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

S. A. Lebedeff Goddard Institute for Space Studies, NASA, New York, N.Y. 10025

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S. Hameed Goddard Institute for Space Studies, NASA, New York, N.Y. 10025

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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.

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.

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