Fractional Dynamics in Random Velocity Fields

We develop an iterative approach, from which an exact systematic calculation of the moments of the probability density of test particles, under a generalized Fickian evolution and in the presence of a stratified random velocity field, can be calculated. The type of fractional diffusion-advection equation studied is useful for transport in anisotropic and heterogeneous media. Our method stresses the relevance of the coupling between anomalous diffusion and convection by stratified random velocity fields.