双层Boussinesq水波方程

从Laplace方程出发，推导了一组适应于波浪在非平整地形上传播的双层Boussinesq水波方程，方程以双层水深积分平均速度表达且具有二阶全非线性特征。通过在动量方程中引入高阶色散项和非线性项进一步提高了方程的色散性和非线性性能。常水深情况下，分析了方程的色散关系和二阶波幅传递函数，并与Stokes解析解进行了比较。结果表明，在0.3%误差下方程可适用水深达kh≈6，在此水深范围内二阶波幅传递函数误差在10%以内。在非交错网格下，建立了基于有限差分方法和混合4阶Adams-Bashforth-Moulton时间积分格式的一维数值模型，模拟了波浪在潜堤上的传播变形，并与实验结果进行了对比，吻合程度较好。

A Double-layer Depth-averaged Boussinesq Model for Water Wave

A double-layer depth-averaged Boussinesq-type model for wave propagation over an un-even bottom is derived. The governing equations are formulated in two depth-averaged velocities within each water layer and of the second-order fully nonlinearity. To improve the model properties, high-er-order terms are introduced to momentum equations and theoretical analyses are made to investi-gate the linear dispersive and nonlinear properties. The optimized model equations show good dis-persion property up to kh≈6 within 0.3%error, and the second nonlinear characteristics are optimized to kh≈6 within 10%error. Based on finite difference method and a composite fourth order Adams-Bashforth-Moulton time integration, one-dimensional equations are solved numerically on non-stag-gered grids. Regular wave evolution over a submerged breakwater is simulated and the computation-al results are compared with the experimental data, the good agreements are found.