A formal perturbation expansion is presented 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 mu denotes the mean of V(x), and V(x) is expressed as mu plus epsilon U(x), then the expansion is in powers of epsilon with mu , U and a fixed. Explicit expressions up to second order in epsilon are obtained which generalize the standard formulae to the case a does not equal 0 0.
ASJC Scopus subject areas
- Applied Mathematics