一个二流体系统中非线性水波的Hamilton描述

卢东强; 戴世强; 张宝善

一个二流体系统中非线性水波的Hamilton描述

上海大学上海市应用数学和力学研究所, 上海 200072

基金项目: 国家自然科学基金资助项目(19672035)

详细信息

作者简介:
卢东强(1972~ ),男,助教,硕士.

中图分类号: O353.2
计量
- 文章访问数: 2422
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- 被引次数: 0
出版历程
- 收稿日期: 1997-12-24
- 修回日期: 1998-08-27
- 刊出日期: 1999-04-15

Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China

摘要

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.
- 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.
- two-fluid system /
- Hamilton’s principle /
- nonlinear water waves /
- shallow water assumption /
- Hamiltonian canonical equations

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参考文献(10)

[1]	Luke L C.A variational principle for a fluid with a free surface[J].J Fluid Mech,1967,27:395~397.
[2]	Whitham G B.Variational methods and application to water waves[J].Proc Roy Soc A,1967,299(1):6~25.
[3]	Zakharov V E.Stability of periodic wave of finite amplitude on the surface of a deep fluid[J].J Appl Mech Tech Phys,1968,2(2):190~194.
[4]	Miles J W.On Hamilton's principle for surface waves[J].J Fluid Mech,1977,83:153~158.
[5]	Milder D M.A note regarding “On Hamilton's princilple for surfaces waves”[J].J Fluid Mech,1977,83:159~161.
[6]	Benjamin T B,Olver P J.Hamiltonian structure,symmetries and conservation laws for water wave[J].J Fluid Mech,1982,125:137~185.
[7]	张宝善,卢东强,戴世强,等.非线性水波 Hamilton 系统理论与应用研究进展[J].力学进展,1998,28(4):521~531.
[8]	Craig W,Groves M D.Ham iltonian long-wave approximations to the water waves problems[J].Wave Motion,1994,19:367~389
[9]	卢东强,戴世强,张宝善.非线性水波无穷维 Hamilton 结构[A].见:程昌钧、戴世强、刘宇陆主编.现代数学和力学(MMM-Ⅶ)[C].上海:上海大学出版社,1997,387~390.
[10]	戴世强.一个二流体系统中两对孤立波的相互作用[J].中国科学,A 辑,1983,26:1007~1017.