Trial of a nonlinear diffusion equation as a model of turbulent diffusion

A nonlinear diffusion equation is demonstrated as a model of turbulent dispersion in the atmosphere. It is based on a similarity solution for two-dimensional dispersion (longitudinal advection and vertical diffusion) from a horizontal line source. The coefficient for the vertical diffusion is a nonlinear function of both concentration and height. The similarity solution for two-dimensional dispersion includes a beta function with arguments that are functions of the parameters for the wind profile and the nonlinear vertical diffusion. The solution is successfully fitted to two sets of Prairie Grass data.