非平整运动海底上n层流动中波浪传播的Hamilton逼近

HAMILTONIAN APPROXIMATION OF WATER WAVES IN A n-LAYER FLOW OVER UNEVEN BOTTOMS

在海洋水域,界面波对大尺度变化流的作用是一种典型的分层流动现象.考虑一不可压缩、无黏的分层势流运动,建立了一个在非平整运动海底上的n层流体演化系统,并对其进行了Hamilton描述.每层流体具有各自的常密度、均匀流水平速度,其厚度由未扰动和扰动部分构成.相对于顶层流体的自由表面,刚性、运动的海底具有一般地形变化特征.在明确指出n层流体运动的控制方程和各层交界面上的运动学、动力学边界条件(包含各层交界面上张力效应)后,对该分层流动力系统进行了Hamilton构造,即给出其正则方程和其下述的正则变量:各交界面位移和各交界面上的动量势密度差.

The interfacial waves on large-scale currents in the ocean is typical of stratified flow. Here, a n-layer fluid evolution system, with constant density and uniform horizontal current velocity in each layer with a thickness consisting of undisturbed and disturbed part, over uneven moving bottoms is developed to illustrate the Hamiltonian description. The rigid and moving bottoms against the free surface in the top-layer flow have a general topography. After clearly stating the governing equations for the n layers of fluids and the kinematical and dynamical boundary conditions (including the effects of the interfacial tension) holding at each interface between the fluid layers, the Hamiltonian formulation of the stratified fluid dynamical system is constructed by giving the canonical equations and the canonical variables which are the interface displacements and the difference in momentum potential density measured at the interfaces.