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A stochastic model for dispersion and concentration distribution in homogeneous turbulence

Published online by Cambridge University Press:  21 April 2006

H. Kaplan  and
N. Dinar
H. Kaplan
Affiliation:
Israel Institute for Biological Research, P.O. Box 19, Ness-Ziona 70450, Israel
N. Dinar
Affiliation:
Israel Institute for Biological Research, P.O. Box 19, Ness-Ziona 70450, Israel
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Abstract

A new approach to contaminant diffusion in homogeneous turbulence is proposed. This approach is based on solving for the Lagrangian trajectories of many particles taking into account the interaction among their velocities. The velocity field at a given instant is composed of many ‘eddies’ distributed randomly and uniformly in space. The velocity of each eddy is proportional to the cube root of its size. In this way the calculated Eulerian correlation function between any two points is consistent with observations. The present model is used to calculate concentration fluctuations, concentration averages and intermittency as functions of location and time. Results were found to be in accordance with experimental measurements. Probability distributions as functions of time and location are also calculated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 190 , May 1988 , pp. 121 - 140
Copyright
© 1988 Cambridge University Press

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References

Batchelor, G. K. 1952 Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Phil. Soc. 48, 345–362.Google Scholar
Chatwin, P. C. & Sullivan, P. J. 1979 The basic structure of clouds of diffusing contaminant. In Mathematical Modelling of Turbulent Diffusion in the Environment (ed. C. J. Harris), pp. 3–31. Academic Press.
Corrsin, S. 1952 Heat transfer in isotropic turbulence. J. Appl. Phys. 23, 113–118.Google Scholar
Csanady, G. T. 1967 Concentration fluctuations in turbulent diffusion. J. Atmos. Sci. 24, 21–28.Google Scholar
Durbin, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279–302.Google Scholar
Egbert, G. D. & Baker, M. B. 1984 Comments on paper ‘The effect of Gaussian particle-pair distribution functions in the statistical theory of concentration fluctuations in homogeneous turbulence’ by B. L. Sawford, Q. J. 1983, 109, 339–353. Q. Jl R. Met, Soc. 110, 1195–1199.Google Scholar
Fackrell, J. E. & Robins, A. G. 1982 Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary layer. J. Fluid Mech. 117, 1–28.Google Scholar
Hanna, S. R. 1981 Turbulent energy and Lagrangian time scale in the planetary boundary layer. In 5th Symp. on Turbulence, Diffusion and Air Pollution, p. 61. AMS.
Hanna, S. R. 1984 The exponential probability density function and concentration fluctuations in smoke plumes. Boundary-Layer Met. 29, 361–375.Google Scholar
Jones, C. D. 1983 On the structure of instantaneous plumes in the atmosphere. J. Hazard. Mater. 7, 87–112.Google Scholar
Kaplan, H. & Dinar, N. 1986a A stochastic model for dispersion and concentration distribution in two dimensional homogeneous turbulence. In Proc. 16th Intl Technical Meeting on Air Pollution Modeling and its Applications, April 6–20. NATO.
Kaplan, H. & Dinar, N. 1986b Comment on the paper: ‘On the relative dispersion of two particles in homogeneous stationary turbulence and the Implication for the Size of Concentration Fluctuations at Large Time.’ Q. Jl R. Met. Soc. (submitted).Google Scholar
Kraichnan, R. H. 1970 Diffusion by a random velocity field. Phys. Fluids 13, 22–31.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1963 Fluid Mechanics. Pergamon.
Lee, J. T. & Stone, G. L. 1983 The use of Eulerian initial conditions in a Lagrangian model of turbulence diffusion. Atmos. Environ. 17, 2477–2481.Google Scholar
Ramsdell, J. V. & Hinds, W. T. 1971 Concentration fluctuations and peak to mean concentration ratios in plumes from a ground-level continuous point source. Atmos. Environ. 5, 483–495.Google Scholar
Richardson, L. F. 1926 Atmospheric diffusion shown on a distance - neighbour graph. Proc. R. Soc. Lond. A 110, 709–737.Google Scholar
Sawford, B. L. 1983 The effect of Gaussian particle-pair distribution functions in the statistical theory of concentration fluctuations in homogeneous turbulence. Q. Jl R. Met. Soc. 109, 339–354.Google Scholar
Sawford, B. L. 1985 Lagrangian statistical simulation of concentration mean and fluctuation fields. J. Climate Appl. Met. 24, 1152–1166.Google Scholar
Sawford, B. L. & Hunt, J. C. R. 1985 Effect of turbulence structure molecular diffusion and source size on scalar functions in homogeneous turbulence. J. Fluid Mech. 165, 373–400.Google Scholar
Sykes, R. I., Lewellen, W. S. & Parker, S. F. 1984 A turbulent transport model for concentration fluctuations and fluxes. J. Fluid Mech. 139, 193–218.Google Scholar
Thomson, D. J. 1986 On the relative dispersion of two particles in homogeneous stationary turbulence and the implication for the size of concentration fluctuations at large times. Q. Jl R. Met. Soc. 12, 890–894.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Wax, N. 1954 Selected Papers on Noise and Stochastic Processes. Dover.