波浪在渗透海床上传播的数学模型及其验证  

Mathematical model for wave propagation over a porous seabed and its numerical validation

作　　者：刘忠波[1] 孙昭晨[1] 房克照[1] 

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

出　　处：《大连理工大学学报》2013年第3期417-422,共6页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(51009018);国家创新性研究群体资助项目(50921001);大连理工大学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：通过引入考虑可渗海床影响的阻力方程,将一组高阶Boussinesq水波方程拓展到可适用渗透海床的情况.在不同厚度介质情况下对新方程进行了理论分析,并将结果与解析解比较,讨论了方程的相速度及衰减率的精确度.在非交错网格下离散该方程,建立了基于高精度有限差分方法和预报-校正时间积分格式的一维数值模型.其中,在预报中采用三阶Adams-Bashforth格式,校正中则采用四阶Adams-Moulton格式.利用所建立数值模型,对渗透潜堤地形上的波浪传播变形进行了模拟,将数值计算结果与相关试验结果进行了比较分析,证明试验结果与数值结果吻合较好,说明这种改进方法是可行、有效的.A resistance equation is introduced for considering the porous effect, and a set of high-order Boussinesq-ty new equations are a pe nal equations for water waves is extended to be applicable for porous seabed. The yzed theoretically in constant water depth with different porous layer depths, and the phase velocity and damping rate are discussed compared with the analytical solutions. In nonstaggered grids, high-precision finite difference and a predicted-correct time-integration scheme are applied to solving the present one-dimensional model. A third-order Adams-Bashforth scheme is adopted in predicting stage and a fourth-order Adams-Moulton scheme is adopted in correcting stage. Numerical computation is carried out upon wave propagating over a submerged porous topography, and the computed results are compared with the experimental ones, and the agreement is relatively good. It is shown that the present method to improve original Boussinesq model for porous seabed is feasible.

关 键 词：BOUSSINESQ方程 渗透 色散性 波浪 

分 类 号：P731.2[天文地球—海洋科学]