The Dynamic Smagorinsky Model in $512^{3}$ Pseudo-Spectral LES of Decaying Homogeneous Isotropic Turbulence at Very High $Re_\lambda$

Abstract

We consider the large-eddy simulation (LES) of turbulent flows, in the classical view where no regular explicit filtering is added to the truncation/projection due to the LES grid. The truncation of the complete field $u_i$ (experimental or from direct numerical simulation, DNS) to the much coarser LES grid corresponds to the incomplete LES field and is noted $\overline{u}_i$. Assuming perfect numerics, the “effective subgrid-scales (SGS) stress” is then obtained as : i.e., the product of LES quantities minus the product of complete quantities, and further truncated to the LES grid. The divergence of that stress (i.e., the “effective SGS force”) represents the effect of the removed scales on the LES scales. As there is no information beyond the LES grid cutoff, the SGS stress (or the SGS force) can only be modeled.