure 5.39 Normalized autospectral density of the <;cy> vorticity (19-July). .............. 125
Figure 5.40 Compensated autospectral density of the <30y> vorticity (l9-Ju1y) ............. 125
Figure 5.41 Autocorrelation of the <cey> vorticity for each day. .................................... 126
Figure 5.42 Autocorrelation of the <3.)Y> vorticity in semilog format. ........................... 126
Figure 5.43 Normalized autospectral density of the u'v' product (25-July) .................... 129
Figure 5.44 Compensated autospectral density of the u'v' product (ZS-July). ................ 129
Figure 5.45 Normalized autospectral density of the u'v' product (l8-July) .................... 130
Figure 5.46 Compensated autospectral density of the u'v' product (18-Ju1y). ............... 130
Figure 5.47 Normalized autospectral density of the u'v' product (l9-July) .................... 131
Figure 5.48 Compensated autospectral density of the u'v' product ( 19-Ju1y). ................ 131

Figure 5.49 Normalized co-spectral density of the u' and v' velocity

components (25-Ju1y). .................................................................................... 132
Figure 5.50 Normalized co-spectral density of the u' and v' velocity

components ( 18-Ju1y). .................................................................................... 132
Figure 5.51 Normalized co-spectral density of the u' and v' velocity

components (19-Ju1y). .................................................................................... 133

xii

Figure 5.52 Coherence of the u' and v' velocity components for all three data sets. ..... 133

Figure 5.53 Normalized autospectral density of the u'w' product ( 18-Ju1y). .................. 134
Figure 5.54 Compensated autospectral density of the u'w' product( 1 8-Ju1y). ................ 134
Figure 5.55 Normalized autospectral density of the u'w' product (19-July). .................. 135
Figure 5.56 Compensated autospectral density of the u'w' product (19-Ju1y). ............... 135

Figure 5.57 Normalized co—spectral density of the u' and w' velocity
components (18-Ju1y). .................................................................................... 136

Figure 5.58 Normalized co-spectral density of the u' and w' velocity

components (19-July). .................................................................................... 136
Figure 5.59 Coherence of the u' and w' velocity components (18, l9-Ju1y). ................. 137
Figure 5.60 Normalized autospectral density of the v'<a):'> product (25-July) ............. 137
Figure 5.61 Compensated autospectral density of the v'<(o:'> product (25-July) .......... 138
Figure 5.62 Normalized autospectral density of the v'<(i):'> product (18-Ju1y) ............. 138
Figure 5.63 Compensated autospectral density of the V'<(1):'> product (18—Ju1y) .......... 139
Figure 5.64 Normalized autospectral density of the v'<(i):'> product (l9-July) ............. 139
Figure 5.65 Compensated autospectral density of the v'<(o:'> product (l9-Ju1y) .......... 140
Figure 5.66 Normalized co-spectral density of v' and <(o:'> (25—Ju1y). ........................ 140
Figure 5.67 Normalized co-spectral density of v' and <(o:'> ( 18-Ju1y). ........................ 141
Figure 5.68 Normalized co-spectral density of v' and <(1):'> (l9-July). ........................ 141

xiii

Figure 5.69 Coherence of v' and <(D:'> over all three evenings. ................................... 142

Figure 5.70 Normalized autospectral density of the W'<(D'\,'> product (l8-Ju1y). .......... 142
Figure 5.71 Compensated autospectral density of the w'<a)),'> product (18-Ju1y) ......... 143
Figure 5.72 Normalized autospectral density of the n"<a)),'> product ( 19-Ju1y). .......... 143
Figure 5.73 Compensated autospectral density of the W'<(1)'\,'> product (19-July) ......... 144
Figure 5.74 Normalized co-spectral density of w' and <(i)),'> (18—Ju1y). ....................... 144
Figure 5.75 Normalized co-spectral density of w' and <w.\.'> (19-Ju1y). ....................... 145
Figure 5.76 Coherence of w' and <0).\,'> for 18. l9-July ................................................ 145

Figure 5.77 Compensated autospectral densities of the velocity-vorticity

products for 18-Ju1y. ....................................................................................... 146
Figure 5.78 Compensated autospectral densities of the velocity-vorticity

products for l9-Ju1y. ....................................................................................... 146

Figure 5.79 Compensated autospectral densities of the velocity-vorticity

products for 25-July. ....................................................................................... 147
Figure 5.80 Normalized PDF of the <a):'> vorticity for each day. ................................ 147
Figure 5.81 Normalized PDF of the <(o\,'> vorticity for each day. ................................ 148

Figure A.1 Drift determination comparison taken on l8-Ju1y (<w,> probe,
first straight wire). .......................................................................................... 154

Figure A.2 Drift determination comparison taken on l8-Ju1y («01> probe,

xiv

second straight wire). ...................................................................................

Figure A.3 Drift determination comparison taken on l8-Ju1y (<wy> probe,

first straight wire). .......................................................................................

Figure A.4 Drift determination comparison taken on l8—Ju1y (<co-y> probe,

second straight wire). ...................................................................................

Figure A.5 Drift determination comparison taken on l9-Ju1y («02> probe,

first straight wire). ........................................................................................

Figure A.6 Drift determination comparison taken on l9-Ju1y («02> probe,

second straight wire). ...................................................................................

Figure A.7 Drift determination comparison taken on l9-July (<cey> probe,

first straight wire). ........................................................................................

Figure A.8 Drift determination comparison taken on 19-Ju1y (<coy> probe,

second straight wire). ...................................................................................

Figure A.9 Drift determination comparison taken on 25—Ju1y («02> probe,

first straight wire). ........................................................................................

Figure A.10 Drift determination comparison taken on 25-Ju1y (<00? probe,

second straight wire). ...................................................................................
Figure A.l l X-wire drift determination comparison taken on l8-Ju1y («02> probe).

Figure A.12 X-wire drift determination comparison taken on 18-Ju1y (<wy> probe).

XV

..154

..155

..155

..156

..156

..157

..157

..158

..158

..159

..159

Figure A.13 X-wire drift determination comparison taken on 19-Ju1y (<wz> probe). .. 160
Figure A. 14 X-wire drift determination comparison taken on 19-Ju1y (<coy> probe). .. 160
Figure A.15 X—wire drift determination comparison taken on 25-July («02> probe). .. 161
Figure 8.] Combined calibration data for 18-July (<-;c,> probe. first straight wire). 162

Figure B.2 Combined calibration data for 18-Ju1y (<-;.J,> probe,

second straight wire). ..................................................................................... 162
Figure B.3 Combined calibration data for l8-July (<Lc‘,> probe. first X-wire). ............. 163
Figure B.4 Combined calibration data for l8-July (<a:,> probe. second X-wire). ........ 163

Figure 8.5 Combined calibration data for 18-July (<;;.‘y> probe, first straight wire). 164

Figure B.6 Combined calibration data for 18-July (<:cy> probe,

second straight wire). ..................................................................................... 164
Figure B.7 Combined calibration data for l8-July (<:-.‘y> probe. first X-wire). ............ 165
Figure 8.8 Combined calibration data for 18-Ju1y (<x),> probe, second X-wire). ........ 165

Figure B.9 Combined calibration data for 19-July (<33? probe, first straight wire). 166
Figure B. 10 Combined calibration data for l9-July (<;-.‘,> probe.

second straight wire). ..................................................................................... 166
Figure 8.1 1 Combined calibration data for l9-July (y<.:.:,‘> probe. first X-wire). ........... 167
Figure B.12 Combined calibration data for 19-July (<x,> probe, second X-wire). ...... 167

Figure B. 13 Combined calibration data for 19-Ju1y (<:c'y> probe. first straight wire). ..168

xvi

Figure B. 14 Combined calibration data for 19-Ju1y (<13; y> probe,

second straight wire). ..................................................................................... 168
Figure B. 15 Combined calibration data for l9-Ju1y (<;t;y> probe, first X-wire). .......... 169
Figure B. 16 Combined calibration data for 19-Ju1y (<:cy> probe, second X-wire). ...... 169
Figure B. 17 Combined calibration data for 25-July (<:.:Z> probe, first straight wire). .. 170
Figure B. 18 Combined calibration data for 25-Ju1y (<;c=z> probe.

second straight wire). ..................................................................................... 170
Figure B. 19 Combined calibration data for 25-July (<3; z> probe, first X-wire). ........... 171

Figure 8.20 Combined calibration data for 25-July (_<:e-,‘> probe, second X-wire). ...... 171

xvii

ARABIC
A, B, n
B

E

E11

512

NOMENCLATURE

Coefficients of hot-wire calibration, equation 4.1.
Log law constant, equation 1.6 (Chapter 1 only).

Voltage output of the anemometer, equation 4.1 (Chapter 4 only).

Autospectral density of the u component of velocity, equation 5.21.

Co-spectral density of the u and v velocity components, equation 5.37.

Autospectral density of the 2 component of vorticity. equation 5.31

Data acquisition frequency.
Gravitational constant.

Coherence spectra, equation 5.39.

Wavenumber in the x-direction, equation 5.23.

Monin-Obukhov length. equation 2.3.

Viscous length scale, equation 1.2.

Integer number of time records for 1/2 micro—circulation domain, equation
4.6.

Normalized correlation function, equation 5.22.

Reynolds number based on the Taylor microscale.

Reynolds number based on the boundary layer momentum thickness.

xviii

Q Velocity magnitude of calibration free stream, equation 4.1.

q Magnitude of velocity measured by hot-wire sensors.

Si]. Rate of strain tensor, equation 5.5

U 0 Free—stream velocity.

u,v,w Components of the velocity vector.

uT Friction velocity computed in the thermally neutral condition, equation 1.1.
(”1) Friction velocity computed in the thermally stable condition, see

Section 2.2.3.

(“1) Friction velocity computed in the thermally unstable condition, see

Section 2.2.3.

an Kolmogorov velocity, equation 5.20.

V Velocity vector.

x, y, z Cartesian coordinates.

GREEK

As Size of the micro-circulation domain used in the vorticity calculation,

equation 4.6.

Ay Separation distance of straight wire sensors in the vorticity probe.
5 Boundary layer thickness.
8 Dissipation, Section 5.2.2.

xix

(Dav Autospectral density of the uv velocity product, Section 5.3.3.

F Circulation, equation 4.7.

n Kolmogorov length scale, equation 5.19.

K Log law constant, equation 1.6 (Chapter 1 only).
K von Karmen constant, equation 2.3.

A Taylor microscale length.

0 Boundary layer momentum thickness.

0 Potential temperature. equation 2.1 (Section 2.2.2 only).
9v Virtual potential temperature, equation 2.3.

1W Wall shear stress.

p Density of air.

v Kinematic viscosity of air.

a) Vorticity. equation 4.10.

C Thermal stability parameter.

SUPERSCRIPTS

+ Wall units.

XX

SUBSCRIPTS

1,2 Differentiates between two hot wires on the same probe.

SYMBOLS

For quantity (1

a' Fluctuating value.
it Root—mean-square value
('1 Time averaged value

xxi

1.0 Introduction

The current research serves to quantitatively describe near wall velocity and vor-
ticity characteristics in a very high Reynolds number turbulent boundary layer flow. This
thesis will also examine the characteristics of local isotropy under these inherently aniso-

tropic conditions. Applications of this research include submarine and aircraft travel

. . . . 6
which exhibit Reynolds numbers on the order of Reg ~ 10 . The current research was

sponsored by the Office of Naval Research (ONR), in hopes that a better understanding of
the near wall motions of these phenomena would help to reduce noise and drag on their

submarines.

The study of the turbulent motions in high Reynolds number boundary layer flows

is made difficult because of the extremely small scales which are present in typical labora-

tory conditions. In order to achieve very high Reynolds number (Ree) flow, current

methods include increasing the free stream velocity U0 or decreasing the kinematic vis-

cosity V of the observed fluid. Achieving a Reynolds number on the order of ReG ~ 106

(typical of a Los Angeles class submarine) with the aforementioned methods would cause
the smallest length scales and time scales of the problem to drop significantly below cur-

rent measurement capabilities [17].

The present research is motivated by the lack of data existing for such high Rey-
nolds number flows. Characteristic trends that have been previously established for
boundary layer flow hold true for a large range of Reynolds numbers. However, the

trends developed from existing data must be extrapolated to cover a range of Reynolds

numbers not achievable with current laboratory techniques. Extending these trends to
cover larger Reynolds numbers without physical evidence is not accurate since many flow

phenomena display a Reynolds number dependence already.

The current research was conducted at the Surface Layer Turbulence and Environ-
mental Science Test (SLTEST) site on the salt flats of western Utah. The SLTEST site
offers a unique opportunity to examine very high Reynolds number flows with large
length scales and relatively smooth walls. This newly founded site utilizes a very large
atmospheric boundary layer developing over the flat desert floor to produce the large
scales crucial for the detailed observations of a high Reynolds number boundary layer
flow. The data were taken over a period of two years (spanning one month each year), and
they were acquired with the Michigan State University (M.S.U.) compact vorticity probe.
The outdoor nature of the SLTEST site made acquiring data a difficult process. As a
result, three days of data were acquired for the current research. Throughout the rest of
this thesis, these three data sets will be referred to by the date on which the data were
taken: l8-July, l9-Ju1y, or 25-July, 2001. Chapter 2 will describe the conditions of the
SLTEST site in more detail. The experimental equipment will be discussed in Chapter 3,
and Chapter 4 will serve to explain the hot-wire anemometry techniques used to acquire
and process the data. Chapter 5 will cover the results obtained at the SLTEST site and
Chapter 6 will present the conclusions. The following subsections of this chapter will
serve to review the turbulent boundary layer characteristics which are relevant to this

research.

1.1 Boundary Layer Overview

Fluid travelling over a flat plate develops a transitional region between the uniform
velocity of the free-stream and the zero velocity at the wall. The latter condition is a result
of the no-slip phenomenon. This transitional region is termed the boundary layer and can
be described as the region of the fluid “where friction plays an essential part” [28]. Turbu-
lent boundary layers have been the focus of a wide range of investigations (see Schlichting
[28], Schetz [27], Pope [24], etc.) which have served to establish characteristics of these
boundary layers under specific conditions. The focus of the current research is to extend

the investigation of these characteristics into a range of much higher Reynold’s number
(
(Ree ~ 10’).

Turbulent boundary layers are typically divided into two regions: the outer layer
and the inner layer. A sizable overlap region exists between these two layers properly
termed the overlap region. The inner layer starts at the wall and extends to include the vis-
cous sublayer, the buffer layer and the overlap region. The outer layer begins with the
overlap region and ends at the free stream (the end of the boundary layer). Fig 1.1 better
illustrates the various layers of a turbulent boundary layer [24]. The shear stress of the vis-
cous wall region is directly influenced by molecular viscosity, while in the outer layer the

direct effect of viscosity on the shear stress is negligible [24].

Experimental data, taken in a turbulent boundary layer, are typically sealed with
appropriate lengths and velocities. Close to the wall. where viscous effects are important,

it is common to describe boundary layer characteristics in plus units or wall units. A fric-

tion velocity, “1» can be defined from the wall shear stress I“, and fluid density p as [24]:

111'
UI E J;— 1.1

l E— 1.2

where v is the kinematic viscosity of the fluid.

The distance away from the wall can then be defined (in wall units) as

.v
y+ I: 1.3

and the velocity in wall units can be defined as

u E — 1.4

The inner layer of a turbulent boundary layer has been observed to exhibit a uni-

versal behavior in both the viscous sublayer and the overlap region. In the viscous sub-
layer (the very near wall region), u+ varies directly with y+, or

u = y 1.5

+ +

for very small y (up to y ~ 10).

The overlap region has also been noted to exhibit a universal behavior when sealed
with inner wall units. In the overlap region of smooth wall turbulent boundary layers, the

log law can be expressed as

my++B ' 15

711-—

where B and K are constants, commonly taken to be [24]

K = 0.41 B = 5.2

These two regions join each other in the buffer layer, where neither equation holds
true. Figure 1.2 demonstrates the universal behavior of the viscous sublayer and the over—
lap region. The linear trend (equation 1.5) can be seen in the very near wall region, and
the log law behavior (equation 1.6) can be seen further away from the wall. The scaling

collapse for a range of Reynolds numbers is also evident in the figure.

Turbulent boundary layers display a Reynolds number dependence in many char-
acteristic trends and statistics. One example of this Reynolds number dependence is the
size of the overlap region in a turbulent boundary layer. Figure 1.3 shows the dependence

of the size of the overlap region as a function of Reynolds number [23]. The experimental

data exhibit a straight line for yuT/v > 30. This straight line represents the log law.

Deviations from this line mark the end of the overlap region. The location where the data

deviate from the log law is dependant on the Reynolds number.

1.2 Literature review

The current research examines the near-wall velocity and vorticity characteristics
in a high Reynolds number turbulent boundary layer. This section will serve to briefly
review the current literature relevant to the present study. Turbulent boundary layers and
the concept of local isotropy have been studied extensively, but rarely at a Reynolds num-
ber comparable to that of the current research. The concept of local isotropy was pre-
sented by Kolmogorov in 1941 as a hypothesis concerning the characteristics of turbulent

flows. Kolmogorov’s hypothesis states that “at sufficiently high Reynolds numbers, the

small scale turbulent motions are isotropic” { 13]. In other words, at high Reynolds num-

6

ber the statistics of the very small scale motions in turbulent flow are ‘invariant with

respect to rotations and reflections of the coordinate axis,” i.e. independent of direction

[24]. This hypothesis was made in the assumption of extremely high Reynolds number

(Ree ——> co) and has been tested up through current laboratory limitations.

The velocity and vorticity characteristics of turbulent boundary layers have been
extensively studied over a range of Reynolds numbers. Those that involve vorticity mea-

surements include Ong and Wallace (1998) who examined the structure and dynamics of
the vorticity field of a turbulent boundary layer at R9 = 1070 [22]. Honkan and Andre—
opoulos (1997) studied vorticity and dissipation in a turbulent boundary layer at

R9 = 2790 [14]. Andreopoulus and Agui (1996) studied the wall vorticity flux dynamics

in a turbulent boundary layer at R9 = 5400 [l]. Klewicki and Metzger (2001) were able

to extend the study of turbulent boundary layers into the range of Re 2 5><106 by the use

of the SLTEST site [16].

The concept of local isotropy in turbulent boundary layers has also been the sub-
ject of extensive investigations covering a range of Reynolds numbers. Mestayer (1982)

studied local isotropy and anisotropy in a high Reynolds number turbulent boundary layer
at R1 = 616 [18]. Saddoughi and Veeravalli investigated Kolmogorov’s 1941 hypothe-
sis of local isotropy in a turbulent boundary layer at R9 = 370, 000 (R). = 1450)[26].

These were the largest Reynolds numbers ever attained under laboratory conditions. The

current research extends the investigation of turbulent boundary layers and the concept of

local isotropy up to R9 : 5x106 and R). = 2500 by use of the SLTEST site. The follow-

ing chapters detail this investigation.

 

 

 

 

 

 

 

 

 

10-4 10-3 0.01 0.1 0.3 1
l l l l 1 l y/(5
OUTER LAYER
overlap region
log-law region
INNER LAYER
viscous wall region
buffer layer
viscous sublayer
y+
l l L l l l l J
l 5 10 30 50 100 1,000 10,000

Figure 1.1 The breakdown of a turbulent boundary layer [24]. The inner y+ and the outer

y/8 are universal [ ¢f(R9) ], but the extents of these regions are R0 dependent.

25

l

l

20

l

15

10

1

 

 

Figure 1.2 Scaling collapse on the inner region of a turbulent boundary layer [24]. 0,

Res = 2, 970; 1:] , Refi = 14, 914; A, Rea = 22, 776; line, the log law.

 

  
  
   

      
 

 

 

 

 

    

 

 

T l I I T Ill] 1 l l l l 1 TIT I *1 l l
30 i—' 10 r— ' -1
__ Law of the wall .
Viscous _
sublayer
0 1 1 1 1 1111 __
2° *— 10
+ --l
u
.1
10 ""
, 1 11111111 1 11114111 1 ll_
10 100 1000

Figure 1.3 The Reynolds number dependence on the size of the overlap region [23].

10

2.0 Experimental Facility and Conditions

The current research was conducted at the SLTEST site in western Utah. The
SLTEST site utilizes a large atmospheric boundary layer which develops over the very flat
desert floor. This unconventional test site allowed for high resolution, near wall velocity
and vorticity measurements in a high Reynolds number turbulent boundary layer. How-
ever, the outdoor atmospheric environment also brought about new issues to address,
including thermal effects and very low-frequency motions.

This chapter serves to describe the SLTEST site in detail and address the new
issues which presented themselves during this research. Section 2.1 presents a general
overview of the SLTEST site. Section 2.2 describes the test site’s data acquisition equip-

ment, including wind monitoring, thermal profiling and shear stress measurements.

2.1 Test Site Overview

The SLTEST facility is located on the US. Army Dugway Proving Grounds in the
Great Salt Lake Desert of western Utah. This region has been observed to provide desir-
able wind and surface conditions for accurate near-wall boundary layer measurements.
The SLTEST site is located at 113° 16’ W, 40° 85’ N and is situated between moun-
tain ranges (forming crude sidewalls to the east and west) as seen in Figure 2.1 [19]. The
SLTEST site is actually the floor of the ancient Lake Bonneville and consists of a very flat
surface. This surface, devoid of vegetation, is formed by the recession of a relatively high
water table in late Spring. This recession leaves the playa smooth, solid and virtually dust

free (playa is defined as a mixture of mud, clay and salt). Measurements reported by the

University of Utah approximate the surface variation of the test site to be less than 1 meter
per kilometer, or about 0.1% [30].
The observed boundary layer develops over a distance of nominally 150 kilome-

ters for northerly winds and about 50 kilometers when the wind is blowing from the south
[17]. These conditions typically result in a boundary layer thickness, 5, on the order of

150 meters and a momentum thickness, 0, on the order of 10 meters [15]. The large

scales associated with this boundary layer contribute to typical Reynolds numbers (based

. (
on the momentum thickness 0 l on the order of Re9 z 5 X 10 ). These large scales along

with the relatively low flow speeds (between 3 and 6 m/s at our probe locations) also

allow for very good spatial resolution of the measurements [15].

2.2 Test Site Capabilities

The conditions at the SLTEST site were continually monitored to characterize the
data taken. The ambient conditions present during the acquisition of each data set were
documented to allow for accurate comparisons to well controlled laboratory results. The
monitored conditions included the wind speed, wind direction, velocity profiles, tempera-
ture profiles, and shear stress measurements at the wall. The following subsections will

discuss the available information at the SLTEST site and how it was acquired.

2.2.1 Wind Monitoring

The SLTEST facility offered equipment to monitor the wind conditions at a range
of elevations above the desert floor. Figure 2.2 demonstrates the four types or measure—

ments available to profile the boundary layer (Sonic tower, Echosonde, Radar wind pro-

12

filer, and FMCW radar) and their active ranges. Hot wire anemometry (the focus of this
research) allowed for accurate measurements in the boundary layer ranging from 1mm to
2m off the surface [30]. Figure 2.3 shows a typical boundary layer profile taken at the
SLTEST site under neutral conditions and averaged over a 1 hour period, courtesy of the
University of Utah’s echosonde equipment.

The outdoor nature of the SLTEST site did not allow for control over the steadi-
ness of the free stream. The facility was equipped, however, with instrumentation to mon-
itor the ‘driving’ atmospheric wind. Questions related to steadiness of the free stream
velocity at the SLTEST site were sufficiently answered by monitoring the prevailing wind
speed and direction. For each of the three days data were acquired, a three-cup anemom—
eter and wind vane (discussed in Chapter 3) were used to verify the steadiness of the wind.

The results for each day are discussed in Section 5.1.

2.2.2 Thermal Effects

This section will address the thermal concerns brought about by the outdoor nature
of the SLTEST facility. Thermal effects can be controlled under typical laboratory condi-
tions to play a minimal role in boundary layer characteristics. However, this was not the
case at the SLTEST site. During the day, the hot desert sun heated the test site floor to a
temperature well above the ambient air. Such a condition is known as unstable, since a
positive buoyancy flux results due to the temperature (and hence a density: p ~ l/T) gra-
dient. This density gradient causes the lower, warmer air to move away from the wall.
The fluctuations measured in a boundary layer under unstable conditions are amplified as
a result of the effects of the positive buoyancy flux. As the sun sets, the ground cools off

and eventually a state of thermal equilibrium is reached. This case is known as the neutral

13

condition. Thermal effects do not play a role in the boundary layer motions under the neu-
tral condition. Following the neutral condition, the ground continues to cool and it even-
tually reaches a temperature lower than that of the surrounding air. The cool ground
creates what is known as a stable condition. In this case, the cooler air initially near the
wall tends to stay near the wall due to the density stratification. This negative buoyancy

flux has a damping effect on the velocity fluctuations within the boundary layer.

The condition of thermal equilibrium was defined by ngQ, where 0 is the

By
potential temperature of the air. Potential temperature is defined as the temperature a par-
cel of dry air would have if it was brought adiabatically from its initial state to the standard
sea level pressure of 1000mb. The potential temperature removes the temperature varia-

tion caused by changes in pressure altitude of an air parcel, and is given by [29]:
v_—_1
P Y
e-rte’l
In this formulation, T and P are the temperature and pressure of the air parcel respectively,

P0 is the reference pressure of 1000‘mb, and y is the heat capacity ratio of the air.

The virtual potential temperature 0v is similar to the potential temperature 0

defined in equation 2.1, but uses the virtual temperature of the air in its computation. The
virtual temperature of moist air is defined as the temperature that dry air must have to
equal the density of the moist air at the same pressure. The virtual potential temperature is

related to the potential temperature by [29]:

0, = 0(1+ 0.61rw— l-L) 2.2

14

where rm, is the water-vapor saturation mixing ratio of the air parcel and rL is the liquid-

water mixing ratio [29].

The relative buoyancy effects were assessed according to the stability parameter
C33):- In this stability parameter, y is the distance of the measurement away from the
wall and L is the Monin-Obukhov length [19],

—uI
L = __ _. 2.3
K(g/0V)v'0v'

 

In the Monin-Obukhov length, uT is the friction velocity (see the next section), g is the

gravitational constant, v' is the wall-normal velocity fluctuation, K is the von Karmen

constant, 0v is the time averaged virtual potential temperature and 0V' is its fluctuating

counterpart. The Monin-Obukhov length L is physically the height at which the buoyancy
term equals the shear production term in the turbulent kinetic energy balance [19]. Posi-
tive C indicates the presence of a stable atmospheric condition while negative C indicates
the presence of an unstable atmospheric condition. The “neutral” condition was taken to

be ICI S 0.1 as was found to be common practice in atmospheric boundary layer research
[13].

Previous work by Klewicki [15] has indicated that a range of up to 2 hours can
exist during the evening where the ambient atmospheric conditions are very close to neu-
tral. The thermal stability parameter was evaluated for each of the three days that data
were acquired. These results are discussed in Section 5.1. It should be noted that this sta-

bility parameter was calculated from the data acquired by a sonic anemometer located at y

15

= 3.185m. This is not the same location of the probes, but still gives a good indication of
the stability condition at the SLTEST site for each evening. Differences between the sta-
bility parameter at y = 3.185 m (the parameter measurement location) and y = 20 cm

(probe location) are assumed to be relatively small.

2.2.3 Shear Stress Measurements

The mean wind shear stress was also monitored in order to accurately normalize
the data for comparison with laboratory measurements. A drag plate (Figure 2.4) consist-
ing of a thin (thickness = 1.27mm) polyethylene cylinder 2.4 meters in diameter was
mounted on a styrofoam base and placed in a shallow pool of water (0.2m). The drag
plate was mounted flush with the surface of the surrounding salt flats. A small amount of
playa was then scattered on the drag plate surface to mimic the surface roughness of the
surrounding ‘wall.’ Force transducers were mounted near the edges of the cylinder on 3
sides of the plate, each separated by 90 degrees. These force transducers recorded the
mean wall shear stress when the wind was blowing from a northerly direction. The drag
plate was able to extract shear stress values as small as 0.01 Pa [19].

The drag plate was located on the north side of the raised access road. As a result,
accurate shear stress measurements could only be acquired with wind blowing from the
northerly direction. However, all three data sets for this research were taken when the
wind blew from the south. To account for this. the drag plate data were previously corre-
lated with a propeller anemometer located 2 meters above the ground. An identical pro-

peller anemometer was then located on the south side of the test site and used to extract

the mean shear stress data in the case of southerly winds. The friction velocity, uT , could

l6

then be computed from the measured mean shear stress and the density of the air by using
equation 1.1.

Data from the University of Utah indicated that the correlation between the drag
plate and propeller anemometer was only valid under the condition of thermal neutrality.
However, some of the data presented were also acquired under thermally stable and ther-
mally unstable conditions. Correlating the propeller anemometer to the drag plate under
thermally stable and thermally unstable conditions would have proven difficult, since the
correlation is dependant on the degree of thermal stability present. The aforementioned
correlation over thermally stable and thermally unstable conditions was not complete at
the time of this work. As a result, the value of the friction velocity that was used for each
data set was computed through a correlation which assumed thermal neutrality, regardless
of the present thermal condition.

To distinguish between the known friction velocity (for the thermally neutral con-
dition) and the estimated friction velocity (for thermally stable or unstable conditions), the

following notation is used. In the condition of thermal neutrality. the friction velocity will

be denoted by “1° In the thermally unstable condition, the friction velocity will be

denoted by (ut)“. In the thermally stable condition, the friction velocity will be denoted

by (“1)5' The friction velocity for each day is discussed in Section 5.1.

17

 

 

   

100km h

 

Figure 2.1 Topographic map of the Dugway area. The SLTEST site is denoted by O.

FMCW Radar
50 - 4k
Radar Wind Profiler m m

 

 

 

 

 

120m - 1km
Echosonde 1
10m - 200m
Sonic Anemometer ii 1 Om
& Hot Wire Tower “""'"'_‘2
Figure 2.2 Sensing capabilities of the SLTEST site [30]
200 - I I
I1.
1 I
150 -
E 100 —
N
50 -
I
I
I I'
o _ I
I 1 I l
0 2 4 6 8
U (m/s)

Figure 2.3 Typical boundary layer profile at the SLTEST site [30].

19

~-‘ . ”tan—m.“

 

stress [30]. (J. Klewicki is shown smoothing the playa to the edge of the housing for the
drag plate.)

20

3.0 Experimental Equipment

A mobile data cart was created to aid in the acquisition of data on the SLTEST site
salt flats. The motivation for the data cart was the unpredictable weather conditions
encountered during the writer’s first year at the SLTEST site. The goal of the data cart
was to be fully mobile, self contained and quickly stored in the transport van in the event
of a microburst. The purpose of the mobile data cart was to enable the author to quickly
set up the equipment and begin data acquisition whenever the proper conditions presented
themselves. The mobile data cart allowed for all the necessary equipment to be quickly
and easily moved to the proper location (north or south of the raised access road) in order
to acquire the desired data in the limited window of time. The mobile data cart required
only a single outside power source (1 10 V supplied by the test site via a long extension
cord) to allow for the equipment to remain powered up during the movements. Local
micro-bursts required that the data cart be quickly retractable to protect the delicate equip-
ment inside.

This chapter details the workings of the mobile data cart in Section 3.1, including
its internal cooling system, the on—board equipment and its self-contained calibration facil-
ity (Section 3.2). Chapter 3 also discusses the additional equipment used on the SLTEST
site, including a three cup anemometer (Section 3.3), wind vane (Section 3.4) and ther-

mistor (Section 3.5).

21

3.1 Mobile Data Cart

The mobile data cart (Figure 3.1) was fabricated from a set of 2’ X 4’ steel storage
shelves and the base of a heavy duty pull cart. The maximum height of the cart was deter-
mined by the storage space of the transport vehicle to be 45” tall. The cart rode on 25.4
cm pneumatic wheels. This choice of wheels made maneuvering through the desert playa
easier. The lower region of the data cart was designed to be a self-contained calibration
facility and will be discussed more in the following section (Section 3.2). The upper
region of the cart housed the equipment necessary for data collection and was easily
accessible through the flip-down doors on either side of the cart (Figures 3.1 and 3.2). The
upper and lower regions of the data cart were kept isolated from each other for fewer cali-
bration disturbances. The outside of the cart was covered in thin sheets of white plastic to
keep the cart as cool as possible. The front of the cart was comprised of a flip-down shelf
designed to support a portable personal computer and keyboard. It was also designed to

include an optional sun-blocking roof to eliminate glare on the face of the monitor.

3.1.1 Cooling System
The mobile data cart was equipped with an internal cooling system. The cooling

system was required because of the high ambient temperatures (typically 95°F = 35°C)
present at the SLTEST site. The equipment on the mobile data cart was calibrated and
typically operated at laboratory temperatures. The purpose of the cooling system was to
provide a similar operating temperature to avoid any thermally related problems with the
equipment. The cooling system worked as follows.

Additional space was added to the back of the cart in the form of an extension and

divided into two regions; see Figure 3.1, sections B and D. The lower extension region

22

(D) was used for both the calibration facility as well as storage of the three-cup anemome-
ter and wind vane. The upper extension region (B) housed the data cart’s cooling system,
and both were accessible through a large (61mm x 77.5mm) door on the back of the cart.
A large (20mm x 201nm x 51mm) basin was constructed and mounted in the upper exten-
sion region of the data cart. The basin was filled with water through a hole in the roof; see
Figure 3.1, label A. A 17” X 10” square of cloth filter material was mounted partially in
the basin and used to wick up the water stored in the basin. A small blower was mounted
outside of the data cart and attached to a diffuser leading into the cooling system. As air
entered the cooling system, it absorbed water from the wet filter material (due to the low
ambient humidity in the desert) and then quickly evaporated, significantly lowering the
temperature of the air stream. This cooled air then travelled throughout the cart (over both
levels of equipment), eventually exiting out the front of the cart. The system was loosely
tested at the SLTEST site with temperature sensing equipment and the temperature imme-
diately behind the cooling system was found to be significantly cooler than the ambient
air. The humidity level was also monitored and observed to be only slightly higher than

the ambient air.

3.1.2 On-board Equipment

The mobile data cart housed all equipment necessary for data acquisition at the
SLTEST site. The data acquisition equipment was stored in the upper region of the cart;
see Figure 3.2. The upper region of the data cart was separated into two levels. The lower
level housed 8 DISA 55m10 anemometers (which were used to control the hot wire probes
utilized in this research) as well as the A/D board (labels B and C). The anemometers had

electrical noise levels on the order of 2 mvolts RMS and frequency responses always in

23

excess of 30 kHz [20]. The A/D board used was an lotech WaveBook 516, which had 16-
bit resolution and lMHz total sampling capabilities over 16 channels. Eight of the chan-

nels were equipped with a sample-and-hold card to allow for simultaneous measurements.

The Iotech board had a range of ilO volts and typical electrical noise of about 10 mV.
The A/D board transferred all data to a BSI FieldGo “luggable” computer for permanent
storage and processing.

The upper level of the data cart contained the pressure transducer, DISA power
supplies, stepper motor control (for the calibration unit described below), probe case, and
drivers for the thermistor, three-cup anemometer and wind vane. The pressure transducer

was an MKS Baratron 220BD differential manometer, with a full scale range of 0.53 in

H20, a resolution of 0.01% of the full scale range (5.3x10_6 in H20) and an accuracy of

i0.15% the reading.

The data cart was wired to run off a single 1 10 volt power supply. Surge protec—
tion strips provided 12 outlets for the equipment. Power for the calibration facility blow-
ers as well as additional cooling fans was supplied directly from the cart’s wiring scheme.
All electronics on the cart connected to a single ground. This single ground was then con-
nected to a grounding rod. Taking advantage of the water table just beneath the test sur-
face (as well as the salty conditions), the rod was driven into the desert floor in order to

properly ground all of the equipment.

24

3.2 Calibration Facility

The hot wire sensors were calibrated using a facility located on the lower level of
the mobile data cart; see Figure 3.1 (F). The calibration facility was designed to provide
the proper range of air speeds to the hot wire probes without interference from the ambient
wind. This section will discuss the construction of the calibration facility while the actual
calibration procedures will be discussed in Chapter 4.

The lower region of the data cart was covered with filter material; see Figure 3.1.
This filter material eliminated the effects of ambient winds on the calibration of the hot
wires and still allowed for the higher pressure air inside the lower region of the unit to
escape. Two small doors on the front of the data cart allowed for access to the front of the
calibration unit. The front half of the calibration facility detached from the fixed base and
rolled forward for probe mounting and alignment; see Figure 3.3. Doors on either side of
the lower region of the data cart (3/4 of the way back. see Figure 3.1) allowed for access to
attach and detach the front half of the calibration unit from the fixed base. The blowers
were mounted on the fixed base of the calibration unit and hung off the back of the data
cart, enclosed in the lower extension region. This allowed for ambient air to be induced
into the facility, used to calibrate the wires, and then be returned through the filter material
to the surroundings.

The calibration unit seen in Figure 3.3 was designed and built specifically for the
mobile data cart. The unit was composed of two parts: a stationary back portion and the
detachable front portion. The two halves were latched together while in use, sandwiching
a thin layer of foam which sealed the connection as well as reduced the vibrational effects

of the blowers. The back half of the calibration unit was secured to the bottom floor of the

25

data cart and utilized two Dayton 4C015 Dual Shaded Pole Blowers, with outputs of 72

CFM at 0.5” H20 each. The blowers were throttled by four aluminum plates connected to

a threaded rod. The external end of the threaded rod was connected to a 1/20th horse-
power gear reduction DC. motor. Limit switches were mounted inside the unit to stop the
throttle plate at fully open and fully closed positions. A 24 volt power supply and main
control switch were added to the system (Figure 3.5) to allow throttling of the motor to
occur from the front of the cart with the flip of a switch.

The calibration facility contained several flow conditioning devices that were used
to ensure a steady and uniformly distributed calibration flow. A top view of the calibra-
tion facility, along with the flow conditioning elements, can be seen in Figure 3.4. Two
vertical pieces of angle stock were mounted directly in front of the blower exits (down-
stream of the throttle plate) in order to disperse the jets formed from the blowers. Addi-
tional elements: a layer a filter material, a 1” thick honeycomb (used to straighten the
flow) and two layers of screen, were place downstream of the vertical angle stock obstruc-
tions. The back plate of the calibration unit (which held the blowers) was mounted to the
unit with a slight air gap on all four sides. This allowed for stable operation at very low
calibration air flow speeds since, for low fan speeds. air would escape out of the back gaps
instead of travelling through the more restrictive passage into the front of the unit.

The front half of the calibration unit was made detachable and designed to roll
from the back position (used for calibration) to the forward position (used for probe
mounting) along a track mounted on the data cart floor. The uniform and steady airflow
received from the back portion underwent a smooth contraction and exited the unit with a

width of 2.54 cm. The probes were mounted to a vertical “D-bracket” which was sus-

26

pended from a rotatable rod with its pivot point located directly over the exit plane. An
11.43 cm gear was also connected to the same rod and connected to a stepper motor by
means of a belt. The stepper motor was computer controlled and used to control the angle
of the probe with respect to the flow. This angle traverse was found to have a resolution of
0.15 degrees, and was adjusted in six degree increments.

Pressure taps located on the front wall of the calibration unit were used to monitor

the pressure change across the contraction. Since the calibration facility’s settling cham-

ber did not represent true plenum, the measured pressure difference, Apm , could not be

1/2
used for the velocity calculation as V = [EA/)] . Instead. an auxiliary calibration:

Ap = f (A pm) was implemented. The static tap readings across the contraction were

compared to readings from a pitot tube located at the exit plane of the facility for a range
of pressures. The data were then curve fit in order to calculate a linear compensation fac-
tor used to transform the static readings into the true total pressure readings. Figure 3.6

displays this calibration information.

3.3 Three-Cup Anemometer

A three-cup anemometer was also used at the SLTEST site to monitor ambient
wind conditions. An R.M. Young #03101-X three cup anemometer was calibrated in a
2’ x 2’ wind tunnel for a range up to 15 m/s. Figure 3.7 shows the calibration curve used
for the three cup anemometer. The anemometer was mounted on a modified tripod 1.5
meters above the test surface; see Figure 3.8. The three-cup anemometer acquired data at

the same rate of the hot wires and was used to verify trends in the data.

27

3.4 Wind Vane

An R.M. Young 03101 wind vane was used on the SLTEST site in order to moni-
tor the direction of the wind during data acquisition. The vane had 360 degree capabilities
with a discontinuity between the 360 degree and 0 degree readings. The wind vane had a
resolution of 1 degree. The vane was also mounted on the modified tripod 1.5 meters
above the test surface; see Figure 3.8. Once the hot wire probe was aligned into the direc-
tion of the wind, a baseline angle reading was taken from the vane. The vane direction
was then monitored over the period of data taking and later used to verify the location of
the probe with respect to the mean wind direction. The readings from the wind vane were

also used to verify trends in the wind shifts observed by the probes. The vane was quoted

to have an accuracy of i5 degrees.

3.5 Thermistor

A thermistor was used to compensate all hot wire probe measurements in order to
account for ambient temperature variations. The thermistor was pre-calibrated and found
to have a sensitivity of 2.03K/Kohm [20]. At the SLTEST site, comparison of the ther-
mistor reading to a portable thermometer showed a large disagreement. The circuitry of
the thermistor was temperature dependant. The discrepancy resulted from the thermistor
driver box being operated at a higher temperature than that of its laboratory calibration.
To account for this, simultaneous readings from both the thermistor and hand-held ther-

mometer unit were taken over a range of ambient temperatures. The temperature pre-

28

dicted by the recorded thermistor voltage was compared to the actual temperature over
this range. The thermistor data were found to differ from the actual temperature by a con-
stant value for the entire range of observed temperatures. The thermistor data were then
offset by this constant value to achieve the actual temperature. Figure 3.9 shows the
actual temperature reading (taken with the hand-held thermometer) compared to the
adjusted thermistor reading for a range of thermistor voltages. All the data were then

curve fit and used to extract the actual temperature from the thermistor voltage.

29

 

 

 

 

 

 

 

 

 

 

A Cooling System Fill Hole

B Upper Extension Region

C Access to Upper Region

D Lowert Extension Region

E Side Access to Calibration Facility
F Lower Region

G Front Access to Calibration Facility
H Flip-Down Computer Shelf

Figure 3.1 Schematic of Mobile Data Cart.

30

 

 

 

 

 

 

A Cup/Vane Driver

B DISA Anemometers (not shown)
C MD Board

D Computer

E Thermistor Driver (not shown)

F Stepper Motor Driver (not shown)
G DISA Power Supply

H Probe Case

I Pressure Transducer

Figure 3.2 Interior view of Mobile Data Cart.

31

 

 

Cross—Flow blower

   
  
 

stepper motor For
probe onguecwfive

motor For
throtfle control

\\\\\ [Manor controctbn

probe support

Figure 3.3 The Data Cart’s portable calibration unit.

Screens
Angle stock
Blower

/

I

Flow Exit

 

 

IrIIFII

 

l 111”
V‘B

__.___

 

l
I
I
I I
I
|

11
ll

 

I

I
l'l’lllllllllllll

r
—-"

 

 

l

 

|
IJlLIIIiIIlIl
I 1'
|
l

11
ITII
1'1 1'1

1 |

11
11

 

 

Ill

 

l l

 

1 l
l l 1
I | l l l l
| l I I

1

 

 

 

 

 

 

 

1 III 1 I'IIIIIIIIITII IlIII I
1

LLIIIIII
III
I
1

 

\‘
/

I Th ttl Plt
Honeycomb Filter ro e ae

Material

Figure 3.4 Top view of the calibration facility showing the flow conditioning.

32

 

 

 

 

 

 

 

 

 

 

—jI Limit Limit It}: Q “"“l
Switch Switch I“ ‘xl ‘
. MAS—It h Power
WI 0
fl —- super
_ 5 I A g: l
__: ____J
m

 

 

Figure 3.5 Wiring diagram for the calibration unit.

Total Pressure vs. Static Reading for Calibration Unit

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.4 —— —
0.35 --
y=1.0112x
92:1

A 0.3
O /
E
9
U)
93
E 0.15
(U
,5 /
1-

0.1 / J .

0.05 /

0 I r Y r r r r
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Static Tap Reading (in. HZO)

Figure 3.6 Total pressure vs. the static tap reading for the calibration unit.

33

0.4

Three Cup Anemometer Calibration

 

 

16.0 -i_
y = 47.152x + 0.3461

R2 = 0.9997 ,0”

 

14.0

 

 

 

12.0

 

 

10.0 ~

 

 

8.0 ..

 

 

 

Velocity (m/s)

6.0

 

 

4.0

2.0 ——
0.0 / r t 17 r r f 1

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Output (V)

 

 

 

 

Figure 3.7 Three cup anemometer calibration.

34

Wind Vane

 
   

3-cup anemometer

 

 

 

/

x
I(
I

 

 

L.

Probe Mounting Location

Figure 3.8 Tripod used to mount the three cup anemometer, wind vane and hot wire

probes.

35

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature (Degrees C)

 

 

 

 

 

 

 

20 a m A
15 . i d m
10 -._____ _. .____ . __-___ -_. ___. ___“-, _ # ___
o Hand-Held Thennometer
5 1' Adjusted Thermistor Reading
0 T I I I I T T I l
1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55

Mster Voltage (V)

Figure 3.9 Thermistor re-calibration due to large ambient temperatures.

36

4.0 Hot Wire Techniques

The data recorded at the SLTEST site were acquired with the Michigan State Uni-
versity compact vorticity probe developed by Foss et. al. [1 1]. This probe consists of two
parallel hot-wires mounted in conjunction with an X-wire array: see Figures 4.1 and 4.2.
The two parallel wires of the compact vorticity probe, separated by a nominal distance of
1 mm, were used to measure two independent velocity magnitudes of the approaching
fluid. The X-wire array is used to measure the angle between the resolved velocity (in the
plane of the X-array) and the probe axis. From these three values, two components of the
velocity vector as well as the corresponding vorticity component could be computed. Sec-
tion 4.1 presents the operation of a single hot—wire sensor, including the calibration at the
SLTEST site and a detailed uncertainty analysis. Section 4.2 presents the workings of an
X-array hot-wire sensor, including its calibration, processing algorithm and uncertainties.
Section 4.3 will cover the MSU. compact vorticity probe, its calibration, processing algo-

rithms and the resulting measurement uncertainties.

4.1 Single wire calibration and uncertainty

A typical single wire hot wire sensor is shown schematically seen in Figure 4.3.
The probes were fabricated using 5,1tm diameter, 3mm long Tungsten wire in the Turbu-
lent Shear Flows Laboratory (TSFL), MSU. The active region of the sensor was con-

structed of Tungsten to be 1mm long and 5pm in diameter. Each end (1mm length) of the

Tungsten was plated with copper to 30pm in order to ensure the main resistance of the

sensor was concentrated in the 1 mm active region. The copper plating also allowed the
Tungsten sensor to be easily soldered to the supporting broaches.

The calibration of the sensors was performed in a “quasi-steady” manner. This
quasi-steady calibration involved slowly traversing a throttle plate across the blower exit,
see Figure 3.4. This process was performed at a constant rate by a DC motor. The veloc-
ity of the calibration stream was varied continuously (albeit non-linearly) from 0.5 m/s to
12 m/s over a 50 second period. The calibration was termed either a ‘spin-up’ (velocity
increasing) or ‘spin-down’ (velocity decreasing). Data samples from the hot—wire sensors,
the pressure transducer and the thermistor were acquired at 200 Hz over this 50 second
period. The pressure reading across the contraction of the calibration facility was used
with the Bernoulli equation to predict the velocities seen by the sensors. Previous work
has shown that under slow throttle plate movements the steady Bernoulli equation is still
valid. The calibration time of 50 seconds was chosen for this reason.

The recorded calibration data were used in conjunction with the modified Collis

and Williams equation [21]

2

E =A+BQ” 4a
where E is the voltage recorded from the hot—wire anemometer and Q is the exit velocity

of the calibration stream. The processing algorithm cycled through a range of ‘n’ values

(from 0.3 to 0.7 in steps of 0.02) while linearly curve fitting E2 verses Q". The curve fit
with the smallest standard deviation was selected and the corresponding values of A, B,
and n were assigned to the wire. An example of a single calibration can be seen in Figure

4.4.

38

The Bernoulli equation was used for the calibration of one sensor on the compact
vorticity probe. This sensor then served as the reference signal for the other three sensors
on the same probe (the other straight wire as well as the X-array). This process allowed
for the sensors to be calibrated over the high frequency fluctuations in the calibration
stream not observable through the less sensitive pressure reading. This high frequency
calibration was necessary to ensure instantaneous velocity differences between the sensors
were real and not a result of the calibration method.

The range of velocities over which the calibrations coefficients were determined
was dependant on the range of velocities observed by the probe during the data acquisition
period. All probes were initially calibrated from 0.5 m/s to 12 m/s in the calibration
stream before (pm-calibration) and after (post-calibration) the data acquisition. The data
recorded from each specific day were then examined to see the range of velocities the hot
wire sensors saw over the period of data acquisition. Figure 4.5 shows an example histo-
gram of the observed velocities for the evening of 25-July, 2001. For this specific exam-
ple, the calibration was then performed spanning a range from 2.5 m/s to 9 m/s.
Calibrations for the other two days (l8-July and l9-July) were performed from 2 m/s to 8
rn/s.

The accuracy of the recorded data set was determined through examination of the
pre- and post-calibration data. Under laboratory conditions, if any discrepancies about the
acquired data were to arise, one could easily discard the existing data set and re—take the
data without hesitation. This was not the case for the current research. As a result, the dis-

crepancies must be quantified so one may assess the accuracy of the resulting data.

The pre-calibration and the post—calibration data sets were examined for each day
data were acquired. The pre-calibration and post-calibration of a sensor produced two
independent sets of A,B, and n constants. For a range of inputted voltages, equation 4.1
was used along with each set of constants to produce two sets of predicted velocities. If a
sensor predicted the same velocities using both the pre- and post-calibration constants,
then the data set was considered accurate. If not, drift had occurred on the sensor. Drift
occurs from a change in the resistance of the sensor over the period of data acquisition.
Drift cannot be accounted for in the data processing routine since one cannot determine
when in the data set the drift occurred. As a result, data sets with large amounts of drift
were discarded.

The amount of drift that a wire had experienced was gauged as follows. The volt-
age data recorded during the post-calibration was processed with the A,B, and n constant
values that were determined from the pre-calibration. A velocity was then calculated from
these data (using equation 4.1) and compared to the Bernoulli velocity calculated from the
recorded pressure. From this, the quality of the data set recorded between the two calibra-
tions could be accurately determined. Figure 4.6 shows an example drift comparison
taken on l9-July. In this plot, it can be seen that the accuracy of this wire is within i2 %
over the entire data range. Differences between the pre- and post-calibrations of up to
10% were accepted for this research. The accuracy of all the straight wire sensors used for
the three data sets can be seen in Appendix A.

The slight offset in most of the pre- and post-calibration data visible in the three
data sets prompted the author to combine the pre- and post-calibrations. Since drift is non-

linear and may occur at any point throughout the data acquisition (be it right after pre-cal-

40

ibration, or right before post-calibration), it was decided that combining the pre-and post-
calibration data would produce the most accurate results. Figure 4.7 demonstrates the pre-
calibration data (lower diamonds), the post-calibration data (upper open circles), and the
best fit trend line through both sets. Using the pre-calibration data alone, typical standard
deviations were on the order of less than 0.05 m/s. Using the combination of both the pre-
and post-calibration data, typical standard deviations increased to a range of 0.05 m/s to
0.20 m/s. The entire set of plots showing the combination of the pre- and post-calibration

data for all the sensors used over the three days can be seen in Appendix B.

4.2 X-wire calibration, processing and uncertainty

An X-wire probe consisted of two hot-wire sensors mounted in an X pattern; see
Figure 4.8. The two wires were oriented at i45° to the probe axis and separated by a dis-
tance of 1 mm (into the page). Each sensor of the X-wire probe was fabricated in the same
manner as a single hot-wire with the same 1 mm active region. Each X-array had the out-

puts El and E2 corresponding to the output voltages of each sensor in the array. Process-

ing techniques discussed in the following paragraphs allowed for these outputs to be
transformed into the speed and angle of the approaching fluid. This allowed for the simul-
taneous measurement of two velocity components. However, since the compact vorticity
probe contained two parallel hot-wires as well as the X-array, the speed predicted by the
X-array was not used.

Each X-array had to be calibrated for a range of angles as well as a range of veloc-
ities. To do this, the vorticity probe(s) was affixed to a D-shape bracket attached to the

calibration unit. The probe was aligned so that the X-array was centered under the pivot

41

point, just downstream of the exit plane. The zero angle alignment was held constant
throughout pre- and post-calibrations by an alignment mark made on the floor of the data
cart. The probes were then rotated to an angle of -36 degrees with respect to the exiting
fluid and either a ‘spin-up’ or ‘spin-down’ was performed on the probes. The probes were
calibrated at 13 discrete angles from -36 degree to +36 degrees in 6 degree increments.
For each specific angle, two sets of A,B, and n constants could then be computed, one for
each wire in the X-array. The calibrations were performed for each angle in the same

manner as described in Section 4.1.

4.2.1 X-wirc processing algorithm

The most accurate algorithm for X-array processing has been the subject of con-
siderable debate. The current research utilizes a “curve-intersection” method proposed by
Morris [21] as an adaptation to the “speed-wire / angle-wire” method proposed by Foss
[9]. In the current method, the X-wire probe is calibrated for 13 angles ranging from
—36° SyS 36° in 6° increments. This results in 13 sets of constants (A,B,n) for each
sensor in the X-array, corresponding to the 13 calibration angles. The experimental data
are acquired as time series values of the voltage pair E], E3. The processing algorithm
begins by picking out the El, E2 voltage pair for each time step. Using this E1, E2 pair,
equation 4.1 is then solved for QI(E|,7/i) and Q2(E2,‘/i), where i = l, 2, ...13. In other
words, for each time step, the algorithm uses the measured voltage and the corresponding
A, B, n values (for each of the 13 calibration angles) along with in equation 4.1 to solve
for the flow speed. This was done each sensor. It is then possible to plot the predicted

velocity verses the corresponding angle (associated with the specific A, B, n constants) for

42

both sensors. The “true” velocity and thus the “true” angle are then represented by the
intersection of these two functions. This is found by curve fitting the nearest points of
each curve with a second order polynomial and then solving for the intersection point.
Figure 4.9 shows an example plot of the 13 predicted velocities of each wire for a given

voltage pair.

4.2.2 X-wire uncertainties

The accuracy of the X-array was determined by the amount of drift the array had
experienced. However, since the current research used X-wires to measure the flow angle
7 and not the speed, determining their drift based on predicted velocity would not suffice.
The amount of X-wire drift was determined using the same method as described in Sec-
tion 4.1, but the predicted angles were examined as opposed to the predicted velocity.
Again, the 13 sets of constants (A, B, and n) for each wire were taken from the pre-calibra-
tion data along with the 13 time series from the post-calibration data (one time series for
each angle). The data were then processed using the algorithm described previously in
Section 4.2.1. For each time series, the predicted angle from the processing algorithm was
then compared to the mechanical angle determined by the physical probe orientation. The
quality of the data set recorded between the two calibrations was then determined from
this comparison.

Figure 4.10 shows an example drift comparison from an X-array taken on l9-July.
It can be seen that the X-wire shows no visible drift, since the pre-calibration A,B, and n
constants correctly predict all 13 angles given the post-calibration time series. In this

case, the lines are all constant over the entire range of data (2 - 8 m/s), and equally spaced

over the entire range of —36° S y S 36° . Typical angle drift on accepted data sets was less

43

than 2 degrees over the range of —18° S yS 18°. Larger variations outside of this range
were accepted due to the difficulty in the measurement of larger angles. The variations of
all the X-wires used for all three data sets can be seen in Appendix A.

The slight offset in most of the pre- and post-calibration data visible in the three
data sets prompted the author to combine the pre- and post-calibration data. The two pre-
can post- calibration data sets were combined into one data set used for calibration follow-
ing the same method described in the straight wire section. The entire set of plots showing
the combination of the pre- and post-calibration data for all the sensors used in the three

data sets can be seen in Appendix B.

4.3 Vorticity Probe

The data for the current research were acquired at the SLTEST site using a four-
wire spanwise vorticity probe, or a “Mitchell” Probe. The probe is a combination of two
parallel hot-wires interlaced within the spacings of an X-wire probe. Figure 4.1 shows the
two dimensional geometry of the Mitchell Probe. while Figure 4.2 shows a perspective
view.

The two straight wires were calibrated as discussed in Section 4. l. The processed
output from these two straight hot-wires gave a time series of the magnitude of the veloc-

ity at each sensor location (these two magnitudes will be referred to as q] and qz). The X-
wire within the Mitchell probe was calibrated using the methods described in Section 4.2
for 13 angles spanning ~36° S yS 36°. The processed X-array data yielded a time series

of the angle 7 acquired at the same instant as q. and q2. The following paragraphs

44

describe the processing used to transform the time series of (ql, q2, 7) into the desired

velocity time series. Section 4.3.1 will review the algorithm used to transform the time

series of (ql, qz, 7) into the vorticity time series and Section 4.3.2 will cover the probe

uncertainties. The spanwise vorticity probe and the corresponding processing algorithm
were originally developed by Foss et a1. and are more thoroughly described in references
[12] and [10].

The coordinate system used throughout the current research was a standard labora-
tory coordinate system as opposed to the standard atmospheric coordinate system. The x-
axis was assumed positive in the flow direction. The y-axis was taken as positive extend-
ing outward normal from the wall (desert floor) and the z-axis was then computed from

the right-hand rule. From the time series of (q,, (12~ y) taken from each probe, the specific

11, v, and w velocity components could be computed as:

 

+
u = (q, 2 612) cos(y) 4.2

 

v = (q, :q2) sin(y) 4.3

for a probe oriented to measure the vorticity in the z-direction (<1:uz>), or:

 

+
u = (‘1‘ 2 42) cos('y) 4.4

 

' +
w = (‘1‘ 2 ‘12Isinm 4.5

for a probe oriented to measure the vorticity in the y-direction (<wy>). All statistical

quantities were averaged over the entire range of files for which the ambient conditions

were considered constant (see Section 5.1).

45

It should be noted that the angle 7 used to compute the velocity and vorticity com-
ponents was the adjusted angle of the fluid with respect to the probe axis (the x-axis). For

the probes oriented to measure <cey>, the angle of the fluid measured by the X-array was
the horizontal (left-right) angle of the fluid. The angles for the <wy> probes were de-

trended according to the analysis presented in Section 5.1 for each independent data set.

For probes oriented to measure <-:..‘~,>, the angle of the fluid measured by the X-array was

the vertical (up-down) angle of the fluid with respect to the probe axis. Slight deviations

from a zero mean reading in the vertical angle meant the <13; Z> probe was not oriented
exactly parallel to the wall. The mean value observed in the <33? angle measurement

was subtracted from the probe for each day, giving the adjusted angle 7 used in the data
processing. Figure 4.1 1 shows the typical distribution of the mean vertical angle. This
specific data set was taken on 18-July, 2001, and had an overall mean value of -0.1

degrees which was subsequently subtracted from each file taken over that evening.

4.3.1 Vorticity Algorithm
A vorticity time series was also computed from the measured values of (ql, qz, 7).

A modified “Taylor’s frozen flow hypothesis” was used along with the convection veloc-
ity of the flow to create a parallelogram shaped micro-circulation domain (in time). Spe-
cifically, unlike the original hypothesis (which was used for the flow downstream of a
turbulence generating grid in a wind tunnel and made use of the time averaged velocity as
the convection speed), the present study has used the average of the two recorded velocity

magnitudes [ ( U) = (q1 + q2)/2] as the convection velocity to create this parallelogram;

see Figure 4.12. The velocities q] and q2 are known at the top and bottom of the micro-

46

circulation domain, indicated by dark circles in the figure. The normal component of
velocity, v, was computed at the left and right sides of the mirco-circulation domain, indi-
cated by open circles. The height of the micro-circulation domain (Ay) was a fixed physi-
cal distance defined by the separation of the two straight wires. The measurement of this
distance will be described in the following section. The length of the mirco—circulation
parallelogram (As) was set to be roughly equal to the domain height (Ay). This was
accomplished as follows. As was defined from the velocities [ql(tn) and q2(tn)] at an

instantaneous time n to be

4.6

 

 

l i=“+m((lj(’i)+q2(ti))At

A.‘ =
1,1(m) 2m + l 2

i=n-m
where m was increased, starting from m = 1, until As" > Ay. When this was accom-
plished, the number of data points spanning As was defined as 2M (M being the integer
number of time records needed to create one half of the mirco-circulation domain). The
number of points spanning As (= 2M) was variable and was dependant on the convective
velocity of the fluid as well as the sampling frequency. Typical values of 2M were
between 6 and 20 time steps [21].

The physical value of Ay and the calculated value of As determined the final size
of the micro-circulation domain. Once this was accomplished, the average value of the
vorticity within that domain was calculated from the velocity circulation around the
domain since

r = 172/1' 4.7
c

and

47

F = Iced/l = ((1)">(AS)(A_\’) 4.8
A

where II is the circulation and V is the magnitude of velocity. For notation purposes, the

mean value of a given quantity during the time interval In _ M < t < t M will be expressed

"'1'

within brackets ( ). For example, the angle of the micro-circulation parallelogram was

the mean value of 7 during the time period of the mirco-circulation:

i=n+M
Z in.) 4.9

i=n-M

l
2M+l

 

<r,,> =

The instantaneous average vorticity (00") was computed by integrating the veloc-
ities (It and q2 along the top and bottom of the mirco-circulation domain. The normal
velocity component at the left and right sides of the micro-circulation interval was com-
puted from v = (qI +q2)(siny)/2. Combining this with equations 4.7 and 4.8, the
instantaneous average vorticity at time n is calculated as:

0,...) — r(t,,_M) _ <qz>-<q.>

AS M 4.10

 

I V
= —— - 1‘ :
<0)” (Ashanl‘v “ I

The process of calculating the instantaneous average vorticity ( (1)") involves
dividing the circulation integral by a very small number [(As)(Ay)]; see equation 4.10.
The accuracy of (01)") therefore depends heavily on the accuracy of the (As)(Ay) product.
Of the (As)(Ay) product, (As) is a mathematically computed from the size of (Ay). How-
ever, (Ay) is a physically measured quantity and its accuracy is limited to the accuracy of
the technique used to measure it. To account for this. a new technique was implemented

for a more accurate measurement.

48

An accurate measurement of the distance separating the two straight wires (Ay)
was obtained by traversing the probe through the shear layer of the calibration facility. A
threaded screw traverse mechanism was used to traverse the Mitchell Probe through the
shear layer, which was very thin with a high velocity gradient. The resulting data were
used to create the plot seen in Figure 4.13. As can be seen in this plot, the two wires pro-
duce identical representations of the shear layer, separated by a small distance. This dis-
tance is the distance which separates the two wires. or (Ay). To compute (Ay), one curve
was shifted along the abscissa by small increments until the two curves lined up (Figure
4.14). For this particular probe, the (Ay) measurement was 1.40 mm. For the other probe

used in the current research, the (Ay) measurement was 1.70 mm. The accuracy of this

measurement was estimated at i004 mm. or a 2.5% uncertainty.

4.3.2 Vorticity probe uncertainties

The amount of uncertainty present in the vorticity measurement was best estimated
by examining the amount of drift that occurred in the straight wires and X-array that com-
prised each probe. The comparison of the pre- and post-calibrations for each straight wire
and each X-array are available to the reader in Appendix A. The combination of both the
pre- and post-calibration data for each wire can be seen graphically in Appendix B.

The spanwise vorticity measurement techniques were not developed as part of the
current research and therefore will only be briefly discussed in this section. A detailed
account of the uncertainty analysis of both the probe and the processing algorithm can be
found in Foss and Haw [12]. From their research. the main source of error in the vorticity
calculation was found to be electronic noise present in the time series data. The contribu-

tion of this electronic noise to the uncertainty of the calculation was found to be on the

49

order of 20 (l/sec.) [12]. The vorticity processing algorithm was performed on data
acquired in the free stream of the calibration unit (at y = 0°), which should theoretically
contain little or no vorticity. Figures 4.15 and 4.16 show this result plotted from a range of
2 m/s to 8 m/s for the two vorticity probes used in this research. It can be seen that at the
higher velocities, the noise level is on the order of 20 (1/sec.). This is relatively small,
since a typical vorticity time series has a standard deviation on the order of 80-90 (l/sec.)

with excursions over 500 (l/sec.) (Figure 4.17).

50

 

 

'V'V VVV , . . .
102929202322»? . . . . O O T
1.4mm
o o i

 

 

 

Figure 4.1 Geometry of spanwise vorticity probe.

 

Flow Direction

Figure 4.2 Perspective view of spanwise vorticity probe.

51

   
 

/ Copper Plating

D5 urn
[Tungsten
../

 

 

 

Figure 4.3 Geometry of a single hot-wire probe.

 

20 1 1 i t i l 1 l

   

132:7.334+4.142v°44

 

16»

l #1 J 1 l

14—

12>

 

 

 

l . I 1 I 1 1 l 1 1 I
8.50 1.00 1.50 2.00 2.50 3.00
Figure 4.4 Sample calibration and fit.

52

 

 

 

 

 

g 0014
g.“ 0.012 - ‘ _
m 0.010 — a _
1: — ‘ ‘
“g 0.008
g 0.006
0
Z 0.004 .

0.002

0.000 g

Velocity (m/s)

Figure 4.5 Normalized histogram of observed velocities from 25-July, 2001.

 

 

 

llll/ll l ll‘llllll
-2; —:

-3 h I I I I I l I I I I I I 0

2 3 i l i '5 6 7 i l ‘ 8
Velocity(m/s)

Figure 4.6 Example drift determination comparison taken on l9-July («02> probe, second

 

 

 

 

 

Percent Difference

 

 

 

 

 

 

 

straight wire).

21"'I"'l"‘l"'l"

 

 

    

20

19

18

VIITTFITTIjITIVlI

17

pre cal

 

4L 1 I 41 I l I I l l I J l I 1 1 I I I

 

 

 

combined
16 c 0 post cal
15 '- 4 l L L g P L I I I I I L J L 1 L I g L L I I
2 3 4 5 7 8

Velocity (m/s)

Figure 4.7 Pre-calibration data, post-calibration data. and the combined trend-line for 19-

July (<wy> probe, first straight wire).

  
      

 

     

 

'9'939396.

202......

Figure 4.8 Geometry of the X-wire probe.

54

 

 

 

 

30-0 ' ' 'firl I F' fl ' ‘ mn' ' 'jfifTVfi' ‘ I ‘ ' '

2.» l l
'5 25.0 ~ _
.2 ~ .
g 20.0 — Wire 1 2
'8 ~ .
+5 15.0 _ 1
...4 J
T: . .
E 10.0 _ Wll'fi 2 ‘l

5.0 — _

00 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14 1 1 4 1 14L144L

1 1 1 1
-40 -30 - 0 -10 0 10 20 30 40

angle (Y)

Figure 4.9 Sample data demonstrating the angle locating algorithm for X-wire processing.

 

 

 

 

 

 

Calibration Angle (Degrees)

 

Velocity (m/s)

Figure 4.10 Example drift determination comparison for an X-wire taken on 19-July

(<coy> probe).

 

1.5 -21.
Imweumm to A

 

 

D»

0.5 A

 

 

 

A A
0.0 ~ A —43 A
A
-0.5 . ,, A

D»

 

 

 

-1.0 -—— ,2,

-1.5 «-

 

 

 

0 5 10 15
File Number

Figure 4.11 Mean vertical angle measured over the evening of 18-July, 2001.

 

SI<U>t

 

 

 

 

 

 

 

tn-M JCrW-‘l tn tn+1 tn+M

20

Figure 4.12 Schematic of the micro-circulation domain used in the vorticity algorithm.

56

12.0

” .O..:‘.£
A 10.0 — .0’ u' 4
(I) . .-
2 , b ' I
\>: 8.0 _ .’ n d
.2 I
E 6.0 ~ .. II 4
O) .
> 40 — . I -
' + . .. Q Wirel
2.0 _ . .l. [j Wire2 *
0M'F..1=:!-.1- 1 1 1 1 d

0.0
0.000 0.050 0.100 0.150 0.200 0.250 0.300

 

 

 

 

Distance (inches)

Figure 4.13 Velocity of each straight wire on the Mitchel Probe as it was traversed through

the shear layer.

12.0

A 10.0

E

v 8.0

2:

8 6.0

T)

> 4.0
2.0

0.
0. 000 0. 050 0.100 0.150 0. 200 0. 250 0. 300 0. 350 0.400

 

 

I fl I I I I I I
l .llll .
l’ _l
l f .
_ If a
I

I I 0 Wire 1
i- . -1

.- [:] Wire2

I
r f d
t 1
0 M a 1 1 1 1 I

 

 

Distance (inches)

Figure 4.14 Collapse of shear layer traverse data used to compute (Ay).

57

<(oz> (1/s)

Figure 4.15 Vorticity probe and processing algorithm verification in a free stream of the

calibration unit.

<002> (Us)

40

o.)
O

20

10*

-10
-20
-30

 

 

 

 

E i
l 1.11 IIIIHI lII I1I II“ i. ll I 1‘ Allitti“
””1"" ' " ‘rl "1"!ll'1' “I l! l ' -
2 ‘ 3‘ 21‘ ‘ 3 ' 6‘ ‘7‘ ‘ ‘ 8
Velocity (m/s)

 

rrrrrr

p.—

kuin‘vv

 

 

“I!" Ill) II 0,").

L I I I I I I I I I I I I J I

C—1

 

)—

 

 

 

 

N fif—Tj—rTTI’I‘IV

4 5 6

Velocity (m/s)

Figure 4.16 Vorticity probe and processing algorithm verification in a free stream.

58

00

500
<(oz> (l/sec) 400

300 fi
200 E
100 E
0 7‘5

— 100
-200
-300

-400 ’ . . 1 1
(10 (12

 

V‘ITV

 

 

 

 

 

L P291 I I I I I

1(14 (16 (18

Time (see)

Figure 4.17 Sample vorticity time series from 25-July, 2001.

59

 

1.0

5.0 Results and Discussion

This chapter will serve to identify the characteristics of the near wall velocity and
vorticity measurements taken in a high Reynolds number boundary layer flow. The data
for the current research were acquired during three days at the SLTEST site. The ambient
conditions present at the SLTEST site varied with each day. Section 5.1 will review the
specific conditions which characterize each day that data were taken. Section 5.2 will
describe the statistics derived from the velocity and vorticity measurements which are rel-
evant to turbulence for these days. Section 5.3 will discuss the spectral properties of the
data taken at the SLTEST site. Section 5.4 will discuss the probability density functions

(PDF’s) of the vorticity and their relevance to this research.

5.1 Daily Specifics

The data that were acquired at the SLTEST site were examined using methods
described in the previous chapters. Acceptable conditions (constant ambient conditions
and accurate hot-wire measurements) existed on three days of experimentation, resulting
in three sets of data (to be referred to as 18-July, 19-July, and 25-July). Two probes were
used for the data taken on 18-July and l9-July, and one probe was used on 25-July. When

two probes were used simultaneously, one probe was used to measure <wz> and the other

probe was rotated 90 degrees and used to measure <3: >. For convenience and organiza-

y
tion, the probes will be referred to as the <t;*:_> probe or the < tz*\.> probe throughout the

rest of this thesis. The purpose of this chapter is to cover in detail the results obtained

from these data sets and compare statistical quantities over the three days. First, however,

60

the specific conditions of each day will be noted followed by the detailed analysis of the

data. Table 5.1displays the specific properties of each data set, including the probe mea-

), the Monin-

surement location (y ), the time duration of the data set (TD

measure uration

Obukov length L __ 0 bu km and the corresponding thermal stability parameter C

Martin

described in Chapter 2. A streamwise length scale L\, was also computed as

L = ET 5.1

x Duration

where 17 is the mean velocity over the entire data set.

5.1.1 18-Ju1y, 2001

Two vorticity probes were used on 18-July, 2001 to measure <coz> and <wy>.

Both probes were mounted 20 cm above the desert floor (y+ = 3800) separated by a
spanwise distance of 2.2 cm. The wind direction was from the south. Twenty-eight files
were acquired at 40 kHz, 60 seconds each. An analysis of the ambient conditions present
during the acquisition of these data showed that the mean friction velocity shifted signifi-

cantly after the 19th file had been acquired. The remaining 9 files were subsequently dis-

carded. The streamwise distance Lx for these 19 files was nominally 4500m. This

allowed for the small scale turbulent quantities to be well converged for this day. For

example, the 18-July data contained over 24,000 records of the streamwise Taylor micros-

cale (Lx/Iu z 24, 000). Conversely, it was not possible to resolve the large scales

present at the SLTEST site as a result of the extremely large scales present and the limited

window of time for data acquisition. For example, the 18-July data contained only 20

61

records of a typical boundary layer thickness (LI/8 z 20). The following paragraphs

present the ambient conditions of 18-July, including the mean wind speed, wind direction,
thermal stability parameter and friction velocity.

Figure 5.1 shows the steadiness of the prevailing wind on l8-Ju1y, spanning the
time period that data were acquired. The top triangles represent the data taken by the three
cup anemometer (located at y = 1.5 m), and the bottom circles and x’s represent the veloc-
ity measured by the two probes (located at y = 20 cm). Data were averaged over 19 one-
minute intervals. Figure 5.2 shows the direction of the wind over this same time period
(again averaged over 19 one-minute intervals) measured by both the wind vane and the

<c0y> probe. From this graph, it can be seen that the wind direction was not constant. The
variations were bounded by —8° S 73 l0 with a mean value of —4.41 ° and an RMS of
259" as observed by the <wy> probe. Since a visible trend was not observed in the hori-
zontal angle measurement, deviations from a mean value were assumed to be a result of
the one-minute averaging technique and not a result of a shift in the mean wind direction
(a shift in the mean wind direction was observed in the l9-July data, see the next section

for how this was handled). For the 18-July horizontal angle data, the mean angle over the
entire evening was subtracted from each individual data file, setting the mean flow angle
over the 19 files to zero.

Figure 5.3 shows the thermal stability parameter, Q, plotted against time for 18-
July, 2001, courtesy of the University of Utah. Data for this day were acquired from 7:50

10 8: 12 pm. As the figure shows, the MSU vorticity data were acquired in a period of

unstable thermal conditions in the range —3 < 2; < —2.

62

Figure 5.4 shows the friction velocity (at) as a function of time throughout the
H

evening of 18-July, 2001. The horizontal bars represent the mean friction velocity over
the entire time period that data were taken. The solid circles overlaid on top of the bars
corresponds to the mean friction velocity over the range of “accepted” files. Accepted
files were files under which the ambient conditions appeared constant (such as the thermal
stability parameter, the mean wind speed and direction, and the friction velocity). From
this figure, it can be seen that after the “accepted" range of files, the mean friction velocity
deviates from what appears to be a constant value, decreasing over time. The mean value
of the friction velocity over these “accepted” files was taken as a constant value for the

evening.

5.1.2 19-July, 2001

Two vorticity probes were also used on l9-July, 2001 to measure <wz> and <wy>.

The probes were again mounted 20 cm above the desert floor (y+ = 3800) and separated
in the spanwise direction by the same distance of 2.2 cm. The wind direction was from the
south. Sixty files were originally acquired at 40 kHz, 60 seconds each. These files were

reduced to 50 files due to a shift in the mean wind direction after the first 10 files had been

taken (these first 10 files were subsequently discarded). The spanwise distance Lx for

these 50 files was nominally 1 1,000m. This allowed for the small scale turbulent quanti-

ties to be well converged for this day. For example, the 19-July data contained over

336,000 records of the streamwise Taylor microscale (111/ I” x 336, 000). The resolution

of the large scales present at the SLTEST site for 19-July was better than 18-July, but still

63

not enough to fully resolve the large scale motions. For example, the l9-July data con-

tained 55 records of a typical boundary layer thickness (Lx/S z 55). The following para-

graphs present the ambient conditions of l9—July, including the mean wind speed, wind
direction, thermal stability parameter and friction velocity.

Figure 5.5 shows the mean wind speed (in one-minute averages) over the period
that data were acquired on 19-July, 2001. The three cup anemometer and both probes are
represented on this graph. The wind speed appears very steady over the fifty one-minute
intervals. Figure 5.6 shows the mean wind direction, in one-minute averages, over this
same period. A general trend was observed in the wind direction data over this time
period. This very low-frequency motion is commonly observed in atmospheric work.
The mean wind direction for 19-July was de-trended by methods frequently used in atmo-
spheric boundary layer work. De-trending is a common practice used to eliminate the ‘red
noise,’ or extremely low—frequency fluctuations, from the data [29]. De-trending basically
involves eliminating the visible trend to produce a constant mean value. The wind direc-
tion data that were acquired at the SLTEST site on l9-Ju1y were de-trended as follows.

The one minute averages of the horizontal flow angle throughout the evening were
independently curve fit for both the wind vane and the probe (see Figure 5.6). A mean dif-
ference was taken between the two curve fits, and the (negative) difference was then
added to the angle measurements recorded by the probe. This in essence shifted the probe
measurements down to the level of the recorded vane measurements. Finally, the (nega-
tive) value of the vane curve fit (corresponding to the proper abscissa location) was sub-
tracted from these readings, de-trending the parabolic shape and placing the mean value of

the probe angle measurements at zero degrees. This process effectively took the parabolic

64

shape of the wind direction measured by the probe and flattened it out across the abscissa.
This process allowed for the use of surrounding information to get more accurate approxi-
mations of the local mean values.

Figure 5.7 shows the stability parameter for the evening of l9-July, 2001. Data for
this evening were acquired between 9:41 and 10:41 pm. As shown, the stability parame-
ter increased quickly on this evening and reached a value near 0.6 over the period that the
data were acquired. This is a significantly large value, indicating a stable (or stratified)
ambient condition. The extent to which this thermal stratification affected the data will be

discussed throughout the rest of this chapter.

Figure 5.8 shows the mean friction velocity (uT)9 for the evening of l9-July,

2001. In this case, the friction velocity appears semi-constant across the entire range of
data taken. However, the “accepted” range did not include the first few files taken during
this evening due to a large direction change in the mean wind direction after the first 15

minutes.

5.1.3 25-July, 20011

On 25-July, 2001, only one probe was used to acquire data. The second probe
(used to acquire data on the previous days) was damaged beyond repair between data sets,

and therefore only records <cez> vorticity were recorded. The probe was mounted at y =

40 cm this time (y+ = 10, 300), and the wind direction was again from the south. Sixty-

five files were originally taken at 40 kHz, 90 seconds each. These files were reduced to 36
acceptable files due to a large shift in both the mean wind speed and direction (as well as

the friction velocity) after the first 36 files had been taken. The remaining files were dis-

65

carded. The spanwise distance L", for these 36 files was nominally 19,000m. This

allowed for the small scale turbulent quantities to be well converged for this day. For

example, the 25-July data contained over 481,000 records of the streamwise Taylor

microscale (Lt/A.“ == 481, 000). The 25-July data produced the largest streamwise dis-

tance Lx , but still was not large enough to accurately resolve the largest motions as evi-

—3 . . .
denced by the very low wavenumber (km 2 10 ) spectral d1str1but1ons. However, the

statistical quantities (17, v , etc.) indicated that convergence was achieved for all three data
sets. For example, the 25-July data contained 94 records of a typical boundary layer thick—

ness (Lx/S z 94). The following paragraphs present the ambient conditions of 25-July,

including the mean wind speed, wind direction. thermal stability parameter and friction
velocity.

Figure 5.9 shows the mean wind speed (one-minute averages) taken on 25-July,
2001. This plot shows a very steady velocity reading from both the three cup anemometer
(located at y = 1.5 1n) and the one probe used to acquire data on this day (located at y = 40
cm). Figure 5.10 shows the mean direction of the wind over this period, measured by the
wind vane. Only one probe was used on this day, so a probe measurement of the angle
was not recorded; see Chapter 4 for more detail. The mean wind direction as measured by
the vane was fairly constant, indicating the <cc,> probe was well aligned with the flow
direction throughout the data set.

The thermal stability parameter for the evening of 25-July, 2001 can be seen in

Figure 5.11. Data were acquired on this evening from 8:20 until 9:24 pm. This figure

66

shows that the entire data set fell within the accepted range to be called a neutral condition
(ICI _<_ 0.1 ). Figure 5.12 shows the mean friction velocity for the evening of 25-July, 2001.
Here, the friction velocity remained constant for the first hour, but steadily decreased after
that. As a result, the “accepted” files were limited to the first hour of data acquisition (36
files).

The format used to discuss the results will present the thermally neutral data set
(ZS-July) first followed by the thermally unstable ( 18-Ju1y) and thermally stable (19-July)
conditions respectively. Although the thermally neutral data were acquired at a larger dis-
tance away from the wall, they will still serve as the baseline condition when compared to
the two other conditions. An attempt to distinguish between the effects of probe location

and the effects of thermal stability will also be made.

5.2 Mean flow statistics

This section describes the mean flow statistics for each data set. The following
paragraphs will present the mean and root-mean-squared (RMS) values of the velocity and
vorticity components for each data set. Section 5.2.1 will describe the formulation of the
Taylor microscale and corresponding Reynolds numbers. Section 5.2.2 will provide a
detailed analysis of the dissipation estimate, and Section 5.2.3 will discuss the length and
velocity scales for each day.

Table 5.2 displays these mean and RMS velocity and vorticity quantities calcu-
lated from the data acquired on the three specific days. The data acquired on 25—July has
noticeably higher mean and RMS values of the velocity than the other two days. The data

from 25-July were taken at a probe location of y = 40cm, while the data from the 18th and

67

pl

Ur

)tt

19th of July were taken at probe locations much closer to the wall (y = 20cm). When
compared to each other, 18-July and l9-July had similar mean values for the three compo-
nents of velocity. However, the RMS values of l8-July were noticeably higher than 19-
July. This difference in the RMS values may be explained by the thermal effects dis-

cussed in Section 5.1. Data taken on 18-July were acquired under conditions that were
considered unstable (C < —0.1 ) while the l9-July data were taken under stable conditions

(C = 0.6 ). The unstable condition present in the 18-July data would cause higher fluctua-
tions from buoyancy effects. The stratification that occurs during the stable condition
would have suppressed the larger fluctuations on l9-July, causing the observed differ—
ences in the fluctuations between the two days.

The mean values of vorticity were not examined. From analysis of the vorticity
probe [12], the mean values have an uncertainty of i20 (Us). The calibration techniques
used on the probe did not ensure an accurate mean vorticity measurement. These tech-
niques did, however, ensure accurate fluctuation measurements. The RMS values of the
spanwise and transverse vorticity can be see in Table 5.2 as well. The vorticity RMS val-

ues for all three days was fairly consistent around 90 (l/sec.).

Table 5.5 displays these same flow data normalized by the friction velocity [ut,
(“1) or (“1), ] for each data set. Compared to the neutral condition (ZS-July), it can be
u .

seen that data from 18—July have significantly higher normalized fluctuation values. This
is due to the unstable thermal condition present during the time those data acquired. Con-

versely, data from l9-July show normalized fluctuation values that are lower than the neu-

68

tral baseline condition as a result of the thermally stable condition present over the data

SCI.

5.2.1 Taylor microscale

The Taylor microscale I and corresponding Reynolds number based on the
microscale RA were computed for each evening of data. The Taylor microscale is a well-
defined quantity that is often used to characterize a turbulent flow [24]. Measurements of
the Taylor microscale were available for each data set and were used to quantitatively
describe the flow by the corresponding Reynolds number, RA“

The Taylor microscale was computed for all three velocity components (if applica-

ble) from the respective autocorrelation of each time series measurement. The corre-

sponding Reynolds number based on this microscale was defined by

 

17K”
R = — 5.2
lu v
171‘,
R = _ 53
Iv v
(”Kw

w
for each velocity component. Table 5.6 shows the values of the Taylor Microscale and
Reynolds number for each day data were acquired.

The Taylor length scales and the Reynolds numbers follow the same trends -- 19-

July has the smallest microscales and also the smallest RA values. The data from l8—July,

which appeared to be a very similar day initially, has similar I values but significantly

69

larger R}. values when compared to l9-July. This trend may be due to the thermal stabil-

ity issues, which suppressed ii on l9-July and increased L? on l8~July, causing the differ-

ence observed in the RI values. The data acquired on 25-July had the largest Taylor
microscale and also the largest R)» values.
An interesting trend was observed between the values of I“ and IV for each data

set. The ratio of Av / I“ for all three days on the SLTEST site was very near 1/3. How-

ever, for isotropic turbulence, this ratio is defined to be l/.,/2 (see equation 5.11) [24].

This relationship between also it“ and Iv explains the large discrepancy found between
the dissipation estimates “a” and “b” discussed in the next section. The relationship

between these two estimates is based on the IV = 7tu/ J2 isotropic relationship.

5.2.2 Dissipation Measurement

The dissipation estimate was treated separately due to the difficulty of the mea-
surement and its importance in the scaling of turbulence quantities treated in the following
sections. This section will discuss in detail the evaluation of the turbulent kinetic energy
dissipation at the SLTEST site.

As shown in Pope [24], the dissipation can be expanded as:

 

 

2
auiaui Buiaui 8 “i"i

e—2v '.'.‘..=v + -- =é+v—-—‘ 5.5
A U YU axiaxi 0x101". axiaxi

70

where E is the “pseudo-dissipation”. The last term of equation 5.5 is very small in virtu-

ally all circumstances and the consequent distinction between 8 and S is seldom made

[24]. As a result, the dissipation estimate becomes:

Buiaui

In Cartesian coordinates, equation 5.6 can be expanded as nine derivatives of the

fluctuating velocity components as:

 

 

3 = at t—I er 43—32 t—t ta +021 43—02 at

Because the direct measurement of all nine terms with adequate spatial resolution is diffi-

 

 

 

cult, equation 5.7 is seldom used to estimate dissipation. Instead, various assumptions are
made which allow for the terms to be reduced and combined. This allows for dissipation
to be more easily measured and estimated with less than nine derivatives.

The dissipation at the SLTEST site measurement location was computed using a
number of assumptions. Each method required the measurement of the spatial derivatives
of the velocity components in the streamwise, spanwise. and / or traverse directions. Spa-
tial derivatives in the streamwise direction were computed using the Taylor microscale

formation [21]

 

 

all; 2 u].
(——) = 2 7 5.8

where I“ is the Taylor microscale of the “i velocity component. Spatial derivatives in
i

the transverse and spanwise directions were only available for the u component of veloc-

71

 

ity. These derivatives were computed directly from the vorticity probe straight wires that
were separated by a fixed distance (Av or Az, depending on probe orientation).

The following paragraphs will describe the various assumptions and correspond-
ing methods used to compute the dissipation estimates. Each estimate will be denoted by
an alphabetical subscript to differentiate between the various methods. Table 5.4 displays
the results of these various estimates.

The most common method used to obtain 8 is to assume that the velocity fluctua-
tions and their derivatives are isotropic. With this assumption, the relationships among the

terms in equation 5.7 leads to the approximation:

814'
e = 15v 5; 5.9

Substituting in the result of the streamwise derivative from equation 5.8, the dissipation

 

can be computed from the u component of velocity as:
e = 30v—’— 5.10

where I“ is the streamwise Taylor microscale. Given the assumption of isotropic turbu-

lence, the relationship
Xv = xu/fi 5.11

is valid, and an equivalent statement of the dissipation can be computed as:

_ , 5.12
8b 15V—

using the measured wall normal Taylor microscale.

72

5|

0 u o "u '2 a u o
In flow that IS isotropic over all measured wavelengths, v = u , and the d1s31pation can

be estimated as:

L) l

8’7' z 15V—7_o 5.13

using the measured wall normal velocity fluctuations.

Similarly, in the assumption of isotropic turbulence IV = KW , and the dissipation can be

estimated as:

e = ISvli— 5.14

using the measured spanwise Taylor microscale.
In homogeneous, isotropic turbulence, the dissipation can be directly related to the

spanwise vorticity by [21]

8d = 3V0), . 5.15

This was calculated using the variance of the spanwise vorticity measured by the compact
vorticity probe.

The next group of estimates attempt to measure several of the terms of equation
5.7 with assumptions that are less stringent than perfect local isotropy. These are referred
to as the “semi-isotropic” relationships. The first assumption is that of “axisymmetric tur-

bulence.” A “semi-isotropic” approximation of E, as given by equation (14) of Browne et

al. [6], is given by:

 

 

 

 

014' 2 011’ 2 011' 2
= 3 — + 2 — + — 5-16
E" v 0x 0_\-' (72’.
Wygnanski and Fiedler [33] used a semi-isotropic calculation that imposed the condition:

I— 0 I—I 0I -0I

where only the last of these terms is measured. Equation 5.7 then takes the form:

I = {002 GI +05 III +507]

The results of these six methods (a -- f) are presented in Table 5.4. From these

 

 

 

 

 

 

 

 

 

results, it can be seen that the dissipation estimates span a large range of values. The iso-

tropic dissipation estimate from the streamwise velocity measurement (ea) predicted the

lowest value while the isotropic dissipation estimate from the lateral velocity measure-

ment (8b) predicted the highest value. The semi-isotropic predictions fell between the

isotropic estimates. The dissipation estimated based on the streamwise velocity compo-

nent (8a) was found to be the most commonly used estimate throughout the reference lit-

erature. For the present data, this estimate was also consistent with the values inferred
from several of the other techniques. Hence, it was selected by the authors as the dissipa-

tion value used to scale the turbulent quantities covered in the remaining sections.

5.2.3 Flow length and velocity scales

This section describes the physical scales of the flow averaged over each data set

and explains how they were calculated. This section will describe the friction velocity

74

[u (“13).9 , or (”1) depending on the ambient thermal condition: see Section 2.2.3], the
u

I,

. . . . . +
kinematic vrscosrty V, the Viscous length scale 1 , and the Kolmogorov length and veloc-
ity scales, 1‘] and an respectively.

Table 5.3 shows the mean flow properties for the three evenings that data were
acquired. The friction velocity was derived from a propeller anemometer correlation to

the drag plate acquired by the University of Utah. The friction velocity recorded on 25-

July (u,C z 0.41 m/s) was significantly higher than the friction velocities measured over

the other two days due to the larger streamwise velocity present on this day. The friction

velocities for l8—July and 19-July were very similar to each other [(1408 2 (1%)“ 20.3

m/s] as a result of similar wind conditions.

The kinematic viscosity v was dependant on the ambient temperature of the SLT-
EST site and was supplied to MSU. by the University of Utah. The temperatures over
the three days were very similar. The ambient temperature during the data acquisition for
18-July was 30.1 degrees celsius. The data from l9-July and 25-July were acquired under
ambient temperatures of 26.7 and 31.0 degrees celsius respectively. The kinematic vis—

cosity of air did not experience a significant difference over this range of temperatures and

—5 2
therefore a constant value of v = 1.6X10 m /s was used.
From the kinematic viscosity and the dissipation (discussed in the previous sec-

tion), the Kolmogorov length scale, I] , was then computed as

1 1/4
I] 2(v‘ /s) 5.19

75

and the kolmogorov velocity as

an E (EV) ”4 5.20

Table 5.3 shows the Kolmogorov length scale I] for each data set. It can be seen

that this length scale was similar for 18-July and l9-July. It should be noted that n was

very insensitive to which dissipation estimate was used in the computation. The Kolmog-
orov length on 25-July was slightly smaller than the other two days.

The resolution of the vorticity probe used to acquire these data can now be com-
pared to the smallest length scales of the flow. More specifically, was the probe micro-
circulation region small enough to resolve scales this small? From Chapter 4, the two
probes had Ay values of 1.397 mm and 1.702 mm respectively. This resulted in a range of

311 < Ay < 4.511 , depending on the specific probe and the specific day. Wallace and Foss

presented an optimal range of 211 < A): < 411 for the best resolution and accuracy of veloc-
ity gradients [32]. Therefore, the vorticity probes used to acquire the data at the SLTEST
were determined to have adequate spatial resolution to resolve even the smallest flow

scales.

The viscous length scale 1+ was defined by equation 1.2. The viscous length
scales of 18-July and l9-July were very close to each other with vales of 1+ 2 0.05mm for

each day. The viscous length of 25—July was significantly smaller at 1+ x 0.04mm.

76

5.3 Spectral Properties

The focus of the current research involved studying the characteristics of local
isotropy under inherently anisotropic conditions. Kolmogorov’s hypothesis states that “at
sufficiently high Reynolds numbers, the small scale turbulent motions are isotropic” { 13].
In the current research, the probes were located at relatively near wall positions which
would prevent the condition of isotropy to occur over larger wavelengths. The current
research will investigate if Kolmogorov’s hypothesis of local isotropy does hold true for
the near wall data acquired at the SLTEST site, and if so, over what wavelengths does the
condition of local isotropy exist?

This section serves to analyze the spectral representation of the velocity and vor-
ticity components measured at the SLTEST site. Section 5.3.1 will present the spectral
representation of the velocity components. Section 5.3.2 will follow with the spectral rep—
resentation of the vorticity components of the flow. Section 5.3.3 will examine the spec-

tral properties of velocity and vorticity products.

5.3.1 Spectral representation of the velocity field

This section details the spectral representation of the velocity measurements
acquired at the SLTEST site. The following paragraphs will discuss the equations used to
perform this analysis. An isotropic model will also be formulated in this section and used
to serve as a point of contrast between the SLTEST data and purely isotropic turbulence.
Section 5.3.1.1 will discuss the results of the u component of velocity, while Sections
5.3.1.2 and 5.3.1.3 will discuss the v and w velocity components respectively.

The autospectral density (power spectrum) of each velocity component was

defined as [5]

77

~ _ )—j21tft
EuiuiU) _ ,lRuiul.(T)(

—00

d1: 5.21

where Ru u is the autocorrelation of the ith-component of velocity and f is the fre-

l l

quency under which the data were acquired. The correlation function R was defined as

 

a(r)b(t+At) 522

 

Rabmt) =

ab
where a and b represent the two signal of interest. If a = b , then R is the autocorrelation
of signal a. If a :6 b , then R is the cross correlation between signals a and b. For the

present data, the pwelch command in Matlab was used to compute the autospectral densi-

ties.

The wavenumber, kl, was computed from the frequency f as:

k1 = 27tf/17 5.23

where it is the mean velocity for the given data set. Wavenumbers have the units of m],
so very low wavenumbers correspond to very large motions in the boundary layer. The

wavenumbers were normalized by multiplying k, by the Kolmogorov lengthscale, I] .

The autospectral density was then computed as a function of wavenumber and normalized

by the kinematic viscosity and dissipation as:
5 1/4
Eui“i(kl )/(ev ) 5.24

for each E
uiui

Component.

78

An isotropic model was formulated based on the assumptions of homogeneous iso-

tropic turbulence. The model spectrum was computed from Pope as [24]:
2/3 —5/3 . .
500 = [Ce x 1.IL(KL) InmcnK) 5.25

where K is the wave number in three dimensional wave number space. The “universal

equilibrium” is represented by the function in square brackets, where C=1.5 represents the

universal constant. The value of 11K was determined for each day using equation 5.19
and the dissipation value (ea ). The functionst andfn are given by:

l

3
thrL) = ——E—L— 5.26
,lKL +eL
and
. 4 4 1/4
.fntan) = exp Ben—litmnK) +cn] . 5.27

These are effectively curve fits to the large and smallest scale motions respectively. The

value of cL=6.78 was used as suggested by Pope [24]. The value of L represents the inte—
gral, or largest scale of motion, and it is specified in terms of the ratio to the Kolmogorov
length scale: L/nK . This ratio was selected to provide the best agreement between the
model spectra and the large scale portion of the experimental spectra, using the measured
E1] spectra as described below. The resulting value was L = 6000 - “K .

The values [3:52, CTI=O were suggested by Saddoughi and Veeravalli [26] in their

measurements of the spectra in a high Reynolds number boundary layer. Pope [24] sug-

79

gested [3:21, cn=0.4. The values of [3 and CT] for the SLTEST data were selected to pro-
vide the best agreement between the model spectra and the small scale portion of the
experimental spectra. This resulted in values of [3:52, cn=0.25 (IS-July), [3:4, cn=0.25
(19-July), and [3:52, ano'2 (25-July). It should be noted that only the large scale and
small scale portions of the model spectra were best fit. The amplitude of the spectra for
the intermediate scales was determined by the universal constant C=l.5 for all three data
sets.

The modeled one dimensional energy spectra was calculated from E(K) from the

isotropic relation:
2
_ °° Em (Kl)
EW(K1) — [Kl—[l — ? :ldK 5.28

The one dimensional model spectrum of the v and w velocity components were

also calculated as:

Evv(Kl) : E

IV H’

_ 1 °° E(I<) KI 2
(Kn) _ 5 xlTl' +(Y) ]d1( 5.29

The isotropic model spectra demonstrate a large region of -5/3 slope for all three
velocity components. A similar slope is apparent in the SLTEST velocity data, but the log
scale of the normalized plots make distinguishing the actual slope difficult. The autospec-

tral densities of the velocity components were compensated by multiplying the spectra by

5/3 . . . . . .
kl . This compensation better differentiates between the Isotropic model slope of -5/3

and the actual slope of the SLTEST data. Any region of -5/3 slope would flatten out into a

80

horizontal line, making deviations from this isotropic slope more apparent. The compen—

sated spectrum was obtained for the EM u component as:

—2/3 5/3
8 k1
“1H1

(kl ) 5.30
for both the modeled and experimental spectra.

5.3.1.1 u-component spectra

This section presents the spectral representation of the u-component of velocity
compared to the isotropic mode] spectrum. The thermally neutral condition (25-July) will
be presented first followed by the thermally unstable (18-July) and stable (19-July) condi-
tions respectively. Both the normalized and compensated spectra will be presented for
these data.

Figures 5.13 through Figure 5.18 show the normalized autospectral densities of the
fluctuations of the u—component of velocity for all three data sets. From the normalized
autospectral density on 25-July, it appears that the model spectra accurately resembles the
longitudinal velocity spectra measured at the SLTEST site for high wavenumbers. The

data appear to follow the -5/3 power law over a large range of wavenumbers (over 3
decades of kin) corresponding to the very high Reynolds number trends observed
through experiments [24]. The compensated spectrum for the same data show the same
character as the model spectrum, but the experimental spectrum never reaches the ampli-

tude of the model spectrum. The experimental spectrum also appears to fall off for lower

wavenumbers faster than the model spectra. The model spectra breaks away from the -5/3

81

region very abruptly, whereas the experimental spectra drifts out of the —5/3 region very
gradually.

Figures 5.15 and 5.16 show the normalized and compensated longitudinal
autospectral densities for 18-July. As can be seen, the two follow the same trend over
larger wavenumbers, but the experimental spectrum overshoots the predicted peak value.
Experimental data by Saddoughi and Veeravalli demonstrate a similar characteristic [26],
but show a flatter region for moderate wavenumbers. The SLTEST data for 18-July does
not appear to contain a region of -5/3 slope. This is very evident by examination of the
compensated spectrum. This lack of a constant region is contrary to what is expected from
high Reynolds number isotropic data (as the Reynolds number is increased, one would
expect the wavenumber range over which this “flat” region covers to expand). Since the
probes were located much closer to the wall on this day (when compared to the 25-July
data), the anisotropic effect is much more evident. This can be seen in Figure 5.16 where
the magnitude of the compensated spectrum tails off quickly for lower wavenumbers.

Figures 5.17 and 5.18 show the normalized and compensated longitudinal
autospectral densities for 19-July. Similar to the 18-July data, these data compare well to
the isotropic model spectra at high wavenumbers, but deviate over the range of moderate
to low wavenumbers. The data exhibit the same overshoot in the compensated spectra and
no distinguishable -5/3 slope. The effect of the wall on the moderate to large scale
motions can be readily observed in the compensated spectrum.

Thermal effects appear to have played little role in the u component velocity spec-
tra. The data acquired under an unstable condition (18-July) closely resemble the data

acquired under the stable condition (19-July). The neutral condition data show a smaller

82

amplitude and a more evident -S/3 slope, but were also acquired farther away from the

wall.

5.3.1.2 v-Component Spectra

The spectral representation of the v-component of velocity compared to the isotro-
pic model spectrum are presented in this section. The thermally neutral condition will
again be presented first followed by the thermally unstable and stable conditions respec-
tively. Both the normalized and compensated spectra will be presented for these data.

Figures 5.19 through 5.24 show the normalized and compensated autospectral den-
sity of the v-component of velocity for all three data sets. The data acquired on 25-July
have a much lower amplitude than the isotropic model. However, the general shape of the
compensated spectrum resembles the experimental data presented by Saddoughi and
Veeravalli [26]. A region exists over moderate wavenumbers where the —5/3 compensated
spectrum appears flat. The wall still appears to effect the lower-to-moderate wavenum-
bers.

For 18-July and 19-July, the general character of the spectra appear very similar to
each other, but they are very different than the model spectra. The effect of the wall is
more evident when compared to the u-component spectra for each data set since we are
now dealing with motions in the wall-normal direction. The data appear to follow the iso-
tropic model for very high wavenumbers, but break away from the model spectra very
early. The compensated spectra show a distinguishable hump for wavenumbers just out—
side of the dissipation range. This trend was also observed by Saddoughi and Veeravalli

[26]. However, the experimental spectra never reach the predicted amplitude of the model

83

spectra and drOp off quickly as the wavenumber decreases. In fact, there is little contribu-
tion to the autospectral density from the very low wavenumbers.

Again, thermal stability does not appear to play a large role in the spectral repre—
sentation of the v-component of the velocity. Data from 18-July and 19-July demonstrate
very similar trends, but differ from 25—July. The main differences between these three

data sets are attributed to the probe location.

5.3.1.3 w-Component Spectra

The autospectral densities representing the w-component of velocity were avail-
able for the two evenings when two probes were used to acquire data (18-July and 19-
July). Figures 5.25 through 5.28 show the normalized and compensated spectra for these
two days. The 19-July data show the large spectral hump consistent with the previous
component spectra. The data also appear to level off before dropping off quickly for
lower wavenumbers. The data from 18-July show a different trend, never reaching the

amplitude of l9—July. These data do not show a pronounced spectral hump. Instead, the

data exhibit what appears to be a constant slope (k” with n< -5/3) over moderate wave-
numbers. The data then tail off quickly for low wavenumbers. The effect of the thermal
condition between these two days cannot be determined since the neutral condition was

not recorded to serve as a baseline condition.

5.3.2 Spectral representation of the vorticity field

The vorticity data taken at the SLTEST site were also analyzed in the frequency
domain. This section serves to present the spectral representation of the vorticity compo-

nents measured over the three days. The following paragraphs will discuss the equations

84

used to perform this analysis as well as formulate the isotropic model to which the results

were compared. Section 5.6.1 will discuss the results of the <0),> vorticity component

while Section 5.6.2 will discuss the <00V> vorticity component.

The autospectral density of each vorticity component was defined as [5]:

00

Ear“) : iRw.w.(T)
I l I

—oo

".12 1tf T
(J

(11? 5.31

where R mi (”1'

is the autocorrelation of the ith‘component of vorticity (computed accord-

ing to equation 5.22) and f is the frequency with which the data were acquired. For the
present data, the pwelch command in Matlab was use to compute the autospectral densi-

ties.

The autospectral density was normalized by the kolmogorov length T] and velocity

2
Ewi(kl )n/un 5.32

(for the <(0i> vorticity component) and computed as a function of the wavenumber, k],

computed from equation 5.23. This autospectral density was plotted against the normal-
ized wavenumber.

The model spectra, which assumes homogeneous isotropic turbulence, was calcu-
lated using the same constants which best fit the u component of velocity for that day (see
Section 5.5). Antonia et a1. [3] derived the isotropic relationship between the one dimen-

sional vorticity spectra and the energy spectra:

85

K 00
_ I E(K).
0.1709) - 7 07"“

(1

1°° E(1() K2

+Kl2ldK. 5.33
4 K1

In the assumption of isotropic turbulence, the vorticity spectrum is independent of orienta-

tion. Therefore, the model used to compute (1)“‘ is the same model used to compute (1)2.

. . . . 5/ 3
The u,v, and w velocrty autospectral densrtres were compensated wrth k1 to bet-

ter differentiate between the —5/3 slope of the model and the actual slope of the SLTEST

data. A similar power law does not exist for the vorticity data. However, it is instructive

to plot the vorticity autospectral densities compensated as k] (1)“). This compensated spec-

trum better demonstrates the relative contributions of the different scales of motion to the

vorticity variance:

((0)2 = ”(0(0)de = jkl ~¢w(kl)d(ln(kl)) 5.34
0 0

The integrand of the second right hand side of equation 5.34 is plotted (in semilog format)
to show the contributions from each normalized wavenumber.

The autospectral densities of the vorticity showed a large contribution from very
low wavenumbers. The autocorrelation of the vorticity data was also included in this sec-
tion for a more complete description of this low wavenumber contribution. The autocorre-
lation was performed according to equation 5.22, and is presented at the ends of Sections

5.6.1 and 5.6.2.

86

5.3.2.1 <wz> Spectra

This section presents the spectral representation of the «02> component of the

vorticity compared to the isotropic model spectrum. The thermally neutral condition (25-
July) will be presented first followed by the thermally unstable (18-July) and stable (19-
July) conditions respectively. Both the normalized and compensated spectra will be pre-

sented for these data. This section concludes with the presentation of the autocorrelation

of the <0)Z > vorticity component.

Figures 5.29 through 5.34 and show the normalized and compensated <wz>

autospectral densities for all three data sets. The normalized model spectra do not accu-
rately predict the measured spectra for any data set. The model spectra level off asymptot—
ically as the wavenumber decreases, whereas the measured spectra continues to rise. This
behavior indicates major contributions from wavenumbers much larger than the distance
between the probe and the wall. This phenomenon is likely due to the pressure distribu-
tion along the wall. According to Panton, “a vorticity flux from a wall results from the
pressure gradients along the wall” [23]. This relationship is described by the following

equation [23]:

0;) 8(1) ~

5 = 418—}, 5.35

The compensated autospectral densities show the actual contribution of these
observed large scale motions to the vorticity variance. The data acquired on 25-July com-
pares well to the isotropic model spectrum. These data show the same general shape as

the model spectrum but with a larger contribution from the lower wavenumbers. The

87

compensated vorticity spectrum for 18-July follows the same basic trend as the model
spectrum, but demonstrates a much larger amplitude. Given that the unstable boundary
layer involves density variations and given the non-barotropic source term in the vorticity
transport equation, it is rational that the vorticity variance is larger for 18-July. These data
also show the larger contribution from the low wavenumbers. The experimental spectrum
from the 19-July data does not follow the model spectra well. Instead, the experimental
spectra demonstrates a large initial spectral hump followed by a second spectral hump
occurring at a much lower wavenumber.

Autocorrelations of the <cez> vorticity were calculated to more thoroughly investi-

gate the size of the large scale motions contributing to the vorticity. The autocorrelations
were determined from equation 5.22. Figures 5.35 and 5.36 show the autocorrelations of

the <wz> vorticity for each day. In these figures, the l9-July data show the first zero of
the <wz> vorticity autocorrelation to be at a location corresponding to 13m. The 18-July

data show the first zero of the autocorrelation occurring at a location corresponding to

35m. Both of these measurements were at 20cm above the desert floor and their nominal

+ .
y values were 3800. The 25—Ju1y data, from a distance of 40cm above the desert floor,
shows the first zero crossing of the autocorrelation at 43m. The observed differences in
these data may be caused by some combination of the thermal effects, a Reynolds number

dependence, or the distance from the floor. The Reynolds number based on the Taylor

microscale RA increases from 19-July to 18-July to 25-July (see Table 5.6), meaning that

the first zeros in the autocorrelations of the <31: ,> vorticity time series’ increase with RA'

The data appear to show a similar Reynolds number dependence when plotted in semilog

88

format. The initial correlation of the vorticity decreases at a more rapid rate as RA

increases.

5.3.2.2 <wy> spectra
This section presents the spectral representation of the <(0v> component of the

vorticity. The <0)“. > component of the vorticity was not acquired over the thermally neu-

tral condition (25—July). As a result, this section will only present the unstable (18-Ju1y)
and stable (19-July) conditions. Both the normalized and compensated spectra will be

presented for these data. This section concludes with the presentation of the autocorrela-

tion of the <00), > vorticity component.

Figures 5.37 through 5.40 show the normalized and compensated <wy> autospec-

tral densities measured on 18-July and 19-July. These data appear to exhibit the same

character observed in the normalized <wz> spectra. The model spectra level off for lower

wavenumbers while the measured spectra continue to increase over this range. This dem-
onstrates a significant contribution from large scale motions to the vorticity fluctuations.

Although my at the wall itself is zero, there may be a flux of toy vorticity out of the wall.
This flux is dependant on the distributions of cox and col on the wall itself [23]. This rela-

tionship is described by [23]:

am. 800 8(1),
)._ x

W _a_x+a?' 5.36

evaluated at the wall.

89

The compensated <60 > vorticity spectra for 18-July exhibit two humps separated

y

by over a decade of normalized wavenumber. This is not the trend observed in the com-

pensated <wz> autospectral density for 18-July. This same anisotropic character was
observed on 19-July. The compensated <wy> data exhibit only one peak at high wave-
numbers. The <c02> data from the same day exhibited two peaks.

Autocorrelations of the <0: > vorticity component were computed in order to

y

observe the larger length scales present. Figures 5.4 l and 5.42 shows the autocorrelations

of the <0) > vorticity for each day. The l9-July data show the first zero of the <60 > vor-

Y y

ticity autocorrelation to be at a location corresponding to 225m. The 18-July data show
the first zero of the autocorrelation to be at 240m. A typical boundary layer thickness was

on the order of 150m.

5.3.3 Velocity-vorticity products

Spectral analysis was also conducted on the products of the velocity and vorticity
flow components. The following paragraphs will discuss the methods used to examine the
products of the velocity components as well as the velocity-vorticity products. These
methods including the autospectral density of the product, the cross-spectral density of

the two components and the coherence of the two components. Section 5.3.3.1 will cover

the u'v' velocity product while Section 5.3.3.2 will cover the u'w' velocity product. The

velocity-vorticity products that were examined in this study included v'<(0z'> and
w'<(r)y'>. Section 5.3.3.3 will discuss the significance of the velocity-vorticity products

and present the results of the v'<007'> product analysis. Section 5.3.3.4 presents the

90

w'<(1)v'> product. Table 5.7 displays the dimensional statistics of all the velocity and

velocity-vorticity products while Table 5.8 shows the normalized correlation coefficients
of these products.
The spectral representation of the velocity and velocity-vorticity products was

examined in two ways. The autospectral density of the combined product was examined

as well as the co-spectral density of the two components. The autospectral density ((Du u
i j

for velocity products or (bum. for velocity-vorticity products) of the product was com-

1 J
puted as follows. A time series of the desired product was constructed by multiplying the
two times series together. The autospectral density was then calculated from this single

time series according to equation 5.21. Autospectral densities including only the velocity
5/3 . . . . . .
products were compensated by k1 . Autospectral densrtres of the velocrty-vortrcrty

products were compensated by kl .

The co-spectral density was defined as [5]:

., .
Ewm = j R1,.11.(T>"'"md‘f 5.37
l J l .l
01'
., .
511.111.“) = ] Ruwroe’mtm 5.38
l J l .l

for the velocity product or the velocity-vorticity product respectively. In these equations,

Ru u is the cross correlation of the velocity components and R“ (0 is the cross correla-
i j i .i

91

tion of the velocity-vorticity components, determined from equation 5.22. The co-spectral
densities were calculated in Matlab using the csd function.
Further correlations between the velocity and vorticity components were investi-

gated by examining the coherence the two signals. The coherence was defined by

2

u.u.
’ .l

Eu.u.(kl)Eu.u.(kl)
l .l .l

l

 

E (kl)!

 

H (k1) = 5.39

11.11.
1 1

where Eu.u.(kl) is the autospectral density of the ”1' component and Eu.“ (k1) is the
l l 1 j

co-spectral density of the “i and 14]. components.

5.3.3.1 u’v' product
This section serves to present the results of the u'v' product for the three data sets.

The statistical value of rT—v' will be presented for each day as well as the normalized coef-

ficient. The autospectral density of the product, the co—spectral density and the coherence
will also be examined. The data will be presented with the thermally neutral data first (25-
July) followed by the thermally unstable and thermally stable data (18-Ju1y and l9-July

respectively).
The dimensional value of u—'_v' for all three days was fairly consistent, varying from

-0.07 to -0.11 (m2/s2). The normalized correlation coefficients, however, varied signifi-

cantly between days. The neutral condition (25-July) had a value of u'—v'/ui = -0.67.

— 7
The 18-July data had a normalized value of u'v'/(141)“ = -0.96. This larger value present
ll

92

on 18-July was a result of the thermally unstable condition present. The data taken at the
same probe location on l9-July had a coefficient of only u'—v'/(ut)2 = -0.77. This resulted
S

from the stable condition that occurred on this day. The unstable condition caused larger
fluctuations from buoyancy effects. The stable condition suppressed these fluctuations,
causing the observed differences between the data sets acquired at the same location.

Figures 5 .43 through 5.48 show the normalized and compensated autospectral den-
sities of the u'v' product for the three data sets. The data follow a slope slightly different
than the -5/3 power law observed in the velocity spectra. The compensated spectra for all

three cases show a peak between 0.07 < kln < 0.1 , followed by a steady decline as wave-
number decreases.

Figures 5.49 through 5.51 show the normalized co-spectral densities of the u' and
v' velocity components for all three data sets. In isotropic turbulence, the u'v' co-spectral

density is zero. For linear shear flows, the u'v' co-spectral density decays more rapidly

. —7/3 —5 /3 .
than the E” autospectral densrty (as kl compared to kI ) so that the anisotropy

decreases with k] [24]. The u'v' co-spectral density from the SLTEST site data decays at
a faster rate than the predicted -7/3 slope for high wavenumbers.

Figure 5.52 shows the coherence of the u' and v' velocity components for all three

days. In this figure, all three sets of data steadily decrease until kit] 2 0.02, where they

level off just above zero. Zero coherence of the u'v' product is a necessary condition for

local isotropy [26]. The SLTEST data indicate the presence of this necessary condition

for a region of local isotropy spanning nearly two decades of kit] (including the dissipa-

tion region).

Thermal effects did not appear to play a large role in the u'v' velocity product

. . “T". 2 . . .
spectra, but were evrdent 1n the u v /uI statistic for each evening.

5.3.3.2 u'w' product
This section presents the results of the u'w' product as determined from the two
days during which data were acquired. The statistical value of u'w' will be presented for

each day as well as the normalized coefficient. The autospectral density of the u'w' prod-

uct, the co-spectral density and the coherence will also be examined. Since the thermally
neutral data (25-July) was not acquired for these products, the data will be presented with

the thermally unstable data (18-July) first followed by the thermally stable data (19-July).

The u'—w' product was available for 18-J uly and l9-July and showed a much lower

correlation than the W statistic (see Table 5.7 and Table 5.8). Figures 5.53 through 5.56

show the normalized and compensated autospectral densities of the u'w' product for these

two days of data. The data do not demonstrate the same region of -5/3 slope observed in
the single component velocity data. The compensated data peak around a normalized

wavenumber of 0.15 with apparent linear slopes on either side.
Figures 5.57 and 5.58 show the normalized co-spectral densities of the u' and w'
velocity components. Again, the data do not appear to follow the predicted -7/3 slope for

linear shear flows [24]. Figure 5.59 shows the coherence of the u' and w' velocity com—

94

ponents for 18 and 19-July. The data show virtually no coherence over the range of
recorded wavenumbers, as is expected for a flow that is “two dimensional” in the time

averaged sense. This character is evident in both sets of data, but it is more amplified in
the data taken on 18—July. The u'w' product does not seem to be effected by the ambient

thermal condition.

5.3.3.3 v'<(0z'> product

The velocity-vorticity products are important when viewed in the context of the
Reynolds averaged Navier Stokes equations. The time averaged momentum equation for

the u component of velocity can be presented in the form [25]:

5.40

 

21—4 1 2 u 811'
Dr p 01- Oy 82.

where
+ w—f + —- 5.41

is the material derivative. Assuming the pressure gradient and viscous effects are negligi-
ble, and ignoring the streamwise and spanwise derivatives, equation 5.40 can be reduced

to:

 

1317 175'
E _ — a), 5.42

where the right hand side of equation 5.42 is the gradient of the Reynolds shear stress.

Using the tensor identity [31]

 

r —— l a 1 r
—u .u.. _ — Eijkujwk + £57110]. 5.43

 

95

the gradient of the Reynolds shear stress can be decomposed to include contributions from
the velocity-vorticity products. Using 1': 1 and ignoring the streamwise gradients, equa-

tion 5.43 reduces to

a __ _ __
— —— u'v' 2: V0)” — Wu) , 5.44
a)» 1. .\

This section serves to present the results of the v'<(1)7'> product as seen over the
three days data were acquired. The following section will present the findings on the
w'<00y'> product. The statistical value of v'wj/ 17(1)Z will be presented for each day. The

autospectral density of the product, the co-spectral density and the coherence will also be
examined. The data will be presented with the thermally neutral data first (ZS-July) fol-
lowed by the thermally unstable and thermally stable data (18-July and 19-Ju1y respec-

tively).
The correlation coefficient, 11107796)? was found to be a relatively small quantity

over all three data sets. Data from 18-July indicated a positive quantity (0.02), while data
from 19 and 25-July indicated a negative coefficient (-0.03 and -0.004 respectively). Fig-

ures 5.60 through 5.65 illustrate the normalized and compensated autospectral densities of

the v'<0)z'> product for the three days data were taken. The compensated spectra for 25-

July and 18-July show a similar peak at high wavenumbers and a similar slope over mod-
erate wavenumbers before tailing off over the smallest wavenumbers. The data for 19-
July show the same initial peak at higher wavenumbers, but show a region of almost con-
stant value over the moderate wavenumbers before finally tailing off for low wavenum-

bers.

96

Figures 5.66 through 5.68 show the co-spectral densities of the v' velocity compo-

nent and the <w7'> vorticity component. These data appear very similar over all three

days, and have a very small region demonstrating the -7/3 slope. This -7/3 slope is pre-
dicted for the co-spectral densities of the velocity components for linear shear flows [24],

but was shown here to serve as a point of comparison.

Figure 5.69 shows the coherence of the v' and <(1)7'> components for all three

days. It can be seen that all the data exhibit the same trend in the coherence. The v' and

<(0,'> components are highly correlated over a very small range of wavenumbers. The
<.

coherence peaks at a value of 0.8 for a normalized wavenumber of about kln z 0.35 (cor-

responding to kl l+ : 0.05 ). The trend drops off fairly quickly (but not symmetrically)

on either side of the peak.

5.3.3.4 w'<(1)y'> product
This section serves to present the results of the w'<(1)\,'> product as obtained from

the two days for which data were acquired. The statistical value of w'wv'/w&)y will be

presented for each day. The autospectral density of the product, the co-spectral density

and the coherence will also be examined. The w'<(1)v'> product was not available on the

day with thermal neutrality. Therefore, the thermally unstable data will be presented first

followed by the thermally stable data (18-July and l9-July respectively).

97

The correlation coefficient, w'va 1226),, was found to be a relatively large quan-

tity over both data sets. The correlation coefficient (w'va 02(1),, 2 0.2) indicates a signif-
icant correlation between the w' component of the velocity and the <00v'> component of
the velocity.

Figures 5.70 through 5.73 show the normalized and compensated autospectral den-

sities of the w'<00v'> product. The character of these plots appears similar to the v'<(r)z'>

autospectral densities. The compensated spectrum from 18-July shows a flattened region
over moderate wavenumbers. The 19-Ju1y data show a large hump at higher wavenum-
bers followed by the decline to an almost constant value. The spectrum then tails off for

the lowest wavenumbers.

Figures 5.74 and 5.75 show the normalized co-spectral densities of w’ and <00y'>

for both days. The data show a linear decrease as the wavenumber increases, but the slope

is visibly not -7/3. Figure 5.76 shows the spectral coherence of w' and <00y'> for both

data sets. Both data sets show similar trends, although slightly offset in amplitude and

wavenumber. The general shape of the coherence is a large correlation at high wavenum-

bers. The coherence peaks around km 2 0.25 for 18-July and km 20.4 for 19-Ju1y.

The observed coherence drops to a value near zero for moderate wavenumbers before ris-

ing again for the lowest wavenumbers.

The correlation between the u' and <(0,'> measurements was also examined, but

provided no consistent character. Table 5.8 shows the correlation coefficient for u'<(1)z'>

98

varies significantly between the three data sets. Spectral analysis showed no coherence

between the two measurements. Figure 5.77 shows the three compensated autospectral

densities of the velocity—vorticity products for l8-July plotted together. The u'<(oz'> and
v'<(oz'> components show similar trend with a hump at higher wavenumbers, while the

w'<(1)y'> data show no hump and a region of constant value.

Figure 5.78 shows the same data for 19-July. Here, all three spectra show the
larger hump for higher wavenumbers and a fairly constant value over a range of moderate
wavenumbers. Figure 5 .79 shows this data for 25-July. The two spectra for 25-July show
the same large hump and semi-constant range. offset by what appears a constant magni-

tude.

5.4 Vorticity Probability Density Functions

The probability density functions (PDF’s) for the measured <(oz'> and <(0y'>

vorticity components were also analyzed. This section presents the normalized PDF’s for
the three data sets and it provides a discussion of the trends associated with Reynolds

number and / or thermal stability.

Figure 5.80 shows the normalized PDF’s for the <(02'> vorticity component. The
three days of data do not collapse very well, but instead exhibit a dependence on R70 The

kurtosis (flatness) of the of <(107’> PDF seams to increase with higher R). values. The sta-

tistical values of the PDF can be seen in Table 5.9. The Reynolds number of each day is

Shown in Table 5.6 and increases from 19-July through 25-Ju1y. It should be noted that

99

this dependence on RA is assumed independent of the thermal effects which may also

contribute to the skewness of the probability distribution functions.

Figure 5.81 shows the normalized PDF’s for the <(1)y'> vorticity component. The

two data sets do not collapse well. The statistics of the PDF can be seen in Table 5.10.

The flatness appears to decrease with an increase in RA’ but a specific trend could not be

inferred due to the uncertainties of the thermal effects.

100

Table 5.1 Data Set Properties

 

 

 

 

 

 

 

 

 

 

 

 

 

18'191)’ l9-July 25-July
ymeasure (cm) 20 20 40
y+ 3800 3 800 10,300
TDuration (min) 19 50 58.5
L, (m) 4583 11,108 18,779
V . - —5 . —5 -5
. [118051110 4.36X10 lSXlO 213X10
L
X
LMonin — Obukov (m) -1 '3 6'1 42-4
i -2.4 .52 .075

 

101

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, 8.0 — ———~-
Velocrty(mls) l A
7 0 -2 A -
A A ‘3 A
6.0 + A AA A A — A 1
A A A A A A
5 0 I 53
4 0 ”—55 U 5 6 6 6 5
4- 1 .
3.0 4— —
2.0 A 3-Cup (y=1.5m) _
X Omega-z probe (y=200m)
1-0 O Omega-y probe (y=200m) —
0.0 I T 1
7:45 7:55 8:05 8:15
Time (p.m.)
Figure 5.1 Mean wind speed for 18-July, 2001.
2.0
Angle (deg) /'\
0.0 44 .- , / T-
-2-o~ I
W at
-4.0 - (fl A;
-6.0 4 l ‘
0!. Esta-"'55" X ‘,
-8.0 3 Um " + Vane
\ I 3-0.1.1.-..—
' \J Probe
-12.0 1 1 1
7:45 7:55 8:05 8:15

Time (p.m.)

Figure 5.2 Mean wind direction for 18-July, 2001.

102

 

 

 

 

 

2.0 F I I i I i I l
C _ Rik—>1 _
I l
0 n} FM I I
'le I I
Y I |
P I I '
I I
-2 — | 4
I I
_ I I I
I I
|
-4 “ l I ‘
6:30 7:30 8:30
Time (p.m.)

Figure 5.3 Thermal stability parameter for 18-July, 2001. (>l< = Time period for MSU data

acquisition.)

0.35

 

0‘1)“ (m/S) . .- .

 

0.3 ~————.——"'—*

 

0.25 '-

0.2

 

0.15

 

 

 

0.1

 

- All

0'05 0 Used

 

 

 

 

 

O T T T i T l

 

7:40 7:48 7:55 8:02 8:09 8:16 8:24
Time (p.m.)

Figure 5.4 Friction velocity as a function of time for 18-July, 2001.

103

8:31

 

1"“ -—

 

 

 

Velocity (mls)

 

 

 

 

 

 

 

 

 

 

2'0 A BCup (y=1.5m) F
1 0 XOmega-y Probe (y=20cm)
' O Omega-z Probe (y=200m)
0.0 T l T 1
9:40 9:55 10:10 10:25 10:40

Time (p.m.)

Figure 5.5 Mean wind speed for l9-July, 2001.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g -440 __ _ #51323: 4 _
2’ ‘
< '6 O Q a 1
«2’3“
'8.0 .‘ —_;.‘
o. o
-10.0 7 . . . . O Vane I"
O
‘12-0 . 6‘" ° II Probe ”
”14.0 I T Y 1
9:40 9:55 10:10 10:25 10:40
Time (p.m.)

Figure 5.6 Mean wind direction for l9-July, 2001.

104

 

 

 

 

 

' ' l l ' 1 l l l I“ I 1 *tr 1
I I
C 0.8 I I ‘II
I I N
0.6 \n' 3 | .-I
' I
0.4 _. (.J I * I -—
' I< >1
0.2 —— I I a
I I
0 — I ~ I -
l |
-0.2 _. | | ._
I |
-0.4 __ I I ~
I I
l l l l l l l L l 3'. l l 1
7:30 8:30 9:30 10:30
Time (p.m.)

Figure 5.7 Thermal stability parameter for I9-JuIy, 2001. (>I< = Time period for MSU data

acquisition.)

 

 

0.4 «— ~g— "

 

 

 

0.35 j__ .

O
(“1)3 (m/s) (BMW. 000
0.25 ~-

 

 

 

 

0'2 0 used
0.15 —d| —

0.1
DIE

 

 

 

 

 

 

 

 

O T ‘F I T I 1

9:21 9:36 950 1004 1019 1033 10:48
Time

Figure 5.8 Friction velocity as a function of time for I9-JuIy, 2001.

105

 

 

10.0 4____- A“-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9.0 A
8.0 ”‘mflw—W
A 7.0 A WW A A
I»
O
E 6.0
V O
E 4.0 +———3— r- #
3.0 0 Probe (y=40cm) ”——
2.0 AS-Cup (y=1.5m) .—
1.0
0.0 I I I I 1
8:15 8:30 8:45 9:00 9:15 9:30
Time (p.m.)
Figure 5.9 Mean wind speed for 25-July, 2001.
31.0 ---- * 77777
29.0 ~——-
27.0 \ e
a 25 0 +__. X M A A
i=1 ' \J / V \J‘
Q 23.0 7'.‘ V
2’
< 21.0 3
19.0
17.0 ~>>
15.0 I I I I I
8:15 8:30 8:45 9:00 9:15 9:30

Time (p.m.)

Figure 5.10 Mean wind direction for 25-July, 2001.

106

 

 

 

 

I I I I I I I 1
I I l
C 0.6 _ I I -_
I l '
0.5 __ I | ..
| I
0.4 _ I | .4
I l
I |
03 — 4‘ >l< >l -
I I .
0.2 _ I I -.
I I
m I ”N“. l
O . ., ..l 31"— “2‘1" I , 3 - .. .l lI . 1
7:30 8:30 9:30

Time (p.m.)

Figure 5.11 Thermal stability parameter for 25-July, 2001. (>I< = Time period for MSU

data acquisition.)

 

 

u. (m/s) 0.5

 

 

 

 

 

 

 

 

0.2 -aII " —-
O. 15 O USBd _
0.1
0.05

O I I l I
8:20 8:34 8:49 9:03 9:18 9:32 9:46 10:01 10:15

Time

 

 

 

 

 

 

 

 

 

 

 

T T I I

Figure 5.12 Friction velocity as a function of time for 25-July, 200].

107

Table 5.2 Mean Dimensional Flow Parameters

 

 

 

 

 

 

 

 

 

 

 

 

 

 

18-July I9-July 25-July
a (m/s) 4.02 3.63 5.35
.7 (mg) -0.02 -0.02 -002
w (m/s) -0.003 —0.008 N/A
17 (m/s) 0‘89 0'74 l-OZ
fi (m/s) 0‘38 0'32 046
a, (m/S) 0.55 0.51 N/A
(:72 (ml/32) 0.79 0.54 1.04
1:5- (mz/sz) 0'14 0'10 0’21
Wj (mz/SZ) 0.31 0.26 N/A
(1); (Us) 845 94.1 84.7
(1')). (Us) 97.0 75.3 N/A

 

 

 

 

108

 

 

Table 5.3 Mean Flow Properties *

 

 

 

 

 

 

 

 

I8-July l9-July 25-July
“1 (m/s) 0.302 0.307 0.412
v (mg/s) 1.6 x 10'5 L6 x I0'5 1.6 x 10'5
“II (m/S) 0.046 0.044 0.048
+ 0.053 0.052 0.039
1 (mm)

 

 

 

 

*The values of at were computed in the assumption of thermal neutral-

ity. I8-July data were acquired under thermally unstable conditions and
l9-July data were acquired under thermally stable conditions. Soc Sec-
tion 2.2.3 for details.

Table 5.4 Dissipation Estimates

 

 

 

 

 

 

 

 

 

 

 

 

18—July l9-July 25-July
2 .3 . . .

8a (m ,b ) 0 27 0 24 0 32
5;. (”Q/33) 1.1 1.0 14

ab' (m2/s3) .20 .20 0.28
E (”s/S3) 0.33 0.57 N/A
C

8.1 ("p/S3) 0.34 .043 0.34
E) (m3/53) 0.62 0.61 N/A
8,- “Hz/S3) 0.32 0.4l N/A

 

 

109

 

 

Table 5.5 Normalized Flow Parameters *

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

18-July l9-July 25-July
2 13.28 I 1.8 13.0
at
D -0.08 -0.07 -0.06
“7
W -0.01 -0.03 N/A
.7;
i} 2.93 2.47 2.47
17.
.. 1.24 1.05 1.1 l
v
17.
2 1.83 1.67 N/A
it;
“I
—; 8.61 5.76 6.1 l
u'“/u
'_2 2 1.54 1.10 1.24
v' /uI
‘_2 2 3.35 2.79 N/A
w' /uT

 

*The values of 141

were computed in the assumption of thermal neutral-

ity. l8-July data were acquired under thermally unstable conditions and
I9-July data were acquired under thermally stable conditions. See Sec-
tion 2.2.3 for details.

110

 

Table 5.6 Taylor Microscale Parameters

 

 

 

 

 

 

 

 

 

 

 

 

18-July l9-July 25-July
7.” (m) 0.037 0.033 0.039
7. (m) 0.013 0.011 0.013
V
7H. (m) 0.024 0.015 N/A
R7. 2062 153.3 2510
14
RX 725 5 I4 850
V
RA 827 485 N/A
11’

 

111

 

 

 

 

 

 

 

    

 

 

 

_ U. .., 2
5 1/4 E 1;
E11(1<I)/(£V ) E 1
4 E
10 E 1
E 1
102 5 I.
E 1
100 if 1
1* Model 1
'2 : '2 d
10 g Q SLTEST ' 1
F 1 1 1111111 1 L1111111 1 1 1111111 1 1 1111111 1 1 1111111
-5 -4 -3 -2 -1 0
10 10 10 10 10 10
kIII
Figure 5.13 Normalized autospectral density of the u-velocity fluctuation (ZS-July).
0,5 . . ......, . .43."... . .......,
r- -1
-2/- 5/3 » a .
8 ku E11(kI) . /’ I
0.4 e O a
: / :
O 3 b / 6% 4
. ~ ‘1 -I
b gb 8 4
A 1 Q l
8‘? .
Model
0 SLTEST
1 11_11111 1 1 1111111 1 1 111111
-3 -2 -l 0
10 10 10 10

 

km

Figure 5.14 Compensated autospectral density of the u-velocity fluctuation (ZS-July).

112

 

*7

 

 

 

6 O
5 1/4 10 o oo
E11(kI)/(8V ) 0°
Hfi
HF
'00
-———— 8000
10‘2 O SLTEST
1 L1111111 1 1 1 11111; L 1LL1L111 1 1 1L111L1 1 1 11111
Hr5 10‘4 Hr3 H12 10'1 100
km

Figure 5.15 Normalized autospectral density of the u-velocity fluctuation (IS-July).

 

   

 

 

 

0,5 4. ...., . ......., ....fi... . ......
p O
-2/3 5/3 . ,
8 k1 E”(1(1) . if 1000
0.4 r 2....f' _
. 4%;
1- O ) 4, -
05:1:er
F (‘11.)1 ..
0.3 — SE; 5
0.2 —- . -
. $9 .
d9 0
~ 8
0, ; o — Model
~ 06 O SLTEST
” o
O O
().() 1 1 111111 1 1 1 111111 1 1 1111111 1 1 1 11J_111
10 5 10'4 10'3 10'2 10‘1 100

Figure 5.16 Compensated autospectral density of the u-velocity fluctuation (IS-July).

113

 

rT TTT—VY—Tr fl T TYYYVII ‘7 V VTY'V—YI Y Yfi‘VVi'l V V 7""in

    
 
  

 

 

 

 

6 0 o
5. “4 r o .:
El 1(kI)/(8V ) 10 ———iO°-'«~, ,
4 _ _
10 . 1
2 _
10 . 1
0 7' Model 1
10 r ‘ 1 1
Q eresr
-2 4 _
10 » .
'4 1 1 1 111111 1 1 1 1 11111 1 1 1 111111 1 1 1 111111 14 1 111111
10
-5 -4 -3 -2 -1 0
10 10 10 10 10 10

km

Figure 5.17 Normalized autospectral density of the u-velocity fluctuation (19-Ju1y).

 

0.6

—2/- 5/3
8 ku EI Kb)
0.5

1 L 1 1 .L 1

0.4

0.3
Model

  
 

0.2

  

SLTEST

0.1

 

 

0.0

 

kITI

Figure 5.18 Compensated autospectral density of the u-velocity fluctuation (19-Ju1y).

114

 

Y I lYll'll I l VT'TYY' V V 'YY'V'I V I I""" I Y VI'71YI

l1.‘ 1 1

 

E22(kI)/(€V5)l/4

111‘ 11111.41]

10

2
10

  

10
Model

   

10 O SLTEST

"U” 11"“ 111"“ IIqu VIII“ III“ 111“ TWWI‘ IIWWVHII‘ [I

 

 

11“ 1111‘ II.“ A.“ 1111” 11‘“ 1111114411

1 11111111 1 1 1111111 1 11111111 1 11111111 1 11111111

10'3 10'2 10"

 

10°

0|
M

km

Figure 5.19 Normalized autospectral density of the v-velocity fluctuation (25-July).

0.8 Y Y YV'I'VT V V YV'IV'I ‘ V TTTTYY' Y Y YYVVIV‘ Y r VYTTTYI

 

YVI

111112;].LJ1

I'IIYI

   
   

‘ V

.273 5/3
8 k1 E220(1)

.0
.1}.
I I I

  

III'II'IIIV

 

 

 

0.1
0'0 5 4 3 2 I i 0
10“ 10’ 10" 10‘ 10. 10
km

Figure 5.20 Compensated autospectral density of the v-velocity fluctuation (ZS-July).

 

T.

 

V T Y'Y'V'I V I 'YTYYYI T T rTIIWIl I Y 'YYY‘VI Y T I VVYI

 

 

 

6
5 1/4 10
E22(1<1)/ (8V )
O oOoq
104
102
10"
—— Model
10'2 O SLTEST
4 ..l l l
105 10'4 10 ‘ 10’-

km

Figure 5.21 Normalized autospectral density of the v-velocity fluctuation (IS-July).

 

0.7
0.6

2/3 5n 0'5
8‘ k1 3220(1)

 

 

 

0.0 V V ' “t“. 5- “ 1 1 1 1111.11 1 1 1 111111 1 1 1 111 ‘
10‘5 10‘4 10'3 10'2 10" 10"

km
Figure 5.22 Compensated autospectral density of the v-velocity fluctuation (IS-July).

ll6

”i...—

 

 

 

 
   

 

 

 

l l fl l l ' I
5 1/4
E22(ki)/(8v) _
4
10 T
2 _
10 -
o _
10 -
L
b Model
-2 __
10
_ O SLTEST
10-4 1 11111111 1 1 1111111 1 1 1 111111 1 1 1 111111 1 1 1111111
-5 -4 -3 -2 -1 0
10 10 10 10 10 10

km
Figure 5.23 Normalized autospectral density of the v-velocity fluctuation (l9-July).

 

0.8 +71%,HW, W", ..m", T.....,
-2/- 5/3
8 1kl 1320(1) ()7

Model ’ ‘

 
 
   
 
 
   

0.6 SLTEST

0.5
0.4
0.3
0.2 :
0.1

0.0 5 -4i 3 2 l ..0
10‘ 10' 10“ 10‘ 10‘ 10

VIYYVIVYTIIfi'V

'11!

1

  

1

 

 

 

Figure 5.24 Compensated autospectral density of the v-velocity fluctuation (l9-July).

117

 

5 1/4 10"
E33(k1)/(8V )

 

10‘2

 

 

1 1 1111111 1 1 1111_1_1L 1 141111111 1 1 1111111 1 1 111111

10'5 10'4 10‘3 10'2 10" 10°

km

Figure 5.25 Normalized autospectral density of the w-velocity fluctuation (IS-July).

 

    

 

 

 

0.8 F t 7 mm, . ......, , .mn, . ......, . ”my:
0.7 :— ,//—f—‘\ _:
0.6 3 / -
0.5 ‘— ' 1
-2/3 5/3 ;
8 k1 E330(1) . meow
0.3 :— 515? _
0.2 L 55%? _
: — Model
0-1 T ‘ o SLTEST 1
0:0 ; AM, > 1 l IL11111 1 11111111 1 1 1J11111 1 1 111114
10‘5 10‘4 10'3 10‘2 10" 10"

km

Figure 5.26 Compensated autospectral density of the w-velocity fluctuation (IS-July).

118

 

 

     

 

 

 

s 1/4 6 ' ' r "' ' r
E33(1<i)/(€\f) 10 ’
4 - _
10 » ‘
2 _
10 - 3
, F Model ‘
0 _ ..
10 ~ 1
__ O SLTEST q
-2 _ _
10 » ‘
10.4 . .......1 . .1 . . ......i . 1......l . ...L...L
-5 -4 -3 -2 -l 0
10 10 10 10 10 10

Figure 5.27 Normalized autospectral density of the w-velocity fluctuation (l9-July).

 

2n m 03
’5 -leE33(kl)

0.6
0.5
0.4
0.3
0.2

YITITYT'IV'

  

Model

  
 

Y'IYVIYI‘T‘

  

Q SLTEST

0.1
0.0

IVIIIVIII

 

 

 

10. lO~ IO— 10

Figure 5.28 Compensated autospectral density of the w-velocity fluctuation (l9-July).

119

 

ffV—Tm—Tr Y T VVVVTTT j’fi' VVIVVYI T TYYWTYT *7

 

 

 

 

 

 

  
    

 

 

 

2 r 1
E (k1)Tl/ 2 °
“)2 u“ 10 g—
” l
l ._ _
10 E
0 __ _
10
-l _ _
2 F "
"' 1 11111111 1 1 1111111 J 11111111 +1 1111111 1 l 111 1
10 -5 -4 -3 —2 -1 V0
10 10 10 10 10 10
km
Figure 5.29 Normalized autospectral density of the <wz> vorticity (ZS-July).
0.06 . , W . _. 4
k E (k )n2/ 2 . —— Model 4
l l * 4
(“z u” 0.05 ~ _
SLTEST
0.04 ~ —
O
,_ O
0.03 — _
0.02 - a
0.01 '_ .1
’ ‘l
o oo 1
0.00 - 1 ‘ 1 M1111 1 ‘ M'I‘,1 L4 111111 1 1 1 1 11111 1 1 1 111111
4 -l 0

10‘5 10' 10‘3 10‘2 10

km

Figure 5.30 Compensated autospectral density of the <wz> vorticity (ZS-July).

120

10

 

 

 

 

 

103 E o' . ...”,
Ew(k1)T]/Un2 2 0 ° 0
Z l() E— 0 (11300 0
I F '1
l() r
10" .
Io" :-
* —— M)d‘l
102 g ‘ "
: O SLTEST
l()‘3 b 1 1 1111111 1 1 1111111 1 1 1111111 1 1 111L111 1 1 141111
10‘5 10‘4 10‘3 10‘2 10" 10"
km

Figure 5.31 Normalized autospectral density of the <xz> vorticity (l8-July).

 

 

 

 

0.08 _ .1 ......., ......., ......n,
his (k1)n2/ 2 007: ’
ml "11 . : —— Model
,- S
0.06 .F o LTEST
0.05 E—
0.04 }
0.03 :—
: o
0.02 :— .
» Cb "
0.01 3° 0 050.9%
_ o
0.00 ’ . ......1
10‘5 10'4

 

km
Figure 5.32 Compensated autospectral density of the <LQZ> vorticity (l8-July).

121

 

 

1?

 

3

 

 

 

 

 

10 WT *‘T 1...... “'
E (k)n/u 2 E °°
(D 1 C 00
Z r1 2 .— 0% 1
10
1 L
10
0 .
10 5
-1 b
10 j
E Model
10'2 r
O SLTEST
10.3 r #1 111111 1 1 1 111111 1 1 1 111111 1 1 1 111111 1 1 1 11111
-5 -4 -3 -2 -l 0
10 10 10 10 10 10
km

Figure 5.33 Normalized autospectral density of the <coz> vorticity (l9-July).

0.10

 

 

 

 

 

 

2 2 ..-... . ......, . ..."... .11., 1 "I
klE (020(1) n / Ur] : Model
0'08 T O SLTEST j
0.06 — -
r 3%
0.04 F <3) 8) _
’- O O J
. (%> ‘
r- O ‘
0.02 — 0 00006) 4
000 h 1 11111111 1 ”.111, ”1.11.1 . 1 11.1111
-5 -4 -3 -2 -
10 10 10 10 10 ' 100
km

Figure 5.34 Compensated autospectral density of the <3cz> vorticity (l9-July).

122

 

 

 

0.100 :

0%“)2

0.050

 

 

0.000 ‘ 3,

 

 

 

19-July

-0050 1111.1,1111111 1 11

0 10 20 30 40
Length (m)

Figure 5.35 Autocorrelation of the <caz> vorticity for each day.

1.00

 

T

(Dz (”z 0-80 l9-July

0.60 L /
18-July

0.40

l

0.20 —
25-July

 

0.00 1 1,

 

_O 20 1 11 1111111 1 1 1111111 L41 111111 1 1 1111111 1 1 1 111111
C

 

 

10 10 10 10
Ax*

10-3 10-2 -| 0 I

Figure 5.36 Autocorrelation of the <wz> vorticity in semilog format, where

Ax* = [(Ax)/( lm)].

123

 

3
10 Y *7 T V ervl'

 

 

 

 

2
E0)y(kl)n/un : O
O
102 3 ”COW
10‘ 5
E
C
10° :
10" :—
10.2 :r -—— Model
E o SLTEST
'3 *- 1 1 1111111 1 1 1 111111 1 11111111 1 1 1 111111 1 1 1
10
10‘5 10'4 10‘3 10‘2 10'1

km
Figure 5.37 Normalized autospectral density of the <xy> vorticity (IS-July).

0.08 . .. .....l . . --....I . . . ...... fl . ......
2 2
klE my(kl)n /Un 0.07

0.06

 

0.05

YIYVTIrYIIIYY

YI—TY

0.04

IIY‘

0.03
0.02

 

0.01

 

fiYIjYYIYY

 

0.00
10'5

 

km

Figure 5.38 Compensated autospectral density of the <wy> vorticity (IS-July).

124

2

10 Y Y C YOYV" V V V I 71", T Y Y YYYYVI Y V V VYV'YI V V " 'YYY'I
OOO

 

2

E(k)/
(oylnun

T 71111

101

I I VII'YVI

1 00

 

r V 11"!"

  

10"

  

hkol

T V 'Vl'l"

Q SLTEST

10'2

I V VIYVI'I

 

 

'3 1 11111111 1 1 1111111 1 L1111_1_L1 1 1 1111111 1 1 1111111

10“
5 10'4 10‘3 10‘2 10'1 10

 

10.
km

Figure 5.39 Normalized autospectral density of the <-:.:-y> vorticity (19-July).

 

 
    
      

 

 

 
 

 

2 2 0.10 L , , , . . ”hm,
kiE (k1)Ti/
OQY un : hhukl .
0.08 P ‘ _
. O SLTEST
L
0.06 _
0.04 — d
0.02 — a
,. 0 000..
0 00 I 1 1 111111 A A LA ““l—’—’1—’T 1 111111 1 1 1 1 11111 I l 1 11111

10'5 10‘4 10" 10‘2 10" 100
km

Figure 5.40 Compensated autospectral density of the (303’) vorticity (19-Ju1y).

[25

 

 

0.100

 

wymy

0.050

 

 

0.000
19-Kny

 

 

 

41050 1 l . 1 . 1 . 1 .
O 50 100 150 200 250

Length (m)

Figure 5.41 Autocorrelation of the <50 > vorticity for each day.

y

 

1.00
0.80
0.60

my my

0.40

0.20

 

0.00

 

 

 

 

.—
_0 20 1 1 1111111 1 11111111 111 1111111 1 1 1111111 1 11111111
0

Figure 5.42 Autocorrelation of the <wy> vorticity in semilog format, where

Ax* = [(Ax)/( lm)].

126

Table 5.7 Dimensional Flow Statistics

 

 

 

 

 

 

 

 

l8-July l9-July 25-July
(7;. (mz/Sz) -0.09 -0.07 -O.ll
u'—w-' (mz/Sz) -0.014 -0.03 N/A
170.2 (m/sz) 16.8 -2.46 ll.9
3.57: (m/sz) 0.59 -().9 -0.l4
W (in/s2) 11.9 7.56 N/A

 

 

 

 

127

 

 

Table 5.8 Normalized Flow Statistics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

18-July l9-July 25-July
'7'". -0.96 -0.77 -0.67
u V
_2’
”I
—.—. -O.26 -0.30 -O.24
a
IT". -0.15 -0.26 N/A
‘7
“I
.—’. -0.03 -0.06 N/A
_“_’_
in},
u'w', 9.7 x 10'3 -l.4 x 10‘3 2.7 x 10'3
143/1+
. . 0.22 -0.04 0. I4
u (0 2
{4(1):
V'w'z 3.4 x 10'4 —5.0 x 10'4 -3.2 x 10'4
LIZ/1+
W 0.02 -0.03 -0.004
‘6):
. . 0.01 0.004 N/A
w u) y
ui/l+
w'm' 0.22 0.20 N/A
.v
Mb).

 

 

 

 

 

l28

 

 

 

 

104 : O. . ......, . . ......, . . ...-..g
51/4 5 ° 0 ‘
cI)uv(kl)/(€V) _ CoO 4
O

103 g 00% a
t ”a :
I 3C? i
L c:% -l
102 =— _.
10‘ g —.
E 3
t 2
10" g _

l 1 1 1 111111 1 1 1_1111111 1 1 1 1

l()
10'3 10'2 10" 100
km

Figure 5.43 Normalized autospectrall density of the u'v' product (ZS-July).

 

-2/3 5/3 0-6
8 k1 (Duv(kl) .
0.5 '—
0.4 ’—
0.3

0.2

lr‘l’TTTTI

I

0.1

l

 

 

0.0 '1 . ~
10"

 

 

Figure 5.44 Compensated autospectral density of the u'v' product (ZS-July).

129

 

Wm

 

I T V

     

-5/3 slope

 

5 1/4 ° 0 o
(Duv(kl)/(3V ) [03 00o
102

 

 

10' p
E
100 E.
-] h
10 '5:
E
'0-2 -3 1 1 1 1 1 1411-7 -1 O
10 10- 10 10

km

Figure 5.45 Normalized autospectral density of the u'v' product ( l 8-July).

 

-2/ 5/3 , r thWfi v . ,
E 3kl (Duv(kl) 0.7 I I

0.6 —
0.5 —

0.4 _

0.2 —

0.1 L

 

 

 

0.0 ‘ '
10

 

km

Figure 5.46 Compensated autospectral density of the u'v' product (IS-July).

I30

 

3 510“ , ,.,.,., 1 “WWW
10' f 5
5 1/4 5 0O x \ - l3 slope
(Duv(kl)/(€V) 2 : 09‘th

10 w ,

l

 

 

 

10 5
0 ‘
10
-1 ’
10 E ,_
'2 b L 4 1 1 1411 4 4 1 1 1 1111 m"?
10 -2 -l O
10 10 10

km

Figure 5.47 Normalized autospectral density of the u'v' product (l9-July).

 

0,40 s

e‘z’3kfi’3cpmik.) 0-35 r

0.30 1
0.25 L
0.20 l
0.15 —
0.10 l
0.05 l

000 1 1 1 111Ll 1 1 1 1 11111 L41 4 111111 ‘|‘
' - 0
10 10

1 1 1 1 4

 

 

 

 

10

km

Figure 5.48 Compensated autospectral density of the u'v' product ( l9-July).

131

4

 

    
  

 

 

 

10 c
C O
5 1/4 5 -7/3 Slope
l312(k1)/(8V ) 2 E d) 008 18 (go
10 F 0311 0 38
£— 0 13
O E
10 g
E-
_2 5
10 g
E
-4 3
10 g gag
E— O
‘6 : 1 1111111 1 1111111 1 1111111 1 11111111 1 111 11110 1 111111
10 -5 1.4 1.3 1.2 -1 0 l
10 10 10 10 10 10 10

km

Figure 5.49 Normalized co-spectral density of the u' and v' velocity components (25-

July).

 

  

 

 

 

4
10
5 1/4 0
E,2(kl)/(ev) 2 E O o -7/3 Slope
10 E oozooscp
O I O
10 g
g
10’2 g
r ®©
-4 ” 0o
10 E m
13%»
-6 : 111111111 111111111 1111111 1 1
10
- -3 -3 -
104 10 10 10l 100

Figure 5.50 Normalized co-spectral density of the u' and v' velocity components (l8-

July).

132

 

    

 

 

 

51/4 10 1 O
E12(k1)/(8V ) g o 00 O -7/3 Slope
1 o. m
102 E 1‘00 21%
P O o O
0 g o 9
10 g
2 E
10' g
E
-4 ;_
10 E %$
00
10'6 r °o
1 1 11111 1 1 1 111111 1 1 11 1 11111111 1 111111 1 1 111 1 111111
-6 5 -4 x 1 0 1

Figure 5.5] Normalized co—spectral density of the u' and v' velocity components (19-

July).

0.35 wrfi

 

0.30 — _

0.25 F o 1 _

T

H “V 0.20 A AA Xx -1

0.15

7 j f 1
D
l

0.10

l

0.05 —

 

 

 

0.00 ‘ ‘ ‘1
10

 

Figure 5.52 Coherence of the u' and v' velocity components for all three data sets.

I33

 

 

 

 

E O o
5 H4 i VX00\\ -5/3 slope
E
L
102 g
10‘ g-
E
I00 g
l()'1 E’
-2 b 1 1 1 141111
10
10'3 10‘2 10" 10"
km

Figure 5.53 Normalized autospectral density of the u'w' product (IS-July).

 

-2/3 5/3 . . . ..1jifi 111.111
3 k1 (pd/10(1) I T

1.50 ~ f Q _
.O 08
11.193
O
O
0 Q?) o
1.00 — o o 1% egg -
0 “if s g.
‘5) 3 .
O ‘13
O
0.50 H 0 WE)

0.00 ‘ ‘ ‘1‘4111’, 1 A 1111111 1 1111
10'3 10" 10" 10°

 

 

.-

 

km

Figure 5.54 Compensated autospectral density of the u'w' product(l8-July).

 

 
   

 

 

 

 

r 6' .1.-.., . fi-.fi...,
3 p 0
5 1,4 10 -5/3 slope
(Du 2(kl )ng) "
102 -
10l :
100 :
'1 1 1111111 4 1 1111111 1 1 111—L111:
10 _ _
102 10‘ 100
km
Figure 5.55 Normalized autospectral density of the u'w' product (l9-July).
1,2 . . ...”-..
—2/3 5/3 ’ l
8 k1 (pm/11(1) (Q <
1.0 — 1

coo

as)?
00000
@119

L O a .
0.8_ $63 @

000’

0.0 00
1%
“2%

 

 

 

0.6 l 00cm <9 31% _‘
p 00000 (32%
0'4 T 0 00 9g) ‘33) ‘
. O 0 1
02 h 1 1111111 1 1 1111111 1 1 111111log‘
10'2 10" 100

km

Figure 5.56 Compensated autospectral density of the u'w' product (l9-July).

I35

 

    

 

 

 

10 : O O o g) -7/3 Slope
El3(k1)/(evs)l/4 2 5 :0 memggofafig

10 r 00 ° 112%
E o 0 0000619195 <29

100 E
:5

10‘2 E— o 00

10'4 5 ° °
E

10.6 : 11111111 111111111 111111111 111111111 #10111

10'5 10'4 10‘3 10'2 10'l 10°
kITl

Figure 5.57 Normalized co-spectral density of the u' and w' velocity components (18—

July).

 

10 _
5 1/4 ; o o
E]3(k1)/(ev )

 

I" 1111111 111]“! 11"“ T11“ 11"“ llml‘ ”I“! llml‘ "W"

5—1
0
I1

 

 

 

0‘
Ji

' >-
h

I

«J

l
N

I

10. 10“ 10 10‘ 10 10 10

Figure 5.58 Normalized co-spectral density of the u' and w' velocity components (19-

July).

136

0.200 i f Y Y‘rrTYl Y 7 V VVVVVI Y V V VYVVV' V V V 'V'V'I

 

0.150 — >< 18-July -

UW

l
I

0.100

r
O

0.050

 

 

 

 

0000 1 1 1111111 A .111111111 1 1 1111111 1. 1__1__111_.L11
-

 

 

 

 

 

10‘4 10'3 10‘2 10'l 10°
kill
Figure 5.59 Coherence of the u' and w' velocity components (18, l9-July).
2 2 10.2 E 1 1 7‘ I fl 1111 f I
(Dv (alaqm /un E O
1
10‘3
10'4
10'5
E
-6 1 11111111 111111111 111111111 1 11111111411111111
10
10'5 10‘4 10'3 10'2 10“ 10°

km

Figure 5.60 Normalized autospectral density of the v'<(1)z'> product (ZS-July).

I37

 

 

 

 

 

10 C 111, fifi 11111, 1 1 1111, 1 1 111111, 1 1 111111,
k (I) (k 113/um2 E
l v I _
(0Z 1
-6 L -
10 : 1
-7 1 1 1011111 1 1 1 111111 1 1 1 1 11111 1 1 1 1111i 1 1 1 111“]
10 -5 -4 -3 -2 -1 O
10 10 10 10 10 10

km

Figure 5.61 Compensated autospectral density of the v'<(1)z'> product (ZS-July).

 

  
   

 

 

 

 

 

l()-2 E Y'V'l I Y T'YYYYI ' V """l ' Y1'V'I'l ' 7 VTVVVIE
2 2 C I
(I) k : :
V0)Z( 1)“ /u~n 1 0 O 1
10‘3 :—
10'4 g
E
10’5 g
' 1 1 1111111 1 1 1111111 1 1 1111111 1 1 1111111 1 11111
106 -5 -4 1% -7 -l 0
10 10 10‘ 10- 10 10
km

Figure 5.62 Normalized autospectral density of the 1"<(1),'> product (l8-July).

138

 

Y Y T Y

klcme<k1>n3l u,,2

10‘6

T TYTYYYI

 

7

fl
0

 

 

l0-7 1 111Q1L1 1 111L1LL114 1L111111 1 11111111 L111111

10'5 10‘4 10‘3 102 10’ 10°

 

km

Figure 5.63 Compensated autospectral density of the v'<(oz'> product (IS-July).

 

 

 

 

l()-2 E r 1 ‘1' T I rrrT Y] j Tl I.
2 2 E
(Dy 0320(1)“ /u-n : o o 000
>- 01m?
10‘3 E 1
10‘4 F a
: 1
10'5 E a
'6 1 1+111111 1 1 1111111 1 1 1111111 1 11111111 1 1411
10
_ - -3 -2 -
10s 104 10- 10 10' 10°
km

Figure 5.64 Normalized autospectral density of the v'<(i)z'> product (19-July).

139

 

T l YYYTYY

Y

1 YYYYYY’

Y O 1
O

 

 

 

 

 

 

  

 

 

 

-4
10 ,0
2 2 0 00
E v (920(1) Tl / u 11 6 E 0 000 030,; -7/3 SIOpe
10. ':E m) 0 1‘180
:5 O 068(133g 986
10 E 00
E o
-10 :
10 E
E
-12 : o
10 E
>- 1 1 1 111111 1 1 1 111111 1 11 11 1 1 1111 1 1 111111 1 1 11_LL
-5 -4 —3 -2 -1 0 1
10 10 10 10 10 10 10
km

Figure 5.66 Normalized co-spectral density of v' and <(o,'> (ZS-July).

I40

 

 

    

 

 

 

 

    

 

 

2 2 0 °
E V (020(1) T] /u n -6 : 0 00 253%?” U _ '7/3 Slope
E ° F303;?“
10_8 E— 1:58008
10-10 E
-12 E 0 ‘
10 E
: . ......l . .....l . ..l .....l . ....l . H...
10'5 10'4 10'3 102 10" 10° 10]
km
Figure 5.67 Normalized co-spectral density of v' and <wz'> (l8-July).
10'4 _
E k 2/u 2 I °
V wz( I) T] Tl EE 0° 000% o -7/3 Slope
10'6 E Efficacy
‘ 9333
— °o 08
E 00° 09
10_8 E? o (9 000
10-10 E
10"2 E 3°C
h . l l ...l . ......l ....l u
110'5 104 10‘ 10'2 10" 10° 101
km

Figure 5.68 Normalized co-spectral density of v' and <wz'> (l9—July).

I41

 

0.9

 

    

 

 

E finfiq . . ..En.‘ fly Trwfij . , ...”
E 1
0 8 i O 25-July _:
>< 19-July 3
0.7 ~ ~ _
: A l8—July " 1
0.6 g— 3-j
H 05 t g
“02 C” 0%?
C 03X.
0.4 :— 0%}?
E 0A);
.— OAS
0.3 :— 0%?
C 09;
0.2 f 0%

" O
" Zn
0.1 f A 0000 2:
: x0 A9 AXA>O>G 0;

0.0 . 1 ...1 1 1 1 1 gm 4
-4 -3 -2 -l O
10 10 10 10 10
km

(bw (k])T|2 / UTE2

 

YfiY'Ylqu T TWTT

_

O

I
b.)

I vtTrnnI

I IV 11""!

_—l
C
l
LA
1 v Hum]

 

I
LII

1 f1 IVY—111'

O

 

1 1 1 1111111 1 1 1 1111111 1 1 1 1L111L1 1 1 1 1 111111 1 1 1 111111
-4 -3 .-2 -l 0
10 l() l() 10 10

km

Figure 5.70 Normalized autospectral density of the w'<(uy'> product (IS—July).

142

 

 

 

 

 

}- I I I I I IIII] I Tfi I IIIII l I I I I I IIII] I I I I ITIIII I I I I I III“
10'5 r
L
3 2 ;
kICDw myaqm /U.n
O
10'6 : ° ° 1
c 0 ..
i o I
.- 1 1 1 1111111 1 1 1 1111111 1 1 1 1111111 1 1 1 1111111 1 1 1111111q
- _ -z _ -
105 104 no 102 101 100
km

Figure 5.71 Compensated autospectral density of the w'<(1)y'> product (IS-July).

 

III I I IIITIII] I I’ IIIIII

 
     

I TTTIIH

_

O

I
b.)

v v r vnrrq

 

 

 

10'4 E
10‘5 E
E
F
-6 1 1 11111111 1 1 11111111 1 41 11111111 1 L111L111
10
10'4 10'3 10'2 10" 100

k T]
I:igure 5.72 Normalized autospectral density of the w'<(1)y'> product (19-July).

 

 

 

 

 

k1¢wmy(k1)n /un ~ I I I
10‘5 E 1
E I
t
O
.. (Q .
CFO ° %
L- (5200 %.
O 250

o a

O

0
'0-6 20 1 1 11111111 1 1 L1111111 1 1 11111111 1 1 11111110
10

10'4 10'3 10‘2 10"

km
Figure 5.73 Compensated autospectral density of the w'<(o\,'> product (l9-July).

 

     

 

 

2 2 10'4
Ewwy(k1)n “in ° ,. -7/3 Slope
10‘6 (52> '
10'8
10-10
10-12 0 0
. ......l 1 1 1.1.1.1 . 11111111 . 1 1.1.1.1 1 1 ......l . 1111111
10'5 10'4 10'3 102 10" 100 10

I:igure 5.74 Normalized co-spectral density of w' and <(o\,'> (l8-July).

I44

 

    

 

 

 

10
E k 2/u 2 C
wmy( 0n n 6 E -7/3 Slope
10' E
10'8 E
E
10-10 E
E
10-12 E
: 1 11111111 141111111 1 . ......l 1 .......l . 1.1.1.11 1 L11111
10'5 10‘4 10‘3 10'2 10‘I 100 10'

km

Figure 5.75 Normalized co-spectral density of w' and <o)y'> (l9-July).

0.8 _ r
0.6 :—
0.5 :—
O.4 :—
0.3 E—
02 E
0.1 '—
0,0 . .....“1 . “H“... . ........1 1......1

10’4 10‘3 10'2 10'1

 

II I I IrTIIII' I I I IIIIIII I I IIIIIIII

I I

 

 

 

km

Figure 5.76 Coherence of w' and <(oy'> for 18, l9-July.

I

2 v
k1(D(k1)n3 / ”n

I

I IIIIII]

I vvvvvrr

 

10'5

p-

 

 

1_1 1111111
10'3

10’2

 

100
km
July.

Figure 5.77 Compensated autospectral densities of the velocity-vorticity products for 18-

 

 

 

F I T I I I I I I Y I ‘
"I.
‘ ' E ,,
A A1 1 A“ “ humufltw’ 1,, .- . _ ' ' 7 ’ I],
-5 A A Q . 1’!”
— ‘ I —1
10 _ (Du m w my\ a, .
,"I
i z E
3 2 » "1,,
k.<1>(k.)n / 11,] ~ "3 d
‘ A
_ ‘ ,, 3’ .
X 1 'I. u l ' I
.. X x x .«cuu‘é‘ ( ‘ 1 ' 2,: 1‘1
X 0 ... r?" ‘01
O (I) 3,. 1. "
1 CO v wz ... A"
L O '-. "
a .
O '0 ‘
o ..- A“
o 1
o "‘4
o 3 ‘
'-. S
1
[0'6 1 1 1 1111111 1 1 1 1111111 1 1 1:11. ‘1
-3 -7 _ l
10 I0 “ 10

 

10°
km
Figure 5.78 Compensated autospectral densities of the velocity-vorticity products for 19-
July.

146

 

1" I l V YTTT'TI' I I I YITTUY

k1<b<knn3l u“2

10‘5

 

 

 

 

10‘6 1 1 1 1111111 1 +11LLJ111 1 1 1 111111

10'3 10'7- 10" 10°
km

Figure 5.79 Compensated autospectral densities of the velocity-vorticity products for 25-

July.

 

  
 

'—
v vnnnl trtwrnI 1TTTTWII v rrnr

 

 

 

Figure 5.80 Normalized PDF of the <(oj> vorticity for each day.

147

 

 

 

Table 5.9 col PDF Statistics

(Dy/(Dy

 

Figure 5.81 Normalized PDF of the <0)\,'> vorticity for each day.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l8-July l9-July 25-July
RMS 84.5 94.1 84.7
Skewness -0.49 -0.26 -0.09
Kurtosis 7.6 5.09 8.66

Table 5.10 coy PDF Statistics

18-July l9-July 25-July
RMS 97.0 75.3 N/A
Skewness -0.26 0.14 N/A
Kurtosis 6.06 8.53 N/A

 

 

 

 

I48

 

 

 

 

6.0 Conclusions

This section presents conclusions made based on the data taken at the SLTEST site
and presented in the previous chapters. The conclusions are presented in numbered order

followed by a discussion of the relevant information needed to justify each conclusion.

1. The SLTEST data support Kolmogorov’s hypothesis of local isotropy at very
high wavenumbers. Large excursions from local isotropy for low wavenumbers was also
documented.

The spectral representation of the velocity field was presented in Section 5.3.1.
All three velocity components agreed well with the isotropic model spectra for very high

wavenumbers. The coherence of the u and v velocity components dropped to near zero for

almost two decades of high wavenumbers (l()_2 S km S 100 ). This lack of coherence

between the u and v velocity components is a necessary condition for the presence of local
isotropy. Similarly, the coherence of the u and w velocity components was nominally
zero over all recorded wavelengths, as expected for a flow that is “two-dimensional” in the
time averaged sense.

The condition of local isotropy did not appear to exist in the moderate to lower

wavenumbers. The autospectral densities of these data appeared to deviate from the iso-

tr0pic model at a range of moderate wavenumbers (km 2 104 ). The effect of the wall

was more evident in the 18- and l9-July data because these probes were located much

closer to the wall. This anisotropic condition was also more prominent in the wall-normal

149

velocity component, where the magnitude of the experimental spectra was far below the

isotropic model spectra.

2. A large range of values were initially found when computing the dissipation
estimate. However, self consistent results could be obtained from several dissipation esti-
mates.

The dissipation estimates were described in Section 5.2.3 and displayed in Table
5.4. Seven dissipation estimates were computed covering a range of assumptions. The
estimates were computed in the assumptions of homogeneous isotropic turbulence and

semi-isotropic, or axi-symmetric, turbulence. The dissipation estimates ranged from
0.2 S 8 S 1.] (l8-July), 0.2 S 8 S 1.0 (l9-July). and 0.28 S e S 1.4 (25—July). However,
with the exclusion of one estimate (81)), the range of the 25-July data was reduced to
0.28 S e S 0.34 for the three remaining estimates (two estimates were unavailable since
only one probe was used on 25-July). Similar results for 118-July and l9-July were
observed. On 18-July, with two estimates excluded (8b and 8‘, ), the range was decreased
to 0.2 S€S0.34 for the five remaining estimates. On l9—July, with three estimates

excluded (8,), 86 and Se ), the range was decreased to 0.2 S e S 0.43 for the four remain-

ing estimates.

3. Buoyancy had a small effect on the measurement of the velocity spectra.

The measurements of the velocity spectra were presented in Section 5.5 for all

three days. Data from 25-July were acquired under thermally neutral conditions, data

150

from l8-July were acquired under thermally unstable conditions, and data form l9-July
were acquired under the thermally stable condition. The autospectral densities of the three
components of the velocity did not appear to be affected by the buoyancy condition. This
was seen in the very similar character of the l8- and 19-July data. These data were

acquired at the same probe location but acquired under different buoyancy conditions.

4. The gradient of the Reynolds shear stress appears to be dominated by the w'my'

component.
The gradient of the Reynolds shear stress is discussed in Section 5.3.3.3. Using a

tensor identity, this gradient can be decomposed into two velocity-vorticity products:
v'tu,‘ and w'to\,' (see equation 5.44). The correlation coefficient of the v'to; component

was found to be a relative small number for each of the three days

(—0.03 S v'wj/i'zti); S 0.02; see Table 5.8). The other velocity-vorticity component
present in the gradient of the Reynolds shear stress, W'my' , was found to consistently dis-

play a relatively large correlation between its velocity and vorticity parts (WW/Mb);

0.2 for both data sets).

Spectral analyses of these velocity-vorticity components showed large coherence

over very high wave numbers. Figure 5.69 demonstrates the coherence of the v' and

<o),'> flow components. The coherence peaks at a value of 0.8 for a wavenumber of
km 2 0.35. This trend is evident for each data set. Figure 5.76 shows the spectral corre-

lation between the w' and <0)‘,'> flow components. The large coherence at high wave-

151

numbers is again evident, peaking at a coherence of 0.76 and a wavenumber of kin z 0.4

(19-July). However, the w' and <(l)\,.> coherence also has a significant low wavenumber

. . —4 . ,
contribution ( ~ 0.4 at a wavenumber kln ~ 0( IO ) ) that was not observed in the v and

<o)z'> coherence spectra.

5. There is a large contribution to the vorticity autospectral densities from very

low wavenumbers.

The autospectral representations of the <0):> vorticity field for the three days are
presented in Section 5.3.2. In all three cases, the experimental spectra continued to
increase as the wavenumber decreased. This character was not observed in the mode]

spectrum which leveled off for lower wavenumbers. The autocorrelation of the vorticity

time signal showed correlations over very large time periods. The length corresponding to

the first zero crossing of the <wz> vorticity autocorrelation varied from day to day. It

ranged from 13m ( l9-July) to 43m (25-July). The correlation appeared to show a depen-

dence on R). (as R). increased, the length of the first zero crossing also increased), but

effects from the different thermal stabilities cannot be excluded.

The same large scale correlations were observed in the <(o‘,> vorticity data (sec-

tion 5.3.2), except with much larger correlation values. The lengths corresponding to the

first zero crossing of the <(i)y> vorticity autocorrelation were 225m (l9-July) and 240m

(18-July). These motions are on the order of a boundary layer thickness (8 2 150m). A

152

dependence on RA, the thermal stability, or both cannot be established given the limited

observations.

6. The kurtosis (flatness) of the probability density function of the <(1)z > vorticity
displays a dependence on RA. This is a result of the “tails” of the PDF, which “rise” with
an increase in RA'

Section 5.4 discusses the PDF’s of the <wz> vorticity. The flatness of the <wz>

vorticity PDF appears to increase with higher RA values. This is evident in Table 5.9 as

well as Figure 5.80. As the Reynolds number is increased, the number of large excursions
in the vorticity fluctuations also increases. This increase in large excursions brings the

“tails” of the PDF “up”, in turn flattening out the shape. It should be noted that this depen-

dence on RA cannot be separated from buoyancy effects (which may also contribute to the

skewness of the probability distribution functions) given this limited data set. The same

trends do not hold true for the <0.)Y> vorticity.

Appendix A: Pre-Post Calibration Comparison

 

 

 

 

 

 

 

 

 

 

 

<1)
0 .
C‘.
e 00 l
«2 ' .
9: l
D
E? —5.0 P .1 . ’ _
a)
o
3-1
Eli
-10.0 a
_15011111111111111111111111
2 3 4 5 6 7 8
Velocity (m/s)
Figure A.1 Drift determination comparison taken on 18-July (<w,> probe, first straight
wire).
5.0 v.4fi..4....,...,...,
a)
8
a) 0.0 '
B
:43 1
Q ‘5'” ‘ l/Wllll/W
*5 NW .
a.)
B —10.0 _
a)
O.
-15.0 _
t
_20.011111111111111111111111
2 3 4 5 6 7 8
Velocity (m/s)

Figure A.2 Drift determination comparison taken on l8-July (<w,> probe, second straight

wire).

154

8.0 ,55

 

 

 

 

 

0)
a r
g 4.0 ~ _
Q 0.0 1‘
0)
a -41) - _.
Q)
CL.
-8.0 a
l
_12.O11111111111111141111111
2 3 4 5 6 7 8
Velocity (m/s)

Figure A.3 Drift determination comparison taken on l8-July (<wy> probe, first straight

wire).

 

 

 

 

12.0......-....,...,...,.-
G.)
U
5 8.0 - 1
5 1
g 40 _ .
Q ' l
g 00 ‘ i 1’ 1.1,“. 1' '13 1'1‘11‘J1fl'11
E _ WW '1’ v V 1 <1
-4.0 -
~ 1
_80 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Li 1 1 1 l 1 1 1
2 3 4 5 6 7 8
Velocity (m/s)

Figure A.4 Drift determination comparison taken on 18-July (<wy> probe, second straight

wire).

155

 

 

 

 

 

 

 

 

 

<1) 0 T
8 :
a) -l l-
3 C
.35 -2 '— -
Q 1
a -3 ‘1
0 cl
8 .
<1) ‘4 ‘ ‘
0.1
-5 - _
-6 l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 1 1 1 1 1 1 1 ‘
2 3 4 5 6 7 8
Velocity (m/s)

Figure A.5 Drift determination comparison taken on 19-Ju1y (<51: Z> probe, first straight

wire).

 

 

 

 

 

ll
lllll lull lll 3

 

Percent Difference
1;) J.
‘2...

 

 

 

 

 

 

 

 

_3 b 1 1 1 l 1 1 1 L 1 1 1 1 1 1 1 l 1 1 1 1 1 1 1 d
2 3 4 5 6 7 8
Velocity (m/s)

Figure A.6 Drift determination comparison taken on 19-July (<wz> probe, second straight

wire).

156

 

Percent Difference
4'}.

 

 

 

 

-5 _

-6 _

'7 I1 -1

' q

_8 I 1 1 4 L1 1 1 1 r 1 1 1 1 1 1 1 1 1 1 1 1 1 1 .,

2 3 4 5 6 7 8
Velocity (m/s)

Figure A.7 Drift determination comparison taken on 19-July (<coy> probe, first straight

wire).

 

 

 

 

 

5.0 7 7 ti rfi V I v f v 1 v v v T r ‘l’ 1 T v v v

01)
U 1
G
2
L2 0.0
1.1...
a 1
H
3:: -5.0 -
0.)
0
8-1

-10.0 1 _

l

 

 

 

_15011111111111111DJ1111111
2 3 4 5 6 7 8

Velocity (m/s)

Figure A.8 Drift determination comparison taken on l9-Ju1y (<wy> probe, second straight

wire).

157

 

 

 

 

 

 

 

 

 

 

g F
s: ’7 T j
d) .
5 8
81:: - _
H
11 -91
E * l
O)
8 -10 —
0) ' 1 .
a. :
-ll — 1
3 l
_12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l 1 1 1 1 1 1 1
2 3 4 5 6 7 8
Velocity (m/s)

Figure A.9 Drift determination comparison taken on 25-July («01> probe, first straight

wire).

 

 

 

 

 

 

-6 T T I T l I T f I T
0 :
E —7 - -
o .
33‘
a: -8 1
H 1
9 -9 ~
5 1
8 '10 7
£3 1
‘11 " Tl
_12 : 1 l 1 1 1 l 1 1 1 1 1 1 1 1 1 1 1 l 1 1 1 '1
2 3 4 5 6 7 8
Velocity (m/s)

Figure A.10 Drift determination comparison taken on 25-July («01> probe, second

straight wire).

158

Angle (Degrees)

Figure A.“ X-wire drift determination comparison taken on l8-July (<wz> probe).

Angle (Degrees)

Figure A.12 X-wire drift determination comparison taken on 18-July (<wy> probe).

 

 

O 0 A r .t' I , 1 I .
""3001 6.10.1 '1'0'0001 Os'u 00.0.9 1“ 10101“! 'm“ 0" ..." 2mm ' 10.!" 1' 'u "'1‘ h' 1 ' ‘0
U

’ a
‘1 009 00'“. “0.3.... .« oOaumAOtu‘Nc no". 0"... .000 "a" 'o’..’ 1114.1 110.. P o

A . A. In.11,015AAI‘51“1__““./a 10‘0”“. IJJ.‘ 1 l“ I. .. 'IH‘O ,11,“ n‘ In I” ,

A
I S
11 11111 I llllll' nl "'I. Illlu lltIIIII. lull .Illlll .Ignlml wnu- l.'_lll -.ul.- [1min II "I ll'H'L 1m 1_u I lul-
'r 0 q 1 Or. I O r ’1
Us 5‘ (I 0 1| 1;.‘|.I\ Um I~' ‘0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 

 

4 5 6 7 8
Velocity (m/s)

 

     
 
 
 
 

. _ . . - .4 , o - ,

. . ‘ .0000 1111‘...” :01”. $110.... $0.01 ...‘1sg.'40!.%.I.‘-"I‘QO.\\. 00'. '00 . 10.19;“ 10.3“ (0“1‘.1.10.'_.’0¢' 1:9,“.

I. I / I . . , l I, z

, 1 . , 9 I

WA 4... 1‘ ‘,::O_I_A 2’1“"; 1 1!.011‘1 “ ‘gll (at. ’“1.’.1.J.“ by “’11....flgfifi’ 1.0%.;1 I‘L‘I‘l,”‘I/L‘J‘”h :1I'14-I’ -I‘

7 'I [1| "fill 74' P'" ‘r 1 “1"qu r
I Lgl.‘._ . |!.Ilt 111...: 11.311 LIQJL I. I Jun“.

0 O . O . , .
O 690 0063 WMm moo"'50141°1v.r11m.«w1m1 «ma-«-
1 1 1 1 1 1 1 1 1 1 1 1 J 1 1 1 1 1

1 1 1

2 3 4 5 6 7 8
Velocity (m/s)

159

 

Angle (Degrees)
8

ans.
OOOO

 

            

, , . ""(I-Il(’. 'l'"'xl(. ,-, .H (rt
(«aqfifimfliE'dufiufc'uu’itimuualrku."1““!va : h“ 0'“ ‘1‘ |‘ ”‘1 '10“ '\ 1‘ t ‘ U11" .‘ «a 1 1.th 1 1 1'11

11111111111111111111111

2 3 4 5 6 7 8

4';
:3

Velocity (m/s)

Figure A.13 X-wire drift determination comparison taken on l9-July («02> probe).

 

40 V Y Y I I 1 Y I T V l I Y Y T— I V I V ' V V I
p
1 141.11%...“111..- . 111.11.111.11 11 1.1.1.1441nuu‘ 1.11 .11 u-uufl- ‘ ‘
' Vv y—r . ' 'I'fl nun-r I ' ' T" WY "‘7' I" WW .1;

 

 

30 f
20 ‘—

T

 

10
O
-10
~20

Angle (Degrees)

     
 

      
   
     

-30 1.1. 11! 11min!“ mum-11mm" ”WI”... I; I" uuunmri nluumollIrl Immmlmufiufluulfium.1 “1.111171171311111 ulueum = rd 1mm :-

    

       

 

         

‘ r . . I A- ' ’ . '
((l’x’h" "'g‘“‘“" '11 '6 -(.\"§"«\’1"“‘(Catuf‘1-‘rg““"Cflf' ’1 t'.('.“".wws (“'1 "“Wl‘ “fl"flfl‘ '9‘!“ “114mm,: "1““ \[ "‘(\"“\“ ‘.'\u “'1“ '.

-40 1 1 1 1 1 1 1 1 1 1 1 L 1 1 1 1 1 1 1 1 1 1 1

2 3 4 5 6 7 8

Velocity (m/s)

Figure A.14 X-wire drift determination comparison taken on l9-July (<wy> probe).

160

 

4O 1 T T I Y Y Y I f I I I f Y Y I I I v I v 1’ f
1 mu.1.111 J1 1414-1114111 .4 .. .. __. 1 .Ln. 1.1.1 .. . IA- _ A... .1- 1 _
- 'levr' ' ‘T'V' "' W'" W" ywr 1 """""'"Y"'" wr V"- n—yy-v ' 1". av ... .7

 

Y

 

30
2O
10

O

 

1'. 'Q'Iu'" q ,
- “ ‘ - 0'1“‘IJ.‘I “1"411'1- ' r ('1 , . .
l O ‘ (I . (\u .NOS , \| 0‘" '0'“! 1611.!“ .(«nlli‘l.“.p'\ 3',‘."\"__“ “4.?“ q. 1“" ‘0‘!“ .‘V ‘44. 1"“ 1'! ‘ 1'“ ‘1, “V "I ' I! .

I

Angle (Degrees)

 

. ' O . I ’
20 I . ;“‘ 9‘...‘ . \ . '1 ‘..4“ ‘l ‘1 (_(“’.Q ‘4‘ I,“ It. ,'. l. "(“I‘l ”‘1‘ (‘1'.‘\,‘,, ,( ‘2‘, 1O].‘ ,‘ ‘c , x “,1. O\‘\‘l ‘ ‘ I ‘ 1 I“ 4 ....
.-

' I
V‘ II], « ’I 0’31””.1‘, ‘LIII‘N’ “-1,”,

1011‘“ :. HI”..’"’( AJIIIMIrw'IoIl.l_’bl!ll)/ m; 1 491,11 ,,_ 1.1.74!" ,,,,,, ,v, “1,, ,., U, , , ‘
, - _ _ _ H -

     
      

‘ "(.1 "(0"1‘ ' ‘ 6.1“ "'10 0'1 «. '1’ 1'1 '1 a I u A -
‘1‘ § .‘ngg ( ~1 ‘1. I"! \. 1 \ I. 1\ O I“! 1‘11‘41 110.111 u."m.1 \I'c‘t 11 ‘(Ha‘ It.‘1’\¢\"‘q ""|"\".‘ 1"1 a. “1‘...

Velocity (m/s)

Figure A.15 X-wire drift determination comparison taken on 25-July (<wz> probe).

16]

Appendix B: Combined Calibration Plots

 

21 ...,,..,2,.,...,2..

           
     
   
 

1'1].
Mw
{. (1» \u‘“

\

 

 

 

19 i
18 €
prc cal :

l7 ‘ -
combined :

l6 ‘ 0 post cal L
. l
15 ’ . . 1 1 . 1 . 1 . . 1 1 . . 1 1 . . . 1 1 1 1 i
3 4 5 6 7 8

Velocity (m/s)

Figure B.l Combined calibration data for 18-July (<x-Z> probe, first straight wire).

 

 

 

 

16
2

E -

15 —
t
14 ~
13 —
combined
12 —
0 post cal

In > 1 1 1 1 1 1 1 1 1 1 L L 1 1 1 1 1 1 1 1 1 1 1

Velocity (m/s)

Figure B.2 Combined calibration data for l8-July ((3),? probe, second straight wire).

I62

19

18

17

 

 

  
  

 

 

 

 

L 0 pre cal _‘

1 combined :

1 0 post cal :

_ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 q

3 4 5 6 7 8
Velocity (m/s)

Figure 8.3 Combined calibration data for l8-July (<x-z> probe, first X—wire).

 

   

 

 

 

 

22 111,
132 :
211
20;
19 precal
combined:
18 -
O postcal 1
17‘11.11111111111111111111J
2 3 4 5 6 7 8

Velocity (m/s)

Figure B.4 Combined calibration data for lS-July (<31:Z> probe, second X-wire).

 

22

21

2O

19

 

pre cal

combined

0 post cal

    

g1

 

 

Figure B.5 Combined calibration data for 18-July (<aoy> probe, first straight wire).

27

26

25

24

23 0 pre cal _
. combined

22 . 0 post cal .

21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d

2 3 4 5 6 7 8

Figure B.6 Combined calibration data for 18-July (<x},> probe, second straight wire).

18
2

Velocity (m/s)

 

YIYrWrTYfi'V

I

 

1,

Tfj

      
 

1 J 1 1

 

 

Velocity (m/s)

164

21.0
20.5
20.0
19.5
19.0
18.5
18.0
17.5

17.0 .-‘
16.5
2

 

 

pre cal
combined

post cal

 

   

 

 

Velocity (m/s)

Figure B.7 Combined calibration data for 18-Ju1y (<~:1:-y> probe, first X-wire).

 

    

 

 

2 15.0
E .
14.5 —
14.0 —
13.5 —
13.0 ~
precal
12.5 _
combined
12.0‘ 0 postcal
11.5 '11114-11111-1111111111
2 3 4 5 6 7
Velocity (m/s)

Figure B.8 Combined calibration data for 18-July (<;1:-y> probe, second X-wire).

165

 

 

    

 

 

 

E .
23 —
1
22 _—
21 _—
20 precal

""" combined 1

19 O postcal q

18 111111111111111‘

3 4 5 6 7 8

Velocity (m/s)

Figure B.9 Combined calibration data for 19-Ju1y (<x,> probe, first straight wire).

 

   
 

 

 

 

2 27 .
E 1
26 1
....... 1
25 -
24 i
23 0 pre cal _‘
combined 1
22 0 post cal j
21 ’ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d
3 4 5 6 7 8

Velocity (m/s)

Figure B. 10 Combined calibration data for 19-J uly («92> probe, second straight wire).

166

 

        
 
    

I.
gd‘d‘ .
I
I“ \
. /' ((l“‘
~ Q

 
     

0

pre cal
combined -

0 post cal ‘

 

 

Velocity (m/s)

Figure B. 1] Combined calibration data for 19-July (<27? probe, first X-wire).

 

214_0...,...,...,...,...,..2

12.0 —

 

 

 

precal
11.5 1
combined
11.0 - post cal ‘
1
10.5 1 1 1 1 1 1
2 3 4 5 6 7 8

Velocity (m/s)

Figure B. 12 Combined calibration data for 19-1 uly («02> probe, second X-wire).

167

 

 
    
 

 

 

 

2 21
E Z
20 e

19 — -

18 — -

17 0 pre cal ‘

combined

16 -

» 0 post ca] 1

15 b 1 1 1 1 1 1 1 l 1 1 1 1 1 1 1 1 1 1 1 14 1 1 1

3 4 5 6 7 8

Velocity (m/s)

Figure B. 13 Combined calibration data for 19-July ( xy> probe, first straight wire).

 

      

 

 

 

17
E2
16
15
14 l
1
13 -
combined 1
12 O postcal ‘1
: 1
H11111111111111111111111
3 4 5 6 7 8

Velocity (m/s)

Figure B. 14 Combined calibration data for 19-Ju1y (<3ay> probe, second straight wire).

168

 

 

        
   
 

1.
2 ~ .
E ~ .
21 ~ -
20 '— 1
C 1
19 ~ -
1 .
18 L pre cal _‘
r , ‘
1 combined -
J, ‘
l7 . 0 post ca] .

 

 

l6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 

U)
4;
L11
0
\l
00

Velocity (m/s)

Figure B. 15 Combined calibration data for l9-July (<31: y> probe, first X-wire).

 

 

 

 

16
2 1-
E .
1.
15—
14—
13
precal
combined
12 1
' O postcal -
117111lg11111111111111LL11‘
2 3 4 5 6 7 8

Velocity (m/s)

Figure B. 16 Combined calibration data for 19-1 uly (<31: y> probe, second X-wire).

169

 

21 vvvvvvvi

      
  

2 .
E .
20 L
19 l

C I

18 ~— _

17 L 0 pre cal j

3 combined 1

l6 1 0 post cal

 

 

15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 P1 1 1 1

 

Velocity (m/s)

Figure B. 17 Combined calibration data for 25-July («02> probe, first straight wire).

20 r..,...,...,...,

 

 

l9

   

18

17

16

   

pre cal

15

 

fV'V‘TIVTTTrTTIV'VIYT

 

1 1 1 1 J L 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 

 

combined
M "V 0 post cal
13 l . . . 1 .1 1 1 . 1 . 1 . . . l . . .
2 3 4 5 6 7 8

Velocity (m/s)

Figure B. 18 Combined calibration data for 25-July (<ZQZ> probe, second straight wire).

170

18

17

16

15

l4

l3

l2
2

 

 

v v 1' Y r *r I
y
-
P
F
L-
y.—
p
u- ‘L x
» . («wt-“e

. W" 0‘
l‘ , .V
p.— (‘6' Q.
s ‘0’
’- ( Ké“ ‘\’\"\§
. (x
h- ‘15.. 43..
“C. .1
p ..O I
no- . fit.
71” Q.
p .U' §O
I.'O-
r- ... ‘O
. \‘s.

r. c‘“ .

.,~(. ‘

«7" ‘

~
1:94:63
:0
p.
b
h

1 1 1 1 1 1 1 1 1 1

 

pre cal

combined

post cal

 

 

Velocity (m/s)

Figure B. 19 Combined calibration data for 25-July («01> probe, first X-wire).

21

20

l9

l8

l7

 

T T I I I V 1 I I I T T I Y

 

3‘ g. r I T

Velocity (m/s)

  
     
     

1 11_1 1 1 1 I 1

pre cal
combined

post cal

1 1 1 1 1 1 1 1 1 1 l

 

\l
00

Figure B.20 Combined calibration data for 25-July (<coz> probe, second X-wire).

171

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