Journal article
Global theorems for boundary‐free viscous incompressible fluid flows of finite energy
Journal of mathematical physics, v 23(4), pp 676-679
Apr 1982
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Abstract
It is shown that the a
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t
i
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n for boundary‐free incompressible fluid flow (i.e., the time‐integral of the kinetic energy of the motion) is an absolute minimum with respect to all velocity‐field transformations u→u* if u* is structured suitably in terms of u and an arbitrary solenoidal test field f. As suggested by this physical minimum principle, inequality analysis is applied to obtain an upper bound on the time derivative of the dissipation integral, from which there follow sufficient conditions for a monotone‐decreasing dissipation integral and a monotone‐decreasing global Reynolds number. The latter result provides an experimentally consistent necessary condition for passage from laminar to turbulent flow. Finally, inequality analysis is employed to derive a time‐dependent lower bound on the maximum velocity gradient in a generic boundary‐free flow of finite energy.
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Details
- Title
- Global theorems for boundary‐free viscous incompressible fluid flows of finite energy
- Creators
- Gerald Rosen - Drexel University
- Publication Details
- Journal of mathematical physics, v 23(4), pp 676-679
- Publisher
- American Institute of Physics (AIP)
- Number of pages
- 4
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Web of Science ID
- WOS:A1982NH85700030
- Scopus ID
- 2-s2.0-36749114454
- Other Identifier
- 991019174223004721
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- Web of Science research areas
- Physics, Mathematical