适合渗透海床上的Boussinesq水波数学模型  

A Boussinesq model for water waves over permeable seabed

作　　者：刘忠波[1,2] 房克照[2] 孙昭晨[2] 

机构地区：[1]大连海事大学交通运输管理学院,辽宁大连116026 [2]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116023

出　　处：《广西大学学报（自然科学版）》2012年第5期870-875,共6页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(51009018);海岸和近海工程国家重点实验室开放基金资助项目(LP1105)

摘　　要：为了数值研究波浪在渗透海床上的传播特性,基于近似到二阶完全非线性的高阶Boussinesq水波方程,通过引入考虑可渗海床影响的动量方程,将方程拓展到可适用渗透海床情况。对该方程常水深情况下进行了理论分析,并与解析解比较,讨论了方程的相速度及衰减率。在非交错网格下离散该方程,建立了预报—校正的有限差分数值模型。利用数值模型模拟了渗透地形上的波浪传播变形,并与相关实验结果进行了比较,实验结果与数值结果吻合较好,说明这种拓展Boussinesq水波方程至渗透海床情况是合适的。In order to study the wave propagation over permeable seabed numerically, Dasel on Boussinesq＇s equations for water waves, a resistance equation was introduced, and thus the equations were applicable to permeable seabed. The new equations were analyzed theoretically for constant wa ter, and the phase velocity and damping rate were compared with the analytical solutions. In non staggered grids, a predictioncorrection scheme was applied to the onedimensional equations. A third order AdamsBashforth scheme was adopted in prediction stage and a fourth order AdamsMoul ton scheme was adopted in correction stage. Numerical computation was carried out upon wave prop agation over a submerged porous topography, and the computed results we~ compared with the ex perimental results. The agreement is relatively good, which shows that the present method is feasible to improve original Boussinesq＇s model for permeable seabeds.

关 键 词：BOUSSINESQ方程 渗透海床 色散性 波浪 

分 类 号：P73[天文地球—海洋科学]