波浪在不平坦海岸底床上传播的平面二维数学模型  

A two-dimensional horizontal numerical model of wave propagation over an uneven coastal 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港口与海岸工程系,海洋工程国家重点实验室,上海200030

出　　处：《中国港湾建设》2014年第1期8-13,共6页China Harbour Engineering

基　　金：海洋工程国家重点实验室自主研究课题(GKZD010056-9)

摘　　要：基于线性波浪理论,利用摄动理论中的多重尺度法,以坡度ε为小参数,Liu和Shi[1]推导出波浪在不平坦底床传播的波幅方程,以及一阶势函数的解析解。为验证该模型是否可用于平面二维波浪传播问题,利用有限差分法,分别对波幅方程和边界条件进行离散和求解,得到因折射、绕射引起的波幅和波向的变化。通过引入绕射因子,使该模型的应用范围更为广泛,并且计算精度得到提高。将计算得到的波向和波高与Berkhoff[2]、Berkhoff等[3]椭圆形浅滩试验值进行比较,表明该模型可以应用于平面二维问题。Based on the linear wave theory, by using the multiple-scale method and a small slope parameter e, Liu and Shi obtain the first-order approximate solutions of the wave potential function, as well as wave amplitude equation, for the prob- lem of wave propagation over an uneven coastal bottom. This study introduces the diffraction factor, which expands Liu and Shit^l＇s application range and improves its accuracy. Both wave amplitude equation and boundary conditions are discretized and solved by the finite difference method. Variations in wave amplitude and direction of wave propagation caused by the refraction and diffraction are obtained. The validation study has been made useing of the experimental results of Berkho^21 or Berkhoff et al^31＇s elliptic shoal test. It is suggested that the present model be applied to two-dimensional wave propagation problems.

关 键 词：多重尺度法 波浪传播 不平坦底床 

分 类 号：TV139.2[水利工程—水力学及河流动力学]