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The Random Force Theory: Application to Meso- and Large-Scale Atmospheric Diffusion

  • F. A. Gifford

Abstract

The physical basis for the random force theory of atmospheric diffusion is briefly reviewed. The random force equation has usually been introduced as an atmospheric analogy to Brownian motion. Here it is derived by assuming a type of Rayleigh friction in the Lagrangian equations of atmospheric motion. Consequences, including the Lagrangian correlation and spectrum, the particle-particle intercorrelation, and cluster and plume dispersion and meandering, are derived and compared with atmospheric observations. The characteristic time-scale of atmospheric diffusion is shown to be governed by the Coriolis effect, a result in good agreement with meso- and large-scale observations.

Keywords

Planetary Boundary Layer Turbulent Diffusion Atmospheric Turbulence Atmospheric Motion Relative Diffusion 
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.

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References

  1. Angell, J. K.: 1960, ‘Analysis of operational 300-mb transosonde flight from Japan in 1957–58’, J. Meteorol. 17, 20–35.CrossRefGoogle Scholar
  2. Barr, S.: 1983, ‘The random force theory applied to regional scale tropospheric diffusion’, Los Alamos Nat. Lab., ESS-7 Div. MS.Google Scholar
  3. Batchelor, G.K.: 1950, ‘The application of the similarity theory of turbulence to atmospheric diffusion’, Quart. J. R. Met. Soc. 76, 133–146.CrossRefGoogle Scholar
  4. Bigg, E.K., Ayers, G.P., and Turvey, D.E.: 1978, ‘Measurement of the dispersion of a smoke plume at a large distance from the source’, Atmos. Environ. 12, 1815–1818.CrossRefGoogle Scholar
  5. Brier, G. W.: 1950, ‘The statistical theory of turbulence and the problem of diffusion in the atmosphere’, J. Meteorol. 7, 283–290.CrossRefGoogle Scholar
  6. Carras, J. N., and Williams, D. J.: 1981, ‘The long-range dispersion of a plume from an isolated point source’, Atmos. Environ. 15, 2205–2217.CrossRefGoogle Scholar
  7. Chadam, J.: 1962, ‘On a theory of turbulent diffusion’, AFCRL Research Note, AFCRL-62–1107, vii and 26 pp. U.S. Air Force.Google Scholar
  8. Charney, J.: 1971, ‘Geostrophic turbulence’, J. Atmos. Sci. 28, 1087–1095.CrossRefGoogle Scholar
  9. Durbin, P. A.: 1980, ‘A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence’, J. Fluid Mech. 100, 279–302.CrossRefGoogle Scholar
  10. Gifford, F. A.: 1982, ‘Horizontal diffusion in the atmoshpere: a La- grangian, dynamical theory’, Atmos. Environ. 16, 505–512.CrossRefGoogle Scholar
  11. Gifford, F. A.: 1983, ‘Atmospheric diffusion in the mesoscale range: the evidence of recent plume width measurements’, Preprint volume, 6th Symp on Turbulence and diffusion, March 22–25, Boston, Am. Meteor. Soc., pp 300–304.Google Scholar
  12. Golitsyn, G.: 1973, ‘Introduction to the dynamics of planetary atmospheres’, Gidrometeoizdat, Leningrad, 103pp, NASA trans. No. TT F-15, 627, Dec. 1974.Google Scholar
  13. Hanna, S. R.: 1979, ‘Some statistics of Lagrangian and Eulerian wind fluctuations’, J. Appl. Meteorol. 18, 518–525.CrossRefGoogle Scholar
  14. Krasnoff, E. and Peskin, R. L.: 1971, ‘The Langevin model for turbulent diffusion’, Geophys. Fluid Dynam. 2, 123–146.CrossRefGoogle Scholar
  15. Kao, S. K.: 1962, ‘Large-scale diffusion in a rotating fluid with applications to the atmosphere’, J. Geophys. Res. 67, 2347–2359.CrossRefGoogle Scholar
  16. Kao, S. K.: 1973, ‘Basic characteristics of global scale diffusion in the troposphere’, Proc. Symp. on Turbulent Diffusion in Environmental Pollution, April 8–14, 1973, Charlottesville, Virginia, Adv. in Geo- phys. 18B, 15–32, (1974).Google Scholar
  17. Lee, J. T., and G. L. Stone: 1983, ‘The use of Eulerian initial conditions in a Lagrangian model of turbulent diffusion’, Preprint volume, 6th Symp. on Turbulence and Diffusion, March 22–25, 1983, Boston, Am. Meteorol. Soc., pp. 13–17.Google Scholar
  18. Levin, A. V.: 1971, ‘Random processes and the Richardson-Obukhov law’, Trudy Ukrainsk. Nautchna-Issled. Gidrometeorol. Inst. 106, 3–12.Google Scholar
  19. Levin, A. V.: 1973, ‘Statistical model of atmospheric diffusion with two relaxation times’, Trudy Ukrainsk. Nautchna-Issled. Gidrometeorol. Inst. 125, 150–157.Google Scholar
  20. Ley, A. J. and Thompson, D. J.: 1982, ‘A random walk model of dispersion in the diabatic surface layer’, to be pub. in Quart. J. R. Met. Soc.Google Scholar
  21. Li, W.-W. and Meroney, R. N.: 1983, ‘Laboratory support for the determination of atmospheric diffusion parameters from field estimates of the Lagrangian scale’, Rep. no. CEP83–84WWL-RNM-3, Dept, of Civil Engrg., Colorado State Univ., Ft. Collins, CO 80521.Google Scholar
  22. Lilly, D. K.: 1983, ‘Stratified turbulence and the mesoscale variability of the atmosphere’, J. Atmospher. Sci. 40, 749–761.CrossRefGoogle Scholar
  23. Lin, C. C. and W. H. Reid: 1963, ‘Turbulent flow’, in Handbuch der Physik VIII/2, 438–523, Springer, Berlin.Google Scholar
  24. Monin, A. S.: 1972, ‘Weather forecasting as a problem in physics’, MIT Press, Cambridge, MA.Google Scholar
  25. Monin, A. S. and Yaglom, A. M.: 1967, ‘Statistical fluid mechanics’, Nauka, Moscow (Trans. MIT Press, Cambridge, MA, 1971).Google Scholar
  26. Novikov, E. A.: 1963, ‘Random force method in turbulence theory’, Soviet Phys. JETP 17, 1449–1454.Google Scholar
  27. Obukhov, A. M.: 1959, ‘Description of turbulence in terms of Lagrangian variables’, Adv. in Geophys. 6, 113–116.CrossRefGoogle Scholar
  28. Reid, J. D.: 1979, ‘Markov chain simulation of vertical dispersion in the neutral surface layer for surface and elevated releases’, Bound.- Layer Met. 16, 3–22.Google Scholar
  29. Richardson, L. F.: 1926, ‘Atmospheric diffusion shown on a distance- neighbor graph’, Proc. R. Soc. Lond. 110A, 709–737.Google Scholar
  30. Sawford, B. L.: 1982a, ‘Comparison of some different approximations in the statistical theory of relative dispersion’, Quart. J. R. Met. Soc. 10B, 191–206.CrossRefGoogle Scholar
  31. Sawford, B. L.: 1982b, ‘Lagrangian Monte Carlo simulation of the turbulent motion of a pair of particles’, Quart. J. R. Met. Soc. 108, 207–213.CrossRefGoogle Scholar
  32. Sawford, B. L.: 1983, ‘The effect of Gaussian particle-pair distribution functions in the statistical theory of concentration fluctuations in homogeneous turbulence’, Quart. J. R. Met. Soc. 109, 339–354.Google Scholar
  33. Smith, F. B.: 1968, ‘Conditioned particle motion in a homogeneous turbulent field’, Atmos. Environ. 2, 491–508.CrossRefGoogle Scholar
  34. Taylor, G. I.: 1921, ‘Diffusion by continuous movements’, Proc. London Math. Soc. 20, 196–211.CrossRefGoogle Scholar
  35. Tennekes, H.: 1978, ‘The exponential Lagrangian correlation function and turbulent diffusion in the inertial subrange’, Atmos. Environ. 13, 1565–1567.Google Scholar
  36. Tennekes, H., and Lumley, J. L.: 1972, ‘A first course in turbulence’, xii and 300 pp., MIT Press, Cambridge, MA.Google Scholar
  37. Thompson, D. J.: 1983, ‘Random walk modelling of diffusion in inhomoge- neous turbulence’, UK Met. Office, Met. 0. 14, T.D.N. No. 144.Google Scholar
  38. Yaglom, A. M.: 1977, ‘Semi-empirical equations of turbulent diffusion in boundary layers’, F1. Dynamics Trans., Polish Acad. Sci., 7, 99–144.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1984

Authors and Affiliations

  • F. A. Gifford
    • 1
  1. 1.Oak RidgeUSA

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