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Diffusion from a continuous source near a surface in steady reversing shear flow

Published online by Cambridge University Press:  21 April 2006

C. Turfus
C. Turfus
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Abstract

The dispersion of continuous emissions from a line-source in a reversed-flow layer is analysed by means of diffusion equations; a family of exact solutions is found in the form of infinite series and/or integrals. It is shown that the concentration within the layer decays exponentially with the streamwise distance in the direction of reversed flow. The ground-level concentration near the source is found to be governed largely by the local mean flow; the value of the diffusivity affects the position of the maximum of ground-level concentration, but has little influence upon its magnitude. A useful upper limit is deduced for the background concentration due to recirculation effects. Further, a simple formula is given for the maximum value of the ground-level concentration for cases where the source is not too near the ground. The predictions for ground-level concentration are validated against experimental data for the particular case of a line source in the recirculating wake behind a two-dimensional backward-facing step. The extension of the analysis to the case of a point source is also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 172 , November 1986 , pp. 183 - 209
Copyright
© 1991 Cambridge University Press

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References

Bender, C. M. & Orszag S. A.1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw Hill.
Castro, I. P. & Snyder W. H.1982 A wind-tunnel study of dispersion from sources downwind of three-dimensional hills. Atmos. Env. 16 (8), 1869–1887.Google Scholar
Corssin S.1974 Limitations of gradient transport models in random walks and in turbulence. International Symp. on Turbulent Diffusion in Environmental Pollution. Adv. Geophys. 18A, 25–60.Google Scholar
Csanady G. T.1973 Turbulent Diffusion in the Environment. Reidel.
Csanady G. T.1983 Dispersal by randomly varying currents. J. Fluid Mech. 132, 375–394.Google Scholar
Elrick D. E.1962 Source functions for diffusion in a uniform shear flow. Austral. J. Phys. 115 (3), 283–287.Google Scholar
Jones, C. D. & Griffiths R. F.1984 Full-scale experiments on dispersion around an isolated building using an ionised air tracer technique with very short averaging time. Atmos. Env. 18 (5), 903–916.Google Scholar
Kay A.1985 The effect of cross-stream depth variation upon contaminant dispersion in a vertically-well-mixed current. (To be published.)
Ludford, G. S. S. & Robertson R. A.1973 Fully diffused regions. SIAM J. Appl. Maths 25, 693–703.Google Scholar
Okubo, A. & Karweit M. J.1969 Diffusion from a continuous source in a uniform shear flow. Limnol. Oceanogr. 14, 514–520.Google Scholar
Pedley T. J.1980 The Fluid Mechanics of Large Blood Vessels. Cambridge University Press.
Robins, A. G. & Castro I. P.1977 A wind tunnel investigation of plume dispersion in the vicinity of a surface mounted cube. I. The flow field. Atmos. Env. 11, 291–297.Google Scholar
Smith F. B.1957 The diffusion of smoke from a continuous elevated point-source into a turbulent atmosphere. J. Fluid Mech. 2, 49–76.Google Scholar
Tani I., Iuchi, M. & Komada H.1961 Experimental investigation of flow separation associated with a step or groove. Aeronautical Res. Inst. Univ. Tokyo, Rep. no. 364.Google Scholar
Taylor G. I.1953 Dispersion of soluble matter in solvent flowing slowly through a tube Proc. R. Soc. Lond. A 219, 186–203.Google Scholar
Turfus C.1985 Stochastic modelling of turbulent dispersion near surfaces. Ph.D. thesis, Dept. Applied Mathematics and Theoretical Physics, University of Cambridge.
Wilson, D. J. & Britter R. E.1982 Estimates of building surface concentrations from nearby point sources. Atmos. Env. 16 (11), 2631–2646.Google Scholar