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The original goal of Large Eddy Simulations of fully developed turbulentflows was to accurately describe large-scale flow features ${\bf u}(\Delta)$ atthe scales $r\geq \Delta$ where $\Delta$ is a size of computational mesh. Theeffect of small-scale velocity fluctuations ($r<\Delta$) was to be accountedfor by effective transport coefficients (subgrid models) in the coarse-grainedNavier-Stokes equations. It is shown in this paper that, due to anomalousinertial range scaling (intermittency) of the moments of velocity difference,the existing subgrid models are intrinsically incapable of quantitativelydescribing flow features at the scales $r<N\Delta$ with $N\approx 10$. Thisincreases computational work approximately by a factor $10^{3}-10^{4}$. Thebreakdown of the widely used Smagorinsky relation for the subgrid viscosity onthe scales $\Delta/L<1$ is demonstrated and a modification accounting forintermittency of the filtered out small-scale fluctuations is proposed.

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