Analytical approximations of the diffusive dispersion in fluid flows

We present a path-integral approach for finding solutions of the convection-diffusion equation with inhomogeneous fluid flow, which are notoriously difficult to solve. We derive a general approximate analytical solution of the convection-diffusion equation which is in principle applicable to arbitrary flow profiles. As examples, we apply this approximation to the diffusion in a linear shear flow and in a parabolic flow in infinite space, and to the diffusion in a linear shear flow over an impenetrable interface. This last case is particularly important for problems involving diffusive transport towards an interface with advection. We compare the analytical approximation with numerical solutions which are obtained from a conventional finite-element time-difference method.