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Determining modes and fractal dimension of turbulent flows

Published online by Cambridge University Press:  20 April 2006

P. Constantin ,
C. Foias ,
O. P. Manley  and
R. Temam
P. Constantin
Affiliation:
Indiana University, Bloomington, IN 47405
C. Foias
Affiliation:
Indiana University, Bloomington, IN 47405
O. P. Manley
Affiliation:
U.S. Department of Energy, Washington DC 20545
R. Temam
Affiliation:
Laboratoire d'Analyse Numérique, CNRS and Université Paris-Sud, 91405 Orsay
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Abstract

Research on the abstract properties of the Navier–Stokes equations in three dimensions has cast a new light on the time-asymptotic approximate solutions of those equations. Here heuristic arguments, based on the rigorous results of that research, are used to show the intimate relationship between the sufficient number of degrees of freedom describing fluid flow and the bound on the fractal dimension of the Navier–Stokes attractor. In particular it is demonstrated how the conventional estimate of the number of degrees of freedom, based on purely physical and dimensional arguments, can be obtained from the properties of the Navier–Stokes equation. Also the Reynolds-number dependence of the sufficient number of degrees of freedom and of the dimension of the attractor in function space is elucidated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 150 , January 1985 , pp. 427 - 440
Copyright
© 1985 Cambridge University Press

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