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.

Keywords

AttractorDegrees of freedom (physics and chemistry)Fractal dimensionDimension (graph theory)TurbulenceReynolds numberFractalSpace (punctuation)Navier–Stokes equationsFlow (mathematics)Mathematical analysisPhysicsMathematicsStatistical physicsCompressibilityMechanicsComputer sciencePure mathematics

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Publication Info

Year
1985
Type
article
Volume
150
Pages
427-440
Citations
210
Access
Closed

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Peter Constantin, Ciprian Foiaş, O. P. Manley et al. (1985). Determining modes and fractal dimension of turbulent flows. Journal of Fluid Mechanics , 150 , 427-440. https://doi.org/10.1017/s0022112085000209

Identifiers

DOI
10.1017/s0022112085000209