Continuous time random walks on moving fluids

The scheme of the continuous time random walk (CTRW) is generalized to include the possibility of a moving background. It is shown that this generalization reproduces in the macroscopic limit the usual diffusion-advection equation and the properties of standard diffusion in a shear flow. The new formalism is then used to derive the corresponding macroscopic equation for CTRW's with infinite mean squared step length and with infinite mean waiting time in a moving fluid. For these two CTRW's we finally include an analysis of the dispersion in three different two-dimensional linear shear flows.