基于激波捕捉类Boussinesq模型对岛礁地形上波浪传播的数值模拟

Shock-capturing Boussinesq modelling of wave transformation over fringing reefs

为了探究激波捕捉类Boussinesq模型在模拟岛礁地形上规则波和不规则波传播的可行性,采用基于完全非线性Boussinesq方程并具有激波捕捉能力的数值模型Funwave-TVD对规则波和不规则波在岛礁地形上的传播进行了数值模拟,通过与试验数据对比,分析模型中空间步长的影响,验证模型在模拟波高、平均水位分布以及波谱空间演变的能力,结果表明:采用合适的空间步长,模型能较好地模拟规则波和不规则波在岛礁地形上的传播和演化过程。对于规则波,较小的空间步长可改善破碎点处波高峰值的预测,并能更好地预测波浪破碎后波高的空间分布,相比结合经验破碎的Boussinesq模型,Funwave-TVD能更好地模拟规则波在岛礁地形上的破碎,以及破碎以后行进涌波的再生成过程;对于不规则波,Funwave-TVD总体而言能较好地模拟涌浪有效波高、次重力波的生成及空间演化和平均水位,但会低估礁坪上次重力波波高,较粗的空间步长也会低估礁坪上涌浪有效波高。

In order to demonstrate the ability of shock-capturing Boussinesq model in predicting regular and irregular wave transformations over fringing reefs, the fully nonlinear Boussinesq model with shock-capturing capability, Funwave-TVD, was utilized to simulate regular and irregular wave transformation over fringing reefs. Predicted wave heights, mean water level and wave spectra were validated with experimental data and the sensitivity of the grid size was investigated. The results show that with a proper grid size, the present model can reasonably reproduce the regular and irregular wave transformation over fringing reefs. For regular waves, fine grid size can improve the prediction of the wave height around and after breaking point. Compared to the Boussinesq model coupled with an empirical breaking model, the present model is more suitable to simulate wave breaking and bore-propagation over fringing reefs. For irregular waves, the present model can reasonably reproduce the significant sea-swell wave height, generation and propagation of infragravity waves and mean water level. But the infragravity wave height over the reef flat is underestimated and coarse grid size can under-predict the significant sea-swell wave height over the reef flat as well.