论文部分内容阅读
讨论了一个二流体系统中非线性水波的Ｈａｍｉｌｔｏｎ描述，该系统由水平固壁之上的两层常密度不可压无粘流体组成，上表面为自由面·文中将速度势函数展开成垂向坐标的幂级数，在浅水长波的假定下，取下层流体的“动厚度”与上层流体的“折合动厚度”为广义位移、界面上和自由面上的速度势为广义动量，根据Ｈａｍｉｌｔｏｎ原理并运用Ｌｅｇｅｎｄｒｅ变换导出该系统的Ｈａｍｉｌｔｏｎ正则方程，从而将单层流体情形的结果推广到分层流体的情形·
The Hamiltonian description of nonlinear water waves in a two-fluid system is discussed. The system consists of two layers of normally ingestible incompressible and non-viscous fluids above the horizontal solid wall and the upper surface is a free surface. The velocity potential function is expanded into vertical coordinates Under the assumption of shallow water longwave, the “dynamic thickness” of the lower fluid and the “folded thickness” of the upper fluid are generalized displacements. The velocity potential at the interface and the free surface is a generalized momentum. According to Hamilton’s principle Using the Legendre transformation to derive the Hamilton’s canonical equations for this system, the result of a single-layer fluid case is generalized to the case of stratified fluid