Solutions to the stochastic transport problem of O(σ V N ) for conservative solutes

A recursive perturbation solution to the eulerian transport problem for a conservative solute in a random conductivity field is reported. The stochastic concentration is given to arbitrary order inσ _ν, the variance of fluctuating velocity. The result gives the stochastic concentration as a perturbation to the deterministic concentration for constant mean flow. The closed form solution is easy to implement numerically via FFT.