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Turbulent dispersion from sources near two-dimensional obstacles

Published online by Cambridge University Press:  29 March 2006

J. C. R. Hunt  and
P. J. Mulhearn
J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
P. J. Mulhearn
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Royal Australian Navy Research Laboratory, New South Wales.
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Abstract

The first part of the paper is an extension of the statistical theory of turbulent diffusion to the problem of turbulent diffusion from a point or line source in an inhomogeneous straining flow such as flow round a two-dimensional body. The new effects which have to be considered are the convergence and divergence of mean streamlines, the inhomogeneity of the mean and turbulent velocities, and the presence of a boundary. We assume that the upstream turbulence intensity $u^{\prime}_{\infty}/\overline{u}_{\infty} $ is weak, i.e. $u^{\prime}_{\infty}/\overline{u}_{\infty} $ [Lt ] 1, and that molecular diffusion is negligible, i.e. $(\overline{u}_{\infty}/u^{\prime}_{\infty})^2[D/(a\overline{u}_{\infty})] $ [Lt ] 1, D and a being the molecular diffusivity and the scale of the obstacle respectively. The theory predicts the mean-square dispersion of the plume about the mean streamline through the source in terms of the Lagrangian statistics of the turbulence. Making the further assumption that the scale LE of the turbulence is large enough to satisfy the condition that ($(u^{\prime}_{\infty}/\overline{u}_{\infty}) $) (a/LE) [Lt ] 1, it is shown that the turbulent dispersion can be calculated in terms of the Eulerian statistics, which can either be measured or in some cases calculated. In the second part we analyse diffusion from various sources in potential flows over two-dimensional obstacles assuming constant (or variable) eddy diffusivity, and compare the results with those of the more rigorous statistical analysis for sources one or two diameters upwind of the obstacle. However, unlike the statistical analysis, this eddy-diffusivity analysis can also be extended to calculate diffusion from sources placed some distance upwind of an obstacle, and an example is given of how this analysis may be applied to calculating concentrations on hills due to distant sources.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 61 , Issue 2 , 6 November 1973 , pp. 245 - 274
Copyright
© 1973 Cambridge University Press

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References

Batchelor, G. K. 1964 Diffusion from sources in a turbulent boundary layer. Arch. Mech. Stosowanej. 16, 661.Google Scholar
Batchelor, G. K. & Proudman, J. 1954 The effect of rapid distortion of a fluid in turbulent motion: Quart. J. Mech. Appl. Math. 7, 83.Google Scholar
Batchleor, G. K. & Townsend, A. A. 1956 Turbulent diffusion. In Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davis), p. 352. Cambridge University Press.
Berlyand, M. E. 1972 Atmospheric diffusion investigations in the U.S.S.R. Appendix to World Met. Office Tech. Note. no. 121.Google Scholar
Boussinesq, M. J. 1905 Sur la pouvoir refroidissant d'un courant liquide ou gazeux. J. de Math. 1, 285. (See also Comptes Rendus, 133, 257.)Google Scholar
Burger, W. 1964 Ein Verfahren zur Berucksitchtigung des Einflusses von Gebauden auf die Schadgasausbreitung in der Atmosphare. Staub, 24, 223.Google Scholar
Gill, A. E. 1960 Forced convection. M. A. thesis, University of Melbourne.
Halitsky, J. 1968 Gas diffusion near buildings. In Met. & Atomic Energy, p. 221. U.S. Atomic Energy Commission.
Halitsky, J. 1969 Validation of scaling procedure for wind tunnel model testing of diffusion near buildings. Dept. Met. & Oceanography New York University, Rep. TR-69–8.Google Scholar
Hino, M. 1968 Computer experiment on smoke diffusion over a complicated topography, Atmos. Environ. 2, 541.Google Scholar
Hinze, J. O. & van der Hegge Zijnen, B. G. 1951 Local transfer of heat in anisotropic turbulence. Inst. Mech. Eng. General Discussion on Heat Transfer, p. 188.Google Scholar
Holford, Lord 1971 Problems for the architect and town planner caused by air in motion. Phil. Trans. Roy. Soc. A 269, 335.Google Scholar
Hunt, J. C. R. 1971 Discussion of ‘Measurements on the release of gaseous activity from a short stack.’ Atmos. Environ. 6, 289.Google Scholar
Hunt, J. C. R. 1973 Turbulent flow round two-dimensional bluff bodies. J. Fluid Mech. 61, to appear.Google Scholar
King, L. V. 1914 On the convection of heat from small cylinders in a stream of fluid: determination of the convection constants of small platinum wires with applications to hot wire anemometry. Phil. Trans. Roy. Soc. A 214, 373.Google Scholar
McCormick, R. A. 1971 Air pollution in the locality of buildings. Phil. Trans. Roy. Soc. A 269, 515.Google Scholar
Pasquill, F. 1962 Atmospheric Diffusion. Von Nostrand.
Pasquill, F. 1971 Atmospheric dispersion of pollution. Quart. J. Roy. Met. Soc. 97, 369.Google Scholar
Pasquill, F. 1972 Factors determining pollution from local sources in industrial and urban areas. Met. Mag. 101, 1.Google Scholar
Rodliffe, R. L. & Fraser, A. J. 1971 Measurements on the release of gaseous activity from a short stack. Atmos. Environ. 5, 193.Google Scholar
Saffman, P. G. 1960 On the effect of the molecular diffusivity in turbulent diffusion. J. Fluid Mech. 8, 271.Google Scholar
Scriven, R. A. 1970 Variability and upper bounds for maximum ground level concentrations. Phil. Trans. Roy. Soc. A 265, 209.Google Scholar
Scriven, R. A. & Moore, D. J. 1962 The estimation of gamma dose rates from shield cooling air in the near vicinity of nuclear power stations. Symp. on Reactor Safety & Hazards Evaluation Techniques, pp. 339–375. Vienna: International Atomic Energy Agency.
Stumke, H. 1964 Inclusion of simplified types of terrain in calculations of turbulent diffusion of gases from chimneys (in German). Staub, 24, 175.Google Scholar
Synder, W. H. & Lumley, J. L. 1971 Some measurements of particle velocity autocorrelation functions in a turbulent flow. J. Fluid Mech. 48, 41.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20 (2), 196.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. M.I.T. Press.