Second Moment Closure Modeling and DNS of Stratified Shear Layers

Abstract

Buoyant shear layers are encountered in many engineering and environmental applications and have been studied by researchers in the context of experiments and modeling for decades. Often, these flows have high Reynolds and Richardson numbers, and this leads to significant/intractable space-time resolution requirements for DNS or LES modeling. On the other hand, many of the important physical mechanisms in these systems, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of the full RANS closure. For the non-stratified case, the SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux, and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.