Large eddy simulations of stratified turbulence: the dynamic Smagorinsky model

Abstract

The dynamic Smagorinsky model for large eddy simulation (LES) of stratified turbulence is studied in this paper. A maximum grid spacing criterion of ${\it\Delta}/L_{b}<0.24$ is found in order to capture several of the key characteristics of stratified turbulence, where ${\it\Delta}$ is the filter scale and $L_{b}$ is the buoyancy scale. These results show that the dynamic Smagorinsky model needs a grid spacing approximately twice as large as the regular Smagorinsky model to reproduce similar results. This improvement on the regular Smagorinsky eddy viscosity approach increases the accuracy of results at small resolved scales while decreasing the computational costs because it allows larger ${\it\Delta}$. In addition, the eddy dissipation spectra in LES of stratified turbulence present anisotropic features, taking energy out of large horizontal but small vertical scales. This trend is not seen in the non-stratified cases, where the subgrid-scale energy transfer is isotropic. Statistics of the dynamic Smagorinsky coefficient $c_{s}$ are investigated; its distribution is peaked around zero, and its standard deviations decrease slightly with increasing stratification. In line with previous findings for unstratified turbulence, regions of increased shear favour smaller $c_{s}$ values; in stratified turbulence, the spatial distribution of the shear, and hence $c_{s}$, is dominated by a layerwise pancake structure. These results show that the dynamic Smagorinsky model presents a promising approach for LES when isotropic buoyancy-scale resolving grids are employed.