On the representation of backscatter in dynamic localization models

Abstract

The dynamic localization model is a recently developed method that allows one to compute rather than prescribe the unknown coefficients in a subgrid scale model as a function of position at each time-step. A realistic subgrid scale model should describe both the direct and reverse (backscatter) energy transfers at the local level. A previously developed dynamic localization model accounted for backscatter by means of a (deterministic) eddy viscosity that could locally assume positive as well as negative values. Here this paper presents an alternative stochastic model of backscatter in the context of the dynamic procedure. A comparative discussion of the merits of stochastic versus deterministic modeling of backscatter is presented. These models are applied to a large eddy simulation of isotropic decaying and forced turbulence. Tests are also performed with versions of the model that do not account for backscatter. The results are compared to experiments and direct numerical simulation. It is shown that the models correctly predict the energy and three-dimensional (3D) energy spectra in decaying turbulence. In the forced case the Kolmogorov 5/3 law seems better predicted by models accounting for backscatter. A relative evaluation of the various versions of the model in terms of predictive capability and cost is provided.