PERTURBATION-THEORY FOR EFFECTIVE DIFFUSIVITY IN RANDOM GRADIENT FLOWS

We investigate a result for the effective diffusivity of particles in a random gradient flow, previously obtained by an intuitively plausibl e renormalization-group argument and very accurately verified by numer ical simulation. We show that, to two-loop order, the result is consis tent with a direct perturbation theory calculation. To the same order in perturbation theory we also derive a 'Ward identity' which guarante es the equality of the ratio of the effective diffusivity to the renor malized coupling with the ratio of the corresponding bare values. The invariance of this ratio under renormalization was an important featur e of the successful renormalization-group calculation.