Navier–Stokes relaxation to sinh–Poisson states at finite Reynolds numbers
作者:
David Montgomery,
Xiaowen Shan,
William H. Matthaeus,
期刊:
Physics of Fluids A
(AIP Available online 1993)
卷期:
Volume 5,
issue 9
页码: 2207-2216
ISSN:0899-8213
年代: 1993
DOI:10.1063/1.858558
出版商: AIP
数据来源: AIP
摘要:
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.
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