RENORMALIZATION OF DRIFT AND DIFFUSIVITY IN RANDOM GRADIENT FLOWS

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a Gaussian random field with homogeneous statistics. The theoretical analysis is confirm ed by numerical simulation. For the purely isotropic case the simulati on, which measures the effective drift directly in a constant gradient background field, confirms the result, previously obtained theoretica lly, that the effective diffusivity and effective drift are renormaliz ed by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a spatial average of lo cal drift, for the renormalization of the effective drift parameter re lative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift t o the gradient of the random held. We find that the numerical simulati on confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.