Skip to main content
SpringerLink
Log in

The random force theory: Application to meso- and large-scale atmospheric diffusion

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Angell, J. K.: 1960, ‘Analysis of operational 300-mb transosonde flight from Japan in 1957–58’, J. Meteorol. 17, 20–35.

    Google Scholar 

  • Barr, S.: 1983, ‘The random force theory applied to regional scale tropospheric diffusion’, Los Alamos Nat. Lab., ESS-7 Div. MS.

  • Batchelor, G. K.: 1950, ‘The application of the similarity theory of turbulence to atmospheric diffusion’, Quart. J. R. Met. Soc. 76, 133–146.

    Google Scholar 

  • 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.

    Google Scholar 

  • Brier, G. W.: 1950, ‘The statistical theory of turbulence and the problem of diffusion in the atmosphere’, J. Meteorol. 7, 283–290.

    Google Scholar 

  • 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.

    Google Scholar 

  • Chadam, J.: 1962, ‘On a theory of turbulent diffusion’, AFCRL Research Note, AFCRL-62-1107, vii and 26 pp. U.S. Air Force.

  • Charney, J.: 1971, ‘Geostrophic turbulence’, J. Atmos. Sci. 28, 1087–1095.

    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 

  • Gifford, F. A.: 1982, ‘Horizontal diffusion in the atmoshpere: a Lagrangian, dynamical theory’, Atmos. Environ. 16, 505–512.

    Google Scholar 

  • 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 

  • Golitsyn, G.: 1973, ‘Introduction to the dynamics of planetary atmospheres’, Gidrometeoizdat, Leningrad, 103pp, NASA trans. No. TT F-15, 627, Dec. 1974.

    Google Scholar 

  • Hanna, S. R.: 1979, ‘Some statistics of Lagrangian and Eulerian wind fluctuations’, J. Appl. Meteorol. 18, 518–525.

    Google Scholar 

  • Krasnoff, E. and Peskin, R. L.: 1971, ‘The Langevin model for turbulent diffusion’, Geophys. Fluid Dynam. 2, 123–146.

    Google Scholar 

  • Kao, S. K.: 1962, ‘Large-scale diffusion in a rotating fluid with applications to the atmosphere’, J. Geophys. Res. 67, 2347–2359.

    Google Scholar 

  • 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 Geophys. 18B, 15–32, (1974).

  • 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 

  • Levin, A. V.: 1971, ‘Random processes and the Richardson-Obukhov law’, Trudy Ukrainsk. Nautchna-Issled. Gidrometeorol. Inst. 106, 3–12.

    Google Scholar 

  • Levin, A. V.: 1973, ‘Statistical model of atmospheric diffusion with two relaxation times’, Trudy Ukrainsk. Nautchna-Issled. Gidrometeorol. Inst. 125, 150–157.

    Google Scholar 

  • 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.

  • 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 

  • Lilly, D. K.: 1983, ‘Stratified turbulence and the mesoscale variability of the atmosphere’, J. Atmospher. Sci. 40, 749–761.

    Google Scholar 

  • Lin, C. C. and W. H. Reid: 1963, ‘Turbulent flow’, in Handbuch der Physik VIII/2, 438–523, Springer,Berlin.

    Google Scholar 

  • Monin, A. S.: 1972, ‘Weather forecasting as a problem in physics’, MIT Press, Cambridge, MA.

    Google Scholar 

  • Monin, A. S. and Yaglom, A. M.: 1967, ‘Statistical fluid mechanics’, Nauka, Moscow (Trans. MIT Press, Cambridge, MA, 1971).

    Google Scholar 

  • Novikov, E. A.: 1963, ‘Random force method in turbulence theory’; Soviet Phys. JETP 17, pp1449–1454.

    Google Scholar 

  • Obukhov, A. M.: 1959, ‘Description of turbulence in terms of Lagrangian variables’, Adv. in Geophys. 6, 113–116.

    Google Scholar 

  • 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 

  • Richardson, L. F.: 1926, ‘Atmospheric diffusion shown on a distanceneighbor graph’, Proc. R. Soc. Lond. 110A, 709–737.

    Google Scholar 

  • Sawford, B. L.: 1982a, ‘Comparison of some different approximations in the statistical theory of relative dispersion’, Quart. J. R. Met. Soc. 10B, 191–206.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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 

  • Smith, F. B.: 1968, ‘Conditioned particle motion in a homogeneous turbulent field’, Atmos. Environ. 2, 491–508.

    Google Scholar 

  • Taylor, G. I.: 1921, ‘Diffusion by continuous movements’, Proc. London Math. Soc. 20, 196–211.

    Google Scholar 

  • Tennekes, H.: 1978, ‘The exponential Lagrangian correlation function and turbulent diffusion in the inertial subrange’, Atmos. Environ. 13, 1565–1567.

    Google Scholar 

  • Tennekes, H., and Lumley, J. L.: 1972, ‘A first course in turbulence’, xii and 300 pp., MIT Press, Cambridge, MA.

    Google Scholar 

  • Thompson, D. J.: 1983, ‘Random walk modelling of diffusion in inhomogeneous turbulence’, UK Met. Office, Met. 0. 14, T.D.N. No. 144.

  • Yaglom, A. M.: 1977, ‘Semi-empirical equations of turbulent diffusion in boundary layers’, Fl. Dynamics Trans., Polish Acad. Sci., 7, 99–144.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 109 Gorgas Lane, 37830, Oak Ridge, TN, USA

    F. A. Gifford

Authors
  1. F. A. Gifford
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gifford, F.A. The random force theory: Application to meso- and large-scale atmospheric diffusion. Boundary-Layer Meteorol 30, 159–175 (1984). https://doi.org/10.1007/BF00121953

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00121953

Keywords

Search

Navigation