Renormalization group analysis of macrodispersion in a directed random flow

We apply ''field theoretic'' methods to the calculation of the effective diffusivity (macrodispersion coefficient) in a random flow. We show how this approach can be utilized to calculate a perturbation series for the effective diffusivity of conservative tracers in an incompressible velocity field with nonvanishing mean. The first-order (i.e., ''one-loop'') approximation of this series coincides with, classical results derived by Gelhar and Axness and Dagan. A renormalization group (RNG) approach is utilized, and the results are compared to the classical first-order perturbation theory. For a moderate variability of the permeability the renormalized theory predicts only small corrections to the longitudinal dispersivity. However, the transverse dispersivity can be larger than that predicted by the first-order perturbation theory by several orders of magnitude. We compare these values to the outcome of Monte Carlo simulations and find that the RNG predictions are in much better, though not perfect, accordance with the results of simulations. Moreover, the results are in good quantitative agreement with reported observations from the Borden Site field experiment.