Evaluation of non-eddy viscosity subgrid-scale models in stratified turbulence using direct numerical simulations

Abstract

This research studies the performance of eddy and non-eddy viscosity subgrid-scale (SGS) models using direct numerical simulations (DNS) of stratified turbulence. Nonlinear and modulated gradient models, as the two common non-eddy viscosity SGS parameterizations, are considered. For comparison, the two common eddy-viscosity SGS parameterizations, i.e. the Smagorinsky and dynamic Smagorinsky models, are also considered. Also, two types of test filters–the Gaussian and spectral filters–are employed to study the performance of these SGS models in stratified turbulence. Our results show that when a Gaussian filter is applied, the SGS fluxes and dissipation rates obtained with the nonlinear and modulated gradient models are very similar to those of the actual SGS motions. On the other hand, the Smagorinsky and dynamic Smagorinsky models yield good results when a spectral filter is applied. The correlation coefficient between the actual and modelled SGS fluxes is very high for the non-eddy viscosity models, and depends on the filter type. Overall, our results suggest that the performance of SGS models depends on the resolution of the buoyancy scale Lb: in order to prevent excessive dissipation around the filter scale Δf, the buoyancy scale Lb should be resolved. The resolution of Lb has already been shown as a requirement in large-eddy simulations of stratified turbulence when eddy viscosity SGS models are employed (Khani & Waite, 2014, 2015). However, the importance of the buoyancy scale Lb has not been studied before in non-eddy viscosity SGS models. This research work provides a strong support for the choice of minimum resolved scale for both eddy and non-eddy viscosity SGS parameterizations, including nonlinear and modulated gradient models, in stratified turbulence through a theoretical scale analysis and using DNS data.