EFFECTIVE DIFFUSIVITY IN NONISOTROPIC GRADIENT FLOWS

We study the effective diffusivity tensor for particles in a random gr adient flow that, statistically, lacks rotational symmetry. The effect ive diffusivity tensor is computed up to two-loop order in perturbatio n theory and the 'Ward identity' that relates this tensor to the effec tive coupling is verified to the same order. We re-examine the renorma lization group calculation that produced a very accurate numerical val ue for the effective diffusivity in the rotationally symmetric case an d formulate two versions based on distinct divisions of the random pot ential held that gives rise to the flow. Both types of renormalization group calculation give good results when compared with numerical simu lations. However, at two-loop order in perturbation theory the two met hods differ in detail from each other and from the exact perturbation calculation. This is in contrast to the corresponding results in the i sotropic case.