A STUDY OF SECOND MOMENT CLOSURE MODELING FOR STRATIFIED WAKES USING DNS ENSEMBLES

Buoyant wakes are widely encountered in ocean environment and undersea vehicle flows. These are typically characterized by high Reynolds (Re) and Froude (Fr) numbers, so turbulence resolving CFD models of such flows, i.e., Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), require significant computational resources. Therefore, Reynolds-Averaged Navier-Stokes (RANS) based models are attractive for these configurations, but their performance hinges on numerous modeling assumptions. The inherently complex dynamics of stratified systems render eddy-viscosity-based modeling inappropriate. RANS Second-Moment Closure (SMC) based modeling is more suitable for such complex systems because they account for flow anisotropy by solving the transport equations of important second-moment terms. For stratified flows, turbulent density fluctuations and their auto- and velocity cross-correlations are dynamically important. Accordingly, at the SMC level of modeling, eleven transport equations are solved, and a range of sub-models are implemented for diffusion, pressure strain and scrambling, and dissipation, in the Reynolds stress, density flux, variance, and dissipation transport equations. In this work, we study the stratified wakes of axisymmetric towed bodies using SMC and DNS. Sub-models in the SMC are evaluated in terms of how well their exact Reynolds averaged form impact the accuracy of the full RANS closure. An ensemble average of 100 DNS realizations is conducted to obtain converged higher-order statistics for direct comparison. For a stratified towed wake at Re = 10000 and Fr = 2, RANS successfully captures the peak mean defect velocity and wake width evolution when accurate initial conditions are provided from DNS. However, RANS over-predicts the wake height, and turbulent kinetic and potential energies, and exhibits larger amplitude oscillations and slower decay rates. Also, RANS predicts a near isotropic decay of normal Reynolds stresses in contrast to the anisotropic decay returned by DNS. The DNS data also provide important physics and modeling insights related to the inaccuracy of the dissipation rate isotropy assumption, and the non-negligible size of pressure-diffusion terms. These results lead to several important recommendations for SMC modeling improvement.