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Diffusion from an elevated point source into a turbulent atmosphere

Published online by Cambridge University Press:  26 February 2010

T. S. Walters
T. S. Walters
Affiliation:
Department of Applied Mathematics, University of Wales, Swansea.
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Summary

A solution is obtained of the problem of diffusion from an elevated point source into a turbulent atmospheric flow over a horizontal ground z = 0. The mechanism of the turbulence is the one considered by D. R. Davies [1[ when he obtained a solution of the same problem in the case when the source is at ground level, the specifications for the mean wind velocity V, and for the across-wind diffusivity Ky, and for the vertical diffusivity Kz, being V αzm, Ky αzm, Kz αz1−m, where m is a constant. Predictions of the solution are that the maximum concentration at ground level of the diffusing matter varies inversely as h1·8 in adiabatic conditions, where h is source height, and that the distance downwind from the source to the point where this maximum concentration is attained varies, in these conditions, as h1·3.

Type
Research Article
Information
Mathematika , Volume 12 , Issue 1 , June 1965 , pp. 49 - 57
Copyright
Copyright © University College London 1965

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References

1. Davies, D. R., Quart. J. Mech. Appl. Math., 3 (1950).Google Scholar
2. Walters, T. S., Mathematika, 11 (1964).Google Scholar
3. Sutton, O. G., Proc. Roy. Soc. (A), 146 (1934).Google Scholar
4. Sutton, O. G.Micrometeorology (McGraw-Hill, 1953).Google Scholar
5. Watson, G. N., A treatise on the theory of Bessel Functions (Cambridge, 1944).Google Scholar