Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-27T16:07:48.762Z Has data issue: false hasContentIssue false
  • English
  • Français

The diffusion of smoke from a continuous elevated point-source into a turbulent atmosphere

Published online by Cambridge University Press:  28 March 2006

F. B. Smith
F. B. Smith
Affiliation:
Department of Mathematics, University of Manchester
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem is to determine the downwind concentration of non-buoyant smoke emitted from a continuous elevated pointsource in a turbulent airstream. The velocity and eddy diffusivity coefficients are represented by related powers of the height above ground, and are independent of the position of the source. Exact solutions are obtained for the zero and second moments of the concentration distribution along lines lying in the cross-wind direction at ground level. In special cases, these moments may also be determined along lines at general height. In one such case the concentration is determined exactly (rather than just the two moments) and it is found that the cross-wind distribution always has a Gaussian form. If it is assumed that in all cases the cross-wind profile is Gaussian, a formulation for the concentration can be given purely in terms of the known zero and second moments. When the source is moving with constant velocity across the wind, the first moment as well as the zero and second moments is exactly determined, and under a similar assumption a formula for the concentration is found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 2 , Issue 1 , January 1957 , pp. 49 - 76
Copyright
© 1957 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bosanquet, C. H. & Pearson, J. L. 1936 Trans. Faraday Soc. 32, 1249.
Davies, D. R. 1950 Quart. J. Mech. Appl. Math. 3, 64.
Davies, D. R. 1954 Quart. J. Mech. Appl. Math. 7, 168.
Jeffreys, H. & Jeffreys, B. S. 1946 Methods of Mathematical Physics. Cambridge University Press.
Pearson, K. 1922 Tables of the Incomplete Γ-Function. H. M. Stat. Office.
Sutton, O. G. 1934 Proc. Roy. Soc. A, 146, 701.
Sutton, O. G. 1947 Quart. J. Roy. Met. Soc. 73, 257.
Sutton, O. G. 1953 Micrometeorology. New York: McGraw-Gill.
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions. Cambridge University Press.