Steady-State Solution of the Semi-Empirical Diffusion Equation for Area Sources

Abstract

Turbulent transport of material emitted from a surface may be described by the steady-state, two-dimensional, semi-empirical diffusion equation. It is shown that, with wind velocity and eddy diffusivity expressed as power functions of the vertical coordinate, this equation can be solved exactly by introducing a similarity variable. The solution gives the vertical distribution of concentration for area sources in terms of the incomplete gamma function. Implications of the solution are discussed.