一个关于流动能量耗散率的minimax变分原理

陈波; 李孝伟; 刘高联

doi:10.3879/j.issn.1000-0887.2010.07.002

一个关于流动能量耗散率的minimax变分原理

doi: 10.3879/j.issn.1000-0887.2010.07.002

上海大学上海应用数学和力学研究所,上海 200072

基金项目: 国家自然科学基金资助项目(10772103);上海市重点学科建设项目资助(Y0103)

详细信息

作者简介:
陈波(1969- ),男,江苏人,讲师,博士(联系人.E-mail:bochen@shu.edu.cn).

中图分类号: O357.1
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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-05-28
- 刊出日期: 2010-07-15

A Minimax Principle on Energy Dissipation of Incompressible Shear Flow

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

摘要

摘要: 流动耗散率是湍流理论的核心概念之一．Doering-Constantin变分原理刻画了流动耗散率的上确界(最大值)．在该文的研究中，首先基于优化理论的视角，Doering-Constantin的变分原理被改写为一个不可压缩剪切流耗散率的minimax型的变分原理．其次，博弈论中的Kakutani minimax定理给出该变分原理中minimizing和maximizing计算过程可交换的一个充分条件．这个结果不仅从一个新的角度揭示了谱约束的内涵，也为Doering-Constantin变分原理和Howard-Busse统计理论的等价性从博弈论的角度提供了理论基础．
- minimax定理 /
- 变分方法 /
- 博弈论 /
- 湍流 /
- 耗散率 /
- 上确界
Abstract: Energy dissipation rate is one of the most important concepts in turbulence theory. Doering-Constantin's variational principle characterizes the upper bounds(maximum) of the tmie-averaged rate of viscous energy dissipation. In present study, an optmiization theoretic point of view was adopted to recast Doering-Constantin's formulation into a minimax principle for the energy dissipation of an incompressible shear flow. Then the Kakutaniminimax theorem in game theory was applied to obtain a set of conditions under which the maximization and the minimization in the minmiax principle are commutative. The results not only elucidate the spectral constraint of Doering-Constantin, but also confirm the equivalence of Doering-Constantin's variational principle and Howard-Busse's statistical turbulence theory.
- minimax theorem /
- variational method /
- gametheory /
- turbulence /
- dissipation rate /
- upper bound

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参考文献(21)

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