Treatment of Interfaces in Random Walk Dispersion Models

The problem of how to formulate random walk dispersion models in situations where the flow properties vary discontinuously across an interface is considered. It is shown how the dispersion model can be made consistent with the assumptions made about the turbulence. The approach does not lead to a unique model, but it is argued that in many cases the rate of diffusion through the interface is limited not by the detailed physics of the interface but by the rates of diffusion on either side of the interface and, in such situations, results may be insensitive to which of the consistent models is chosen. Some simulations are presented to illustrate these ideas.