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

: 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 wavenumber k range, are determined for the eddy viscosity and eddy diffusivity coefficients and it is shown that higher order nonlinearities do not contribute as k right arrow 0, but have an essential role as k right arrow kc, the cutoff wavenumber separating the resolvable scales from the subgrid scales. The recursive renormalization transport coefficients and the associated eddy Prandtl number are in good agreement with the k-dependent transport coefficients derived from closure theories and experiments.... RNG, Passive scalar, Transport coefficients.