Field-theoretic approximations for normal diffusion in random velocity fields.

Abstract

The motion of a classical Brownian particle entrained in a fluid with random, time-independent velocity fields is discussed. Two approaches to calculating the disorder-averaged Green's function are presented, both based upon a functional-integral formulation. A renormalization group (RG) approach proves to be less satisfactory than does a self-consistent perturbation theory approach, which reproduces the well-known direct interaction approximation. An explicit comparison of the results with Monte Carlo data is made in two dimensions. The relationship between the present results and the case of diffusion in a solid, where RG provides a superior answer, is discussed in physical terms.