The overreaching goal of this study is utilizing data-driven methods and sophisticated mathematical tools for modeling and simulation of turbulent transport of passive scalars. We focus on embedding the intrinsic nonlocal nature of the turbulence into our models. We study the nonlocal dynamics in the context of (i) subgrid-scale (SGS) modeling for largeeddy simulation (LES), and (ii) the turbulent cascade under large-scale anisotropic sources. Moreover, we implement stochastic modeling methodologies to systematically investigate the contributing mechanisms leading a high-speed hydrodynamic transport system into instability and chaos, as well as discovering the anomalies in the featured characteristics of the transport.First, we present a computational-statistical framework to obtain high-fidelity data for homogeneous isotropic turbulent (HIT) flow and passive scalar transport. A parallel implementation of the well-known pseudo-spectral method in addition to the comprehensive record of the statistical and small-scale quantities of the turbulent transport are offered for executing on distributed memory CPU-based supercomputers.Afterwards, we investigate the inherent nonlocal behavior of the SGS passive scalar flux through studying its two-point statistics obtained from the filtered direct numerical simulation (DNS) data for passive scalar transport in HIT flow. We propose a statistical model for microscopic SGS motions by considering the filtered Boltzmann transport equation (FBTE) for passive scalar. In FBTE, we approximate the filtered equilibrium distribution with an γ-stable Levy distribution that incorporates a power-law behavior to resemble the observed nonlocal statistics of SGS scalar flux. Through generic ensemble-averaging of FBTE, we formulate a continuum-level closure model for the SGS scalar flux appearing in terms of a fractional-order Laplacian that is a nonlocal operator.Moreover, we revisit the spectral transfer model for the turbulent intensity in the passive scalar transport (under large-scale anisotropic forcing), and a subsequent modification to the scaling of scalar variance cascade is presented. Accordingly, we obtain a revised scalar transport model using fractional-order Laplacian operator that facilitates the robust inclusion of the nonlocal effects originated from large-scale anisotropy transferred across the multitude of scales in the turbulent cascade. We provide an a priori estimate for the nonlocal model, and examine the model through a new DNS. We conduct a detailed analysis on the evolution of the scalar variance, high-order statistics of scalar gradient, and two-point statistical metrics of the turbulent transport to compare the developed nonlocal model and its standard version.In another study, a deep learning surrogate model in the form of fully connected feedforward neural networks is developed to predict the SGS scalar flux in the context of large eddy simulation of turbulent transport. The deep neural network (DNN) model is trained and validated using filtered DNS dataset at P eλ = 240, Sc = 1 that includes the filtered scalar and velocity gradients as input features. Using the transfer learning concept, we generalize the performance of this trained model to turbulent scalar transport regimes with higher P eλ and Sc numbers with a relatively low amount of data and computations.Finally, in stochastic modeling of hydrodynamic transport, we study the flow dynamics inside a high-speed rotating cylinder after introducing strong symmetry-breaking disturbance factors at cylinder wall motion. We perform a statistical analysis on the fluctuating fields characterizing the fingerprints and measures of intense and rapidly evolving non-Gaussian behavior through space and time. Such non-Gaussian statistics essentially emerge and evolve due to an intensified presence of coherent vortical motions initially triggered by the flow instability due to symmetry-breaking rotation of the cylinder. We show that this mechanism causes significant memory effects in the flow so that noticeable anomaly in the time-scaling of enstrophy record is observed in the long run apart from the onset of instability.
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