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Phys. Rev. Lett. 51, 617–620 (1983)

New Representation of Navier-Stokes Equations Governing Self-Similar Homogeneous Turbulence

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C. Foias
Indiana University, Bloomington, Indiana 47505

O. P. Manley
U.S. Department of Energy, Washington, DC 20545

R. Temam
Laboratoire d'Analyse Numérique, Centre National de la Recherche Scientifique and Université Paris-Sud, F-91405 Orsay, France

Received 9 May 1983; published in the issue dated 22 August 1983

A new form of the Navier-Stokes equation resulting from a change of variables is presented. The new form has several advantages: It yields a new asymptotic behavior of the flow for long times and vanishingly small viscosity. In addition an interpretation of the new equation in terms of a simple random walk yields immediately not only the Kolmogorov 2/3-power law but also an intermittency exponent well within the experimental uncertainty.

© 1983 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.51.617
DOI:
10.1103/PhysRevLett.51.617
PACS:
03.40.Gc, 47.10.+g, 47.25.-c