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

注意:本論文已在《應用數學和力學(英文版)》1999,34(4):331-336.發表
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Applied Mathematics and Mechanics - English Edition, Vol. 20, No. 4, pp. 343-349, Apr 1999.

Lu Dongqiang, Dai Shiqiang, Zhang Baoshan

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

 

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.
Key words: two-fluid system; Hamilton's principle; nonlinear water waves; shallow water assumption; Hamiltonian canonical equations

一個二流體系統中非線性水波的Hamilton描述
盧東強 戴世強 張寶善

(上海大學應用數學與力學研究所)

摘要: 討論了一個二流體系統中非線性水波的Hamilton描述,該系統由水平固壁之上的兩層常密度不可壓無粘流體組成,上表面為自由面.文中將速度勢函數展開成垂向坐標的冪級數,在淺水長波的假定下,取下層流體的“動厚度”與上層流體的“折合動厚度”為廣義位移、界面上和自由面上的速度勢為廣義動量,根據Hamilton原理并運用Legendre變換導出該系統的Hamilton正則方程,從而將單層流體情形的結果推廣到分層流體的情形.

關鍵詞: 二流體系統; Hamilton原理; 非線性水波; 淺水假定; Hamilton正則方程
中圖分類號: O353.2   文獻標識碼: A
文章編號:1000-0887(1999)04-0331-06

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