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 cons idered using recursive renormalization-group procedures in the differe ntial subgrid shell thickness limit. It is shown explicitly that the h igher-order nonlinearities induced by the recursive renormalization-gr oup procedure preserve Galilean invariance. Differential equations, va lid 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-->O, but pla y an essential role as k-->k(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.