Recent Developments in Closure and Boundary Conditions for Lagrangian Stochastic Dispersion Models

  • William L. Physick
Part of the NATO • Challenges of Modern Society book series (NATS, volume 22)


Until the definitive paper of Thomson (1987), arguably the most pressing problem in Lagrangian particle modelling was which form of the Langevin equation should be used for inhomogeneous, non-stationary, non Gaussian turbulence to ensure well-mixedness, i. e. to ensure that particle accumulations did not occur in regions of low turbulence. Since that time, the major topics of research in Lagrangian dispersion modelling have been associated with convectively unstable conditions. This review paper focuses on two recent topics: (1) the closure problem associated with specification of the probability density function (PDF) for vertical turbulent fluctuations, and (2) the most appropriate boundary conditions to apply at the ground and at the top of the convectively mixed layer, particularly when simulating the fumigation1 process. The reviewed studies emphasise the importance of turbulence and concentration data from a laboratory saline water tank (Hibberd and Sawford, 1994) for testing the closure schemes and the various methods for incorporating entrainment processes into stochastic models.


Probability Distribution Function Mixed Layer Convective Boundary Layer Entrainment Rate Closure Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anfossi, D., Ferrero, E., Tinarelli, G., and Alessandrini, S., 1997, A simplified version of the correct boundary conditions for skewed turbulence in Lagrangain particle models. A tmos. Environ., 31:301–308.Google Scholar
  2. Baerentsen, J.H., and Berkowicz, R, 1984, Monte Carlo simulation of plume dispersion in the convective boundary layer. Atmos. Environ. 18:701–712.CrossRefGoogle Scholar
  3. Deardorff, J.W. and Willis, G.E., 1982, Ground-level concentrations due to fumigation into an entraining mixed layer. Atmos. Environ. 16:1159–1170.CrossRefGoogle Scholar
  4. Deardorff, J.W., Willis, G.E., and Stockton, B.H., 1980, Laboratory studies of the entrainment zone of a convectively mixed layer. J. Fluid Mech. 100:41–64.CrossRefGoogle Scholar
  5. Du, S., Wilson, J.D., and Yee, E., 1994, Probability density functions for velocity in the convective boundary layer, and implied trajectory models. Atmos. Environ. 28:1211–1217.CrossRefGoogle Scholar
  6. Hibberd, M.F., and Luhar, A.K., 1996, A laboratory study and improved PDF model of fumigation into a growing convective boundary layer. Atmos. Environ. 30:3633–3649.CrossRefGoogle Scholar
  7. Hibberd, M.F., and Sawford, B.L., 1994, A saline laboratory model of the planetary convective boundary layer. Boundary-Layer Met. 67:229–250.CrossRefGoogle Scholar
  8. Lenschow, D.H., Mann, J, and Kristensen, L., 1994, How long is long enough when measuring fluxes and other turbulence statistics? J. Atmos. Oceanic Technol. 11:661–673.CrossRefGoogle Scholar
  9. Luhar, A.K., and Britter, R.E., 1989, A random walk model for dispersion in inhomogeneous turbulence in a convective boundary layer. Atmos. Environ. 23:1911–1924.CrossRefGoogle Scholar
  10. Luhar, A.K., and Sawford, B.L., 1995, Lagrangian stochastic modelling of the coastal fumigation phenomenon., J. Appl. Meteor. 34:2259–2277.CrossRefGoogle Scholar
  11. Luhar, A.K., and Sawford, B.L., 1996, An examination of existing shoreline fumigation models and formulation of an improved model. Atmos. Environ. 30:609–620.CrossRefGoogle Scholar
  12. Luhar, A.K., Hibberd, M.F., and Hurley, P.J., 1996, Comparison of closure schemes used to specify the velocity pdf in Lagrangian stochastic dispersion models for convective conditions. Atmos. Environ. 30:1407–1418.CrossRefGoogle Scholar
  13. Thomson, D.J., 1987, Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech, 180:529–556.CrossRefGoogle Scholar
  14. Thomson, D.J., and Montgomery, M.R., 1994, Reflection boundary conditions for random walk models of dispersion in non-Gaussian turbulence. Atmos. Environ., 28:1981–1987.CrossRefGoogle Scholar
  15. Thomson, D.J., Physick, W.L., and Maryon, R.H., 1997, Treatment of interfaces in random walk dispersion models. J. Appl. Meteor., in press.Google Scholar
  16. Weil, J.C., 1990, A diagnosis of the asymmetry in top-down and bottom-up diffusion using a Lagrangian stochastic model. J. Atmos. Sci. 47:501–515.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • William L. Physick
    • 1
  1. 1.CSIRO Division of Atmospheric ResearchAspendaleAustralia

Personalised recommendations