破碎带波浪的数值模拟

Numerical modeling of waves in surf zone

基于一组色散关系得到改进的完全非线性Boussinesq方程建立了一个波浪模型可以模拟近岸水域的波浪变浅、破碎以及在海滩上的爬高等多种变形。波浪破碎引起的能量衰减是在动量方程中引入一个在空间和时间上都只作用于波前的涡粘项来模拟。动海岸线边界用窄缝法处理。波浪爬高用非线性浅水方程推导的非破碎波浪在斜坡上爬高的解析解来验证。本模型还模拟了波浪在斜坡上不同类型的破碎变形过程,并将其波高和平均水位的沿程变化和物理模型实验的结果比较,两者符合良好。

Based on a set of enhanced fully nonlinear Boussinesq equations, a numerical wave model is established in this paper, which features the capability of modeling various wave transformations such as shoaling, breaking and runup on the beach. An eddy viscosity term, which is spatially and temporally localized to the front face of the wave, is added to the momentum equation serving as wave breaking force term to simulate the dissipation of energy due to wave breaking. The moving shoreline is treated with a slot method. Run-up of non-breaking waves is verified against the analytical solution for nonlinear shallow water waves. The model is applied to study various types of wave breaking on the plane sloping beaches. The comparison of computed results comprising the variations of wave height and mean water level along the flume and the experimental data is conducted and their agreement is very good.