一种适用于非均匀地形的高阶Boussinesq水波模型

Higher Order Boussinesq-Type Equations for Water Waves on Uneven Bottom

推导了适用于变地形情况的高阶Boussinesq波浪模型· 该模型采用自由表面边界条件作为时间步进方程,利用势函数满足的Laplace方程的解析解形式建立了自由表面边界速度和底面边界速度之间的关系,使得问题封闭· 以0.5倍相对水深处的速度为基本未知量,在对Laplace方程解析解进行级数求逆时保留水深梯度的高阶项,改进了速度场的Taylor展开式· 对于线性特性,进行了线性浅化和Booij反射的验证性计算· 为了检验有背景流动情况下拓展的Boussinesq模型的性态,对波_流相互作用问题进行了数值模拟· 数值计算结果与现有理论解或其他完全势流的数值解吻合良好。

Higher order Boussinesq_type equations for wave propagation over variable bathymetry were derived. The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain. The free surface velocities and the bottom velocities were connected by the exact solution of the Laplace equation. Taking the velocities on half relative water depth as the fundamental unknowns, terms relating to the gradient of the water depth were retained in the inverse series expansion of the exact solution, with which the problem was closed. With enhancements of the finite order Taylor expansion for the velocity field, the application range of the present model was extended to the not so mild slope bottom. For linear properties, some validation computations of linear shoaling and Booij's tests were carried out. The problems of wave_current interactions were also studied numerically to test the performance of the enhanced Boussinesq equations associated with the effect of currents. All these computational results confirm perfectly to the theoretical solution as well as other numerical solutions of the full potential problem available.