Intermittency and relative scaling of subgrid-scale energy dissipation in isotropic turbulence

Abstract

The rate at which large-scale kinetic energy in turbulent flows is transferred to, or from, unresolved scales (smaller than a filter scale Δ) is given by Π(x,t)=−τijS̃ij, where τij is the subgrid stress, and S̃ij is the resolved strain-rate tensor. The spatial distribution of Π(x,t) is computed from DNS of isotropic turbulence, and is found to be highly intermittent with increasing levels of intermittency as the filter size decreases. Relative scaling exponents of high-order moments of Π are measured using extended self-similarity, and are compared to those of longitudinal velocity structure functions. Reasonably good agreement is found, both sets of exponents clearly departing from the Kolmogorov (1941) theory. Relative scaling exponents of the SGS dissipation as predicted by several models are measured a priori from the DNS, and are compared to those of the true dissipation. We find the constant and spectral eddy viscosity models to be significantly less intermittent, and the local dynamic model to be much more intermittent than the true SGS dissipation field. The traditional and volume-averaged dynamic Smagorinsky models, together with the similarity model, yield more realistic levels of intermittency.