ANALYTICAL GUASSIAN SOLUTIONS FOR ANISOTROPIC DIFFUSION IN A LINEAR SHEAR-FLOW

An extended diffusion equation is derived which takes into account anisotropic transport of mass in a shear flow. Analytical solutions for systems with spatially linear but time-dependent flow and sedimentation velocities, a time-dependent diffusion tensor as well as linear sinks and sources are determined. Considering only systems in spatially infinite domains, the solutions for Gaussian initial distributions are derived. Then, starting from this general case, the two- and three-dimensional solutions are deduced for a horizontal and linear shear flow which generalize the results of former Gaussian plume models. Further, it is shown that the extended diffusion equation can be treated by solution methods of the Fokker-Planck equation. Finally, it is discussed how the time-dependent diffusion tensor can be determined from the first and second moments of these solutions.