具有精确色散性非线性波浪方程的改进  

Improvement of nonlinear wave equations with precise dispersion

作　　者：卞宏伟 邹志利[1] 徐杰 BIAN Hongwei;ZOU Zhili;XU Jie(State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology,Dalian 116024,China;College of Transportation Engineering,Dalian Maritime University,Dalian 116026,China)

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024 [2]大连海事大学交通运输工程学院,辽宁大连116026

出　　处：《海洋工程》2025年第1期116-128,共13页The Ocean Engineering

基　　金：国家自然科学基金资助项目(51879033)。

摘　　要：以自由表面处的速度和波面升高为变量建立了一组新的具有精确色散性的非线性波浪方程。该方程对以往由速度势为变量的方程进行了改进,克服了方程不能考虑有旋波浪运动的不足;方程增加了适用于一般情况的二阶水底坡度项,使其能够考虑水平二维水底快变地形的影响。方程的数值求解时间上采用五阶差分格式,空间上采用四阶差分格式,减少了数值误差。方程模拟了五阶Stokes波理论解、潜堤和浅滩试验,并与高阶Boussinesq方程的数值结果进行了比较,通过模拟Bragg反射试验对方程新加入的二阶水底坡度项进行了验证。A new set of nonlinear wave equations with precise dispersion was established using the velocity at the free surface and wave surface elevation as variables.The proposed equations improve upon previous equations,which were based on velocity potential,by overcoming their inability to account for rotational wave motion.Moreover,a second-order seabed slope term applicable to general conditions was added,enabling the equations to consider the effects of rapidly changing two-dimensional seabed topography.A fifthorder difference scheme was used for time discretization and a fourth-order difference scheme for spatial discretization,reducing numerical errors.The equations simulated the theoretical solution of fifth-order Stokes wave,submerged breakwater and shoal experiments,and compared the results with those of the high-order Boussinesq equations.The newly introduced second-order seabed slope term was further validated through the simulation of Bragg reflection experiments.

关 键 词：精确色散性 非线性 波面升高 差分格式 自由表面 

分 类 号：P731.2[天文地球—海洋科学]