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Criteria for the selection of stochastic models of particle trajectories in turbulent flows

Published online by Cambridge University Press:  21 April 2006

D. J. Thomson
D. J. Thomson
Affiliation:
Meteorological Office, Bracknell, Berks RG12 2SZ. UK
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Abstract

Many different random-walk models of dispersion in inhomogeneous or unsteady turbulence have been proposed and several criteria have emerged to distinguish good models from bad. In this paper the relationships between the various criteria are examined for a very general class of models and it is shown that most of the criteria are equivalent. It is also shown how a model can be designed to satisfy these criteria exactly and to be consistent with inertial-subrange theory. Some examples of models that obey the criteria are described. As an illustration some calculations of dispersion in free-convective conditions are presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 180 , July 1987 , pp. 529 - 556
Copyright
© 1987 Cambridge University Press

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References

Arnold, L. 1974 Stochastic Differential Equations: Theory and Applications. Wiley.
Baerentsen, J. H. & Berkowicz, R. 1984 Monte Carlo simulation of plume dispersion in the convective boundary layer. Atmos. Environ. 18, 701–712.Google Scholar
Batchelor, G. K. 1949 Diffusion in a field of homogeneous turbulence. I. Eulerian analysis. Austral. J. Sci. Res. 2, 437–450.Google Scholar
Deardorff, J. W. 1978 Closure of the second- and third-moment rate equations for diffusion in homogeneous turbulence. Phys. Fluids 21, 525–530.Google Scholar
De Baas, A. F., van Dop, H. & Nieuwstadt, F. T. M. 1986 An application of the Langevin equation for inhomogeneous conditions to dispersion in a convective boundary layer. Q. J. R. Met. Soc. 112. 165–180.Google Scholar
Durbin, P. A. 1983 Stochastic differential equations and turbulent dispersion. N ASA reference publication 1103.
Durbin, P. A. 1984 Comment on papers by Wilson. et al. (1981) and Legg and Raupach (1982). Boundary-Layer Met. 29. 409–411.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. R. Met. Soc. 1983, 109, 339–353). Q. J. R. Met. Soc. 110, 1195–1199.Google Scholar
Feller, W. 1966 An Introduction to Probability Theory and its Applications, Vol. 2. Wiley.
Gihman, I. I. & Skorohod, A. V. 1974 The Theory of Stochastic Processes I. Springer.
Gihman, I. I. & Skorohod, A. V. 1975 The Theory of Stochastic Processes II. Springer.
Githman, I. I. & Skorohod, A. V. 1979 The Theory of Stochastic Processes III. Springer.
Hanna, S. R. 1979 Some statistics of Lagrangian and Eulerian wind fluctuations. J. Appl. Met. 18, 518–525.Google Scholar
Hanna, S. R. 1981 Lagrangian and Eulerian time-scale relations in the daytime boundary layer. J. Appl. Met. 20, 242–249.Google Scholar
Hunt, J. C. R. 1985 Turbulent diffusion from sources in complex flows. Ann. Rev. Fluid Mech. 17, 447–485.Google Scholar
Janicke, L. 1983 Particle simulation of inhomogeneous turbulent diffusion. In Air Pollution Modelling and Its Application II, pp. 527–535. Plenum.
Kaimal, J. C., Wyngaard, J. C., Haugen, D. A., Coté, O. R., Izumi, Y., Caughey, S. J. & Readings, C. J. 1976 Turbulence structure in the convective boundary layer. J. Atmos. Sci. 33, 2152–2169.Google Scholar
Legg, B. J. 1983 Turbulent dispersion from an elevated line source: Markov chain simulations of concentration and flux profiles. Q. J. R. Met. Soc. 109, 645–660.Google Scholar
Legg, B. J. & Raupach, M. R. 1982 Markov-chain simulation of particle dispersion in inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerian velocity variance. Boundary-Layer Met. 24. 3–13.Google Scholar
Ley, A. J. 1982 A random walk simulation of two-dimensional diffusion in the neutral surface layer. Atmos. Environ. 16. 2799–2808.Google Scholar
Ley, A. J. & Thomson, D. J. 1983 A random walk model of dispersion in the diabatic surface layer. Q. J. R. Met. Soc. 109, 867–880.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, Vol. 1. M.I.T. Press.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, Vol. 2. M.I.T. Press.
Nieuwstadt, F. T. M. 1980 Application of mixed-layer similarity to the observed dispersion from a ground level source. J. Appl. Met. 19, 157–162.Google Scholar
Pasquill, F. 1974 Atmospheric Diffusion, 2nd edn. Wiley.
Reid, J. D. 1979 Markov chain simulations of vertical dispersion in the neutral surface layer for surface and elevated releases. Boundary-Layer Met. 16, 3–22.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. J. R. Met. Soc. 109, 339–353.Google Scholar
Schuss, Z. 1980 Theory and Applications of Stochastic Differential Equations. Wiley.
Smith, F. B. 1984 The integral equation of diffusion. In Air Pollution Modelling and Its Application III, pp. 23–34. Plenum.
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. (2) 20,196–211.Google Scholar
Thomson, D. J. 1984 Random walk modelling of diffusion in inhomogeneous turbulence. Q. J. R. Met. Soc. 110, 1107–1120.Google Scholar
Thomson, D. J. 1986a A random walk model of dispersion in turbulent flows and its application to dispersion in a valley. Q. J. R. Met. Soc. 112, 511–530.Google Scholar
Thomson, D. J. 1986b On the relative dispersion of two particles in homogeneous stationary turbulence and the implications for the size of concentration fluctuations at large times. Q. J. R. Met. Soc. 112. 890–894.Google Scholar
Van Dop, H., Nieuwstadt, F. T. M. & Hunt, J. C. R. 1985 Random walk models for particle displacements in inhomogeneous unsteady turbulent flows. Phys. Fluids. 28. 1639–1653.Google Scholar
Willis, G. E. & Deardorff, J. W. 1976 A laboratory model of diffusion into the convective planetary boundary layer. Q. J. R. Met. Soc. 102, 427–445.Google Scholar
Wilson, J. D., Thurtell, G. W. & Kidd, G. E. 1981a Numerical simulation of particle trajectories in inhomogeneous turbulence, I: Systems with constant turbulent velocity scale. Boundary-Layer Met. 21, 295–313.Google Scholar
Wilson, J. D., Thurtell, G. W. & Kidd, G. E. 1981b Numerical simulation of particle trajectories in inhomogeneous turbulence, II: Systems with variable turbulent velocity scale. Boundary-Layer Met. 21, 423–441.Google Scholar
Wilson, J. D., Thurtell, G. W. & Kidd, G. E. 1981c Numerical simulation of particle trajectories in inhomogeneous turbulence, III: Comparison of predictions with experimental data for the atmospheric surface layer. Boundary-Layer Met. 21. 443–463.Google Scholar
Wilson, J. D., Legg, B. J. & Thomson, D. J. 1983 Calculation of particle trajectories in the presence of a gradient in turbulent-velocity variance. Boundary-Layer Met. 27. 163–169.Google Scholar
Wyngaard, J. C., Coté, O. R. & Izumi, Y. 1971 Local free convection, similarity, and the budgets of shear stress and heat flux. J. Atmos. Sci. 28, 1171–1182.Google Scholar
Yaglom, A. M. 1972 Turbulent diffusion in the surface layer of the atmosphere. Icr. Atmos. Oceanic Phys. 8, 333–340.Google Scholar