Determining modes and fractal dimension of turbulent flows

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 th...

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Bibliographic Details
Published in:Journal of fluid mechanics 1985-01, Vol.150, p.427-440
Main Authors: Constantin, P., Foias, C., Manley, O. P., Temam, R.
Format: Article
Language:English
Subjects:
boundary layers
Exact sciences and technology
Fluid dynamics
fluid mechanics
Fundamental areas of phenomenology (including applications)
heuristics
Navier Stokes equations
Physics
turbulence
Turbulent flows, convection, and heat transfer
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112085000209