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Kakutanim inimax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.
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 time-averaged rate of viscous energy dissipation.In present study,an optimization 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 Kakutani minimax theorem in game theory was applied to obtain a set of conditions under which the maximization and the minimization in the minimax 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.
出处
《应用数学和力学》
CSCD
北大核心
2010年第7期772-780,共9页
Applied Mathematics and Mechanics
基金
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)
关键词
minimax定理
变分方法
博弈论
湍流
耗散率
上确界
minimax theorem
variational method
game theory
turbulence
dissipation rate
upper bound
