The Integral Equation of Diffusion

  • F. B. Smith
Part of the Nato · Challenges of Modern Society book series (NATS, volume 5)


Various theories are now available to describe the dispersion of passive material released from a source into the atmosphere. These theories include the eddy-diffusivity equation of diffusion, statistical theory, similarity theory, higher-order closure solutions of the basic equation of motion and continuity, and rondom walk modelling. All these methods explicitly or implicitly require some knowledge of the Lagrangian character of the turbulence field. Some methods only apply to rather idealised states of flow (e.g. statistical theory only applies to uniform flow with homogeneous turbulence) whereas others are much more versatile — (e.g. random walk modelling). Some are simple in concept and application, others are much more complex. In recent years the virtues of random walk modelling have been recognized and the technique widely exploited.


Turbulent Velocity Source Strength Random Walk Modelling Homogeneous Turbulence Cumulative Concentration 
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  1. Hanna, S.R., 1979 Some statistics of Lagrangian and Eulerian wind fluctuations. J.Appl.Met., 18, 4.ADSCrossRefGoogle Scholar
  2. Reid, J.D., 1979 Markov-chain simulations of vertical dispersion in the neutral surface layer for surface and elevated releases. B.L. Met., 16, pp 3–22.Google Scholar
  3. Smith, F.B., 1968 Conditioned particle motion in a homogeneous turbulent field: Atmos. Environ., 2, pp 491–508.CrossRefGoogle Scholar
  4. Taylor, G.I., 1921 Diffusion by continuous movements. Proc. London Math. Soc., Ser.2., 20 p 196.zbMATHCrossRefGoogle Scholar
  5. Thomson D., and Ley A., 1982 A random walk dispersion model applicable to diabatic conditions. Internal Met Office Note T.D.N. 138.Google Scholar
  6. Wilson, J.D., Thurtell, G.W. and Kidd, G.E., 1981 Numerical simulations of particle trajectories in inhomogeneous turbulence. Part II: systems with variable turbulent velocity scales. B.L. Met., 21, pp 423–441.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • F. B. Smith
    • 1
  1. 1.Meteorological Office BracknellBerkshireUK

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