Anisotropic Subgrid-Scale Modelling: Comparison of LES with High Resolution DNS and Statistical Theory for Rapidly Rotating Turbulence

Abstract

Rotating homogeneous turbulence is known to exhibit strongly anisotropic features at low Rossby number, as well as a modified dynamics. These are the result of the presence of inertial waves due to the Coriolis force. The spectral distribution of kinetic energy in spectral space also reflects this strong anisotropy through a dependence of the energy on the wavevector orientation at almost all wavenumbers. Up to now, subgrid scale models for large eddy simulation are not adapted to describing strongly anisotropic dissipative scales, therefore we introduce a means of deriving an eddy viscosity from the orientation-dependent structure function equation. Only at the end of the derivation of a first version, the model is simplified by neglecting directional anisotropy in the final eddy viscosity, in a first stage for assessing the method. In order to illustrate qualitatively the relevance of the approach, and to prepare improved anisotropic subgrid-scale modelling, we compare the results of high Reynolds number large eddy simulations based on this model to energy density spectra obtained at lower Reynolds number by direct numerical simulations, and to spectra obtained by a recent two-point statistical model. The subgrid-scale model is shown to perform well, all the more when looking at the reduction of interscale energy transfer due to rotation, quantified here by the dependence of the velocity derivatives skewness on the micro-Rossby number.