Anomalous scaling of structure functions and sub-grid models for large eddy simulations of strong turbulence

The original goal of Large Eddy Simulations of fully developed turbulent flows was to accurately describe large-scale flow features ${\bf u}(\Delta)$ at the scales $r\geq \Delta$ where $\Delta$ is a size of computational mesh. The effect of small-scale velocity fluctuations ($r<\Delta$) was to be accounted for by effective transport coefficients (subgrid models) in the coarse-grained Navier-Stokes equations. It is shown in this paper that, due to anomalous inertial range scaling (intermittency) of the moments of velocity difference, the existing subgrid models are intrinsically incapable of quantitatively describing flow features at the scales $r<N\Delta$ with $N\approx 10$. This increases computational work approximately by a factor $10^{3}-10^{4}$. The breakdown of the widely used Smagorinsky relation for the subgrid viscosity on the scales $\Delta/L<1$ is demonstrated and a modification accounting for intermittency of the filtered out small-scale fluctuations is proposed.