广义缓坡方程

Extended Mild-Slope Equation

运用表面波Hamilton方法和缓坡逼近假定 ,分析缓变三维流场和非平整海底对波浪传播的影响 ,推导出广义缓坡方程· 海底地形由两个分量组成 :慢变分量 ,其水平长度尺度大于表面波的波长 ;快变分量 ,其振幅与表面波的波长相比为一小量 ,但是其频率与表面波频率相当· 该广义缓坡方程具有广泛的适用范围 ,以下著名的缓坡方程成为它的特例 :经典的Berkhoff缓坡方程 ;包含环境流效应的Kirby缓坡方程 ;描述波状海底特征的Dingemans缓坡方程· 另外 ,同时也得到了描述环境流场和快变海底效应的广义浅水方程·

The Hamiltonian formalism for surface waves and the mild_slope approximation were empolyed in handling the case of slowly varying three_dimensional currents and an uneven bottom, thus leading to an extended mild_slope equation. The bottom topography consists of two components: the slowly varying component whose horizontal length scale is longer than the surface wave length, and the fast varying component with the amplitude being smaller than that of the surface wave. The frequency of the fast varying depth component is, however, comparable to that of the surface waves. The extended mild_slope equation is more widely applicable and contains as special cases famous mild_slope equations below: the classical mild_slope equation of Berkhoff, Kirby's mild_slope equation with current, and Dingemans's mild_slope equation for rippled bed. The extended shallow water equations for ambient currents and rapidly varying topography are also obtained.