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

Abstract

We continue a previous work in which {\em a priori} estimates were derived on subgrid stress and subgrid flux for filtering schemes used in the turbulence modelling method of Large-Eddy Simulation (LES). The estimates were derived there as rigorous consequences of the exact subgrid stress formulae from Navier-Stokes equations under the conditions assumed for velocity fields in the Parisi-Frisch ``multifractal model.'' It was also shown that these assumptions are realistic in an extended inertial range. Therefore the estimates must be obeyed by any faithful subgrid model and we use them here to evaluate some popular models of the subgrid stress (Smagorinsky, Bardina, etc.) We also examine the effects of the choice of filter function on the magnitudes of subgrid stress and transfer. Under mild assumptions on the filter these quantities are determined by local-in-wavenumber, inertial-range interactions and can be modelled in a universal way. However, one common choice of filter---the sharp cutoff filter in Fourier space ---does not satisfy the modest 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.