The `Multifractal Model' of Turbulence and {\em A Priori} Estimates in Large-Eddy Simulation, II. Evaluation of Stress Models and Non-Universal Effects of the Filter

摘要

We continue a previous work in which {\em a priori} estimates were derived onsubgrid stress and subgrid flux for filtering schemes used in the turbulencemodelling method of Large-Eddy Simulation (LES). The estimates were derivedthere as rigorous consequences of the exact subgrid stress formulae fromNavier-Stokes equations under the conditions assumed for velocity fields in theParisi-Frisch ``multifractal model.'' It was also shown that these assumptionsare realistic in an extended inertial range. Therefore the estimates must beobeyed by any faithful subgrid model and we use them here to evaluate somepopular models of the subgrid stress (Smagorinsky, Bardina, etc.) We alsoexamine the effects of the choice of filter function on the magnitudes ofsubgrid stress and transfer. Under mild assumptions on the filter thesequantities are determined by local-in-wavenumber, inertial-range interactionsand can be modelled in a universal way. However, one common choice offilter---the sharp cutoff filter in Fourier space ---does not satisfy themodest required conditions and we show that the associated flux, including``backscatter'' effects, may be spuriously dominated by nonlocal-in-wavenumber,convective processes of a non-universal type.