Navier--Stokes relaxation to sinh--Poisson states at finite Reynolds numbers
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755-3528 (United States)
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
- Bartol Research Institute, University of Delaware, Newark, Delaware 19716 (United States)
A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier--Stokes fluid to a most probable,'' or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables.
- DOE Contract Number:
- FG02-85ER53194
- OSTI ID:
- 6076880
- Journal Information:
- Physics of Fluids A; (United States), Journal Name: Physics of Fluids A; (United States) Vol. 5:9; ISSN 0899-8213; ISSN PFADEB
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
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IRREVERSIBLE PROCESSES
NAVIER-STOKES EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
RELAXATION
REYNOLDS NUMBER
TURBULENT FLOW
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VISCOUS FLOW