摘要
本文用一种新方法研究粘性正压流体流动问题的变分原理.这一方法的特点是引入了一般非线性正压流体的静水压力能密度和余能密度的概念,建立了一般正压流体物态方程的泛函极值原理、粘性非线性正压流体流动问题的广义功率消耗原理和一些有关的广义变分原理.建立的泛函中,含有可供任意选择的参数函数.文中还指出在粘性流体力学的若干已知的变分原理中,自变函数σ_(ij)需限制在对称张量范围内.
This paper presents a new method for studyingthe variational principles of viscous barotropic fluid flow. Thefeature of the method is that two ideas, the deasity of stationa-rv water presure energy and the density of the complementaryenergy, are introduced. The extremum principle of the constitu-tive functional of the physical state equations of the barotropicfluids, the generalized variational principle of power loss andseveral other generalized variatioal prineiples concerned areestablised. All the uarious functionals established iu this paperinclude the parameter functions which may be arbitrarily chosen. This paper also points out that the indepeadent variable fun-ctions σ_(i?) of some known variational principles in viscous fluiddynamics should be confined in the range of symmetrical tensors.
关键词
粘性
流体
流动
广义
变分原理
Viscous fluid
flow
Generalized variational principles
Barotiopic fluid
