Renormalization-group estimates of transport coefficients in the advection of a passive scalar by incompressible turbulence

Abstract

The advection of a passive scalar by incompressible turbulence is considered using recursive renormalization-group procedures in the differential subgrid shell thickness limit. It is shown explicitly that the higher-order nonlinearities induced by the recursive renormalization-group procedure preserve Galilean invariance. Differential equations, valid for the entire resolvable wave-number k range, are determined for the eddy viscosity and eddy diffusivity coefficients. It is shown that these higher-order nonlinearities do not contribute as k\ensuremath{\rightarrow}0, but play an essential role as k\ensuremath{\rightarrow}${\mathit{k}}_{\mathit{c}}$, the cutoff wave number separating the resolvable scales from the subgrid scales. The transport coefficients and the associated eddy Prandtl number are in good agreement with the k-dependent transport coefficients derived from closure theories and experiments.