Diffusion in a turbulent phase space

  • Michael F. Shlesinger
  • Bruce J. West
  • Joseph Klafter
A. Classical Nonlinear Dynamics and Chaos
Part of the Lecture Notes in Physics book series (LNP, volume 278)


We introduce a novel stochastic process, called a Lévy Walk, to provide a statistical description of motion in a turbulent fluid. The Lévy Walk describes random (but still correlated) motion in space and time in a scaling fashion and is able to account for the motion of particles in a hierarchy of coherent structures. When Kolmogorov's -5/3 law for homogeneous turbulence is used to determine the memory of the Lévy Walk, then Richardson's 4/3 law of turbulent diffusion follows in the Mandelbrot absolute curdling limit. If, as suggested by Mandelbrot, that turbulence is isotropic, but fractal, then intermittency corrections follow in a natural fashion.


Brownian Motion Random Walk Fractal Brownian Motion Persistence Length Homogeneous Turbulence 
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. 1.
    S. Alexander and R. Orbach, J. Phys. (Paris) Lett. 43: L–625 (1982).CrossRefGoogle Scholar
  2. 2.
    M. F. Shlesinger, J. Stat. Phys. 10, 421 (1974).ADSCrossRefGoogle Scholar
  3. 3.
    B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York 1983).MATHGoogle Scholar
  4. 4.
    L. F. Richardson, Proc. Roy. Soc. London Ser A 110, 709 (1926).ADSCrossRefGoogle Scholar
  5. 5.
    H. G. E. Hentschel and I. Procaccia, Phys. Rev. A27, 1266 (1983).ADSCrossRefGoogle Scholar
  6. 6.
    F. Wegner and S. Grossman, Zeits, für Physik B59, 197 (1985).Google Scholar
  7. 7.
    A. N. Kolmogorov, C. R. (Dokl.) Acad. Sci USSR 30, 301 (1941).ADSGoogle Scholar
  8. 8.
    M. F. Shlesinger, B. J. West, and J. Klafter, Phys. Rev. Lett (Submitted).Google Scholar
  9. 9.
    M. F. Shlesinger and J. Klafter, Phys. Rev. Lett. 54, 2551 (1985).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Michael F. Shlesinger
    • 1
  • Bruce J. West
    • 2
  • Joseph Klafter
    • 3
  1. 1.Physics DivisionOffice of Naval ResearchArlington
  2. 2.Division of Applied Nonlinear ProblemsLa Jolla InstituteLa Jolla
  3. 3.Corporate Research Science LaboratoryExxon Research and Engineering CompanyAnnandale

Personalised recommendations