Analysis of spectral eddy viscosity and backscatter in incompressible, isotropic turbulence using statistical closure theory

Abstract

The spectral eddy viscosity and backscatter viscosity in three-dimensional, incompressible, unforced, nonhelical, isotropic turbulence are decomposed into a sum of contributions corresponding to the Reynolds and cross-stresses, and studied numerically as a function of different assumed kinetic energy spectra. The eddy viscosities and backscatter viscosities are computed using the kinetic energy transfer obtained from the eddy-damped quasinormal Markovian (EDQNM) closure model as a function of k/kc (where kc is the cutoff wave number) using the sharp Fourier cutoff filter. The behavior of the Reynolds and cross-contributions is studied using a Kolmogorov kinetic energy spectrum, a family of spectra with small wave number scaling proportional to k, and a spectrum from an EDQNM calculation that includes both a k4 energy production subrange and a dissipation subrange. The principal results of this theoretical investigation and sensitivity study are (1) the main contributions from the Reynolds and cross-components of the eddy viscosity arise from modes with k/kc≪1 and k/kc≲1, respectively; (2) the contributions from the Reynolds and cross-components of the backscatter viscosity are of the same order, which are nearly zero for k/kc<1 and rise sharply near the cusp k/kc↑1, and; (3) for both the eddy and backscatter viscosity, the Reynolds components are more sensitive to the details of the production subrange than are the cross-components. The implications of these results for subgrid-scale modeling in spectral large-eddy simulations of incompressible, isotropic turbulence are discussed.