Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System
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摘要: 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.
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关键词:
- 二流体系统 /
- Hamilton原理 /
- 非线性水波 /
- 浅水假定 /
- Hamilton正则方程
Abstract: In this paper,it is dealt with that the Hamiltonian formulation of nonlinear water waves in a two-fluid system,which consists of two layers of constant-density incompressible inviscid fluid with a horizontal bottom,an interface and a free surface.The velocity potentials are expanded in power series of the vertical coordinate.By taking the kinetic thickness of lower fluid-layer and the reduced kinetic thickness of upper fluid-layer as the generalized displacements,choosing the velocity potentials at the interface and free surface as the generalized momenta and using Hamilton's principle,the Hamiltonian canonical equations for the system are derived with the Legendre transformation under the shallow water assumption.Hence the results for single-layer fluid are extended to the case of stratified fluid. -
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