We investigate a result for the effective diffusivity of particles in a random gradient flow, previously obtained by an intuitively plausible renormalization-group argument and very accurately verified by numerical simulation. We show that, to two-loop order, the result is consistent with a direct perturbation theory calculation. To the same order in perturbation theory we also derive a 'Ward identity' which guarantees the equality of the ratio of the effective diffusivity to the renormalized coupling with the ratio of the corresponding bare values. The invariance of this ratio under renormalization was an important feature of the successful renormalization-group calculation.
No takes yet. Share an insight, caveat, or question.
Dean et al. (1995) studied this question.