波浪在缓变海底上传播的一个简单数学模型  

A simple mathematical model of wave propagation over a gently sloping sea bottom

作　　者：彭延建[1] 刘应中[1] 时钟[1] 

机构地区：[1]上海交通大学船舶海洋与建筑工程学院海洋工程国家重点实验室港口与海岸工程系,上海200030

出　　处：《海洋通报》2010年第3期302-309,共8页Marine Science Bulletin

基　　金：国家自然科学基金(水利科学50679040);上海交通大学特聘教授基金(DP2009012)

摘　　要：基于Liu和Shi(2008)的波浪势函数零阶、一阶近似解,采用四阶龙格-库塔法,对缓变海底上一维波浪传播理论模型进行了数值求解,并对波浪在定常坡度的斜坡地形、双曲正切地形为例的传播、变形进行了研究。为了更逼真地描述流体质点的波动特性,将在Euler坐标系下得到的解转换至Lagrange坐标下的解,并绘制Lagrange坐标下坡度为0.2的海滩上的一个波周期内临近破碎前的波形的详细变化过程。此外,计算得到了变水深区域波浪速度势以及自由面的分布,并与Athanassoulis and Belibassakis[34]的结果进行了对比,表明本文模型比保留了六个瞬息项的后者更有效。Based on the zero-order and first-order approximate solutions of the wave potential function in Liu and Shi[33],using the fourth-order Runge-Kutta method,the numerical solution has been made for the theoretical model of one-dimensional wave propagation over a gently sloping sea bottom in this paper.This paper also elucidates how waves propagate and deform over sloping bottom with a constant slope and hyperbolic tangent-shaped topography.To clearly depict the undulating motions of water particles,calculated solutions of the present model are transformed from the Euler coordinate system into the Lagrange coordinate system.Details of successive wave profiles prior to breaking on a beach at a slope of 0.2 over one wave period are plotted in the Lagrange coordinate system.Furthermore,the wave potential and free-surface elevation over the variable bathymetry regions are calculated by the present model and then compared with Athanassoulis and Belibassakis＇[34] results.The present results are more efficient than the latter obtained by retaining six evanescent modes.

关 键 词：波浪传播 缓变海底 波形 摄动 

分 类 号：TV139.2[水利工程—水力学及河流动力学]