摘要
通过变分原理 ,将哈密顿体系的理论引入到平面粘性流体扰动的问题中 ,导出一套哈密顿算子矩阵的本征函数向量展开求解问题的方法。基于直接法求解流体力学基本方程 ,导出流场一般特征关系 ,通过本征值的求解及本征向量的叠加 ,得到波扰动解 ,继可分析流场端部效应。从而在该领域用在哈密顿体系下辛几何空间中研究问题的方法代替了传统在拉格朗日体系欧几里德空间分析问题的方法。为流体力学的研究提供一条新途径。
The traditional solution methods of fluid dynamic mechanics, which were described based on one kind of variable, belong to the Euclidian space under the Lagrange system formulation. It's difficult to deal with some complex domain. In this paper, the new dual variables and Hamiltonian function are introduced first. It is thus that the problem is promoted to symplectic geometrical under the conservative Hamiltonian system. Furthermore, the solution based on the expansion of enginvectors of Hamiltonian operator matrix is derived. The disturbance of plane viscous flow is solved directly. Then, the general characteristic relation of flow field is deduced. By virtue of solving the proper value and superposing the proper vector, the solution of wave disturbance in plane viscous flow with low Reynolds number is obtained. Finally, the edge efficiency of flow field may be analysis. A new solution procedure for the research of the fluid mechanics is put forward.
出处
《应用力学学报》
CAS
CSCD
北大核心
2001年第4期82-86,共5页
Chinese Journal of Applied Mechanics
