A Perturbation Expansion for Diffusion in a Random Velocity Field

We present a formal perturbation expansion for the large scale effective drift velocity and diffusion matrix of a medium with stationary random velocity, $V(x)$, and constant nonrandom diffusion matrix, a, on a small scale. If μ denotes the mean of $V(x)$, and we express $V(x)$ as μ + ε U(x), then the expansion is in powers of ε with μ, U and a fixed. We obtain explicit expressions up to second order in ε which generalize the standard formulae to the case a ≠ 0.