Similarity solution of a specialized diffusion equation

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Abstract
The differential equation of diffusion when the wind velocity and the vertical and lateral diffusivities are power functions of height is equation image where x, y, and z are measured respectively in the down‐wind, vertical, and cross‐wind directions, and D1 and D2 are physical constants defined in the text. Exact solution of this equation for the case of a point source and for m = k is presented in this paper. In the systematic search for this solution, dimensional analysis has been utilized to the optimum advantage. Although the solution is restricted to the special case m = k, it shows the important characteristics of atmospheric diffusion from a point source.

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