# The Dispersion of Slightly Dense Contaminants

## Abstract

Existing theoretical models of dense gas dispersion vary greatly in degree of complexity from simple layer averaged (integral equation) approaches to the use of complex turbulence models, the latter usually employing some form of eddy diffusivity closure approximation. However there remain several aspects of the problem which are poorly understood, and may therefore not be adequately modelled. For example the question of how “entrainment” (however it may be defined) or eddy diffusivities can be related to stability. Evidently a careful look at the dynamics of dense contaminant dispersion is called for. Our research, which we review here, is an attempt to study in some detail one aspect of the dispersion dynamics in particular, namely the effects of stable stratification, which may be set up in dispersing plumes or clouds, on the turbulence. We shall describe three approaches to the problem. Firstly, the use of Rapid Distortion Theory to investigate structural changes to homogeneous turbulence with varying degrees of stable stratification in the presence of a mean velocity gradient. Secondly, a Lagrangian dynamical model of fluid element motions (as previously employed in studies of mixing in homogeneous stratified turbulence) is introduced in the context of the present problem. Finally, an experimental program is described.

## Keywords

Internal Wave Fluid Element Stable Stratification Inertial Subrange Bulk Richardson Number## Preview

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## References

- Batchelor G.K and Townsend A.A (1956) Turbulent Diffusion. in Surveys in Mechanics, ed. Batchelor and Davies,C.U.P.Google Scholar
- Bradbury L.J.S and Castro I.P (1971) A pulsed-wire technique for velocity measurements in highly turbulent flows. J.F.M, 49, 657–691.CrossRefGoogle Scholar
- Castro I.P and Cheun B.S (1982) The measurement of Re stresses with a pulsed-wire anemometer. J.F.M, 118, 41–58.CrossRefGoogle Scholar
- Csanady G.T. (1964) Turbulent diffusion in a stratified fluid. J. Atmos. Sci., 21, 439–447CrossRefADSMathSciNetGoogle Scholar
- Durbin P.A. (1980) A random flight model of inhomogeneous turbulent dispersion. Phys. Fluids, 23(11)Google Scholar
- Ellison T.H. and Turner T.S. (1960) Mixing of dense fluid in a turbulent pipe flow. J.F.M., 8, 514–544.CrossRefMATHMathSciNetGoogle Scholar
- Fackrell J.E. (1979) A flame ionization detector for measuring fluctuating concentration. J. Phys. E. Sci Instr, 13, 888–893.CrossRefADSGoogle Scholar
- Fackrell J.E. and Robins A.G. (1982) Concentration fluctuations and fluxes in plumes from point sources in turbulent boundary layers. J.F.M., 117, 1–26.CrossRefGoogle Scholar
- Hanna S.R. (1981) Lagrangian and Eulerian time-scale relations in the daytime boundary layer. J. Appl. Met., 20, 242–249.CrossRefADSGoogle Scholar
- Hunt J.C.R. (1978) A review of the theory of rapidly distorted turbulent flow and its applications. Fluid Dynamics Trans., 9, 121–152.Google Scholar
- Krasnoff and Peskin (1971) The Langevin model for Turbulent diffusion. Geophys. Fluid Dynamics, 2, 123–140CrossRefADSGoogle Scholar
- Monin A.S. and Yaglom A.M. (1971) Statistical fluid mechanics. M.I.T. Press, Camb., Mass.Google Scholar
- Narasimha R., Sethuraman S., Prabhu A., Rao K. N., and Prasad C.R. (1981) The response of the atmospheric boundary layer to a total solar eclipse. Fluid Mechanics Report 81 FM6, Indian Institute of Science, BangaloreGoogle Scholar
- Pearson H. J., Puttock J. S. and Llint J. C.R. (1983) A statistical model of fluid element motions and vertical diffusion in a homogeneous stratified turbulent flow. J.F.M., 129, 219–249.CrossRefMATHGoogle Scholar
- Tennekes H. and Lumley J.L. (1972) A first course in Turbulence. M.I.T. Press.Google Scholar
- Townsend A.A. (1976) The Structure of Turbulent Shear Flow. C. U. P., 2nd edition.MATHGoogle Scholar