Bounds for the mean dissipation of 2-D enstrophy and 3-D energy in turbulent flows

A rigorous statistical definition of the average enstrophy dissipation in two-dimensional flows, and of the average energy dissipation in three-dimensional flows leads to the establishment of rigorous lower bounds on the corresponding cut-off wave numbers. That in turn permits us to conjecture the c...

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Bibliographic Details
Published in:Physics letters. A 1993-03, Vol.174 (3), p.210-215
Main Authors: Foias, C, Manley, O.P, Temam, R
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Physics
Turbulent flows, convection, and heat transfer
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Summary:A rigorous statistical definition of the average enstrophy dissipation in two-dimensional flows, and of the average energy dissipation in three-dimensional flows leads to the establishment of rigorous lower bounds on the corresponding cut-off wave numbers. That in turn permits us to conjecture the corresponding lower bounds on the number of degrees of freedom in those flows. For a particular commonly considered strong body force driving a turbulent two-dimensional flow, an improved upper bound on the number of degrees of freedom is found.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(93)90760-W