论一类四阶Boussinesq方程的变浅性能

Boussinesq 类水波模型在港口、海岸以及海洋工程领域应用广泛，但以前对这类模型的变浅性能的研究不够充分. 针对Madsen 和Sch?ffer 提出的一组四阶Boussinesq 方程，从理论和数值两个方面对这一问题进行了探讨. 理论分析了其变浅性能，指出该文献中参数α₂ 和β₂ 的取值是不合理的，并重新确定其取值. 在交错网格下建立了基于混合4 阶Adams-Bashforth-Moulton 格式的预报-校正数值模型. 数值模拟了两个典型算例: 一是缓变平坡地形上波浪的传播变形，二是波浪在淹没梯形潜堤上的波浪演化过程. 计算结果分别与解析结果、物理模型实验结果进行了比较，发现变浅系数的取值对数值结果影响很大，新参数比原文参数模拟结果的吻合程度更高，这佐证了理论分析. 

ON SHOALING PROPERTY OF A SET OFFOURTH DISPERSIVE BOUSSINESQ MODEL

When Boussinesq model is applied to compute wave transformation from deep water to shallow water, the proper shoaling effect is essentially important for accurately predicting wave evolution. Improper shoaling parameters value results in bad shoaling property, and decreases the applicability of the Boussinesq model. Based on a fourth order dispersive Boussinesq equations proposed by Madsen and Sch?ffer (1998), theoretical analysis was reinvestigated, and we pointed out that the α₂ and β₂ values in the reference of Madsen and Sch?ffer was not proper and re-determined their values. Numerical model was established in staggered grids, and a composite fourth order Adams-Bashforth-Moulton scheme was applied to solve time integration and the model was solved by a predictor-corrector-iteration algorithm in finite difference method. Numerical simulations were applied to two typical cases: One was linear wave propagation over a slow-varying depth, and the other was nonlinear wave evolution over a submerged sill. The computed results with present parameter values were compared against the relevant analytical solution and experimental measurements. Both of the agreements are quite good, which validates the theoretical shoaling analysis numerically.