斜坡叠加起伏海床对波浪反射的修正缓坡方程有限差分解  

Finite Difference Solution of the Modified Mild Slope Equation for Wave Reflection by a Slope With Superimposed Undulating Seabed

作　　者：倪云林 张希疆 于姜梅 沈良朵 NI Yunlin;ZHANG Xijiang;YU Jiangmei;SHEN Liangduo(College of Marine Engineering Equipment,Zhejiang Ocean University,Zhoushan,Zhejiang 316022,P.R.China;Zhoushan Ecological Environment Low Carbon Development Center,Zhoushan,Zhejiang 316021,P.R.China)

机构地区：[1]浙江海洋大学海洋工程装备学院,浙江舟山316022 [2]舟山市生态环境低碳发展中心,浙江舟山316021

出　　处：《应用数学和力学》2024年第5期606-621,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51879237);省属高校基本科研业务项目(2021JZ008)。

摘　　要：基于修正缓坡方程,建立了方程求解的有限差分模型,研究了斜坡叠加起伏海床对波浪的反射.首先,对波浪入射平面斜坡以及水平海床上单周期、双周期正弦沙纹的反射问题进行了验证,结果与他人的数值解、解析解及实验数据吻合较好,证明了该模型的正确性.接着,讨论了抛物形斜坡的上凸高度及下凸深度,斜坡叠加单周期正弦沙纹的数量、高度及长度,斜坡叠加双周期正弦沙纹的高度对波浪反射系数的影响.结果表明,反射系数随抛物形斜坡上凸高度的增大而减小,随下凸深度的增大而增大.斜坡叠加单周期正弦沙纹对波浪反射的规律与水平海床基本一致,相比水平海床Bragg共振相位下移的幅度随沙纹数量增加,先减小后保持不变的情况,斜坡叠加沙纹共振相位下移的幅度随沙纹数量增加先减小后增大.波浪入射斜坡叠加双周期正弦沙纹地形,随叠加的两个沙纹高度分别增加,Bragg共振峰值均相应地增加,共振带宽几乎不受影响,主振峰值的相位下移幅度减小,这与单周期沙纹中随沙纹高度增加,共振相位下移幅度更大的情况相反.对比发现:当固定沙纹的数量、长度、高度,不论是水平海床还是斜坡海床,双周期正弦沙纹对波浪的反射强度以及激发的共振带宽均大于单周期正弦沙纹,共振相位下移的幅度则小于单周期沙纹;斜坡叠加正弦沙纹对波浪的反射强度要大于水平海床,零反射的现象不再存在,主振峰值的相位下移幅度较水平海床更大.A finite difference model was established to solve the modified mild slope equation,and the reflec-tion of waves on the slope with superimposed undulating seabed was studied.Firstly,the reflection problems of incident waves on straight slope terrain,singly periodic sinusoidal sand ripples and doubly periodic sinusoidal sand ripples superimposed on the horizontal seabed,were verified in excellent agreement with the numerical and analytical solutions and experimental data of others,to prove the correctness of the model.Then,the influ-ences of the upper convex height and lower convex depth of the slope with superimposed parabolic terrain,the number,height,and length of the slope with superimposed singly periodic sinusoidal sand ripples,and the height of the slope with superimposed doubly periodic sinusoidal sand ripples on wave reflection coefficients,were explored.The results show that,the reflection coefficient decreases with the upper convex height and in-creases with the lower convex depth on the parabolic slope.The law of wave reflection of slope with superim-posed singly periodic sinusoidal sand ripples is the same as that of the horizontal seabed.Compared with the horizontal seabed,where the amplitude of the resonance phase downshift decreases with the number of sand ripples and then stays unchanged,the amplitude of the resonance phase downshift of the slope with superim-posed sand ripples firstly decreases and then increases with the number of sand ripples.In the slope with super-imposed doubly periodic sinusoidal sand ripples terrain,the peaks of the Bragg resonance increase with the heights of the 2 superimposed sand ripples,respectively,where the resonance bandwidth is almost unaffected,and the phase downshift amplitude of the peak Bragg primary resonance decreases,which is contrary to the sit-uation that the amplitude of resonance phase downshift increases with the height of the singly periodic sand rip-ples.With the fixed number,length,and height of sand ripples,the reflection intensity of doubly period

关 键 词：修正缓坡方程 有限差分法 斜坡海床 Bragg共振反射 相位下移 共振带宽 

分 类 号：P731.22[天文地球—海洋科学]