Evaluation of eddy viscosity-based models in decaying rotating stratified turbulence

Abstract: The results of large eddy simulation (LES) using three sub-grid scale models, namely: constant coefficient Smagorinsky, dynamic Smagorinsky, and a dynamic Clark model, for rotating stratified turbulence in the absence of forcing using large-scale isotropic initial condition, are reported here. The LES results are compared to in-house direct numerical simulation (DNS) for establishing grid-independence requirements. Three cases with varying ratios of Brunt-Vaisala frequency to the inertial wave frequency, N / f, have been chosen to evaluate the performance of LES models. The Reynolds number and N / f are chosen as (a) Case 1: Re = 3704, N / f = 5, (b) Case 2: Re = 6667, N / f = 40, and, (c) Case 3: Re = 6667, N / f = 138. This framework is used to illustrate the relative magnitudes of the stratification and rotation which is observed in geophysical flows. Various quantities including turbulent kinetic energy (tke), turbulent potential energy (tpe), total dissipation, potential and total energy spectra, and their fluxes, are analyzed to understand the predictive capability of the various LES models. Results show that all the SGS model predictions are very similar, with the classical Smagorinsky model displaying the highest deviation compared to DNS. The effect of an increase in the value of N / f is also seen in the results of LES with an increase in the oscillations observed in the evolution of tke and tpe and a reduction in dissipation. The spectral analysis shows that the dynamic Clark and Smagorinsky models predict the large-scale physics (\kappa < 10), while the small scales (10 < \kappa < 64) energy is under-predicted.