The runup of initial Gaussian narrow-banded and wide-banded wave fields and its statistical characteristics are investigated using direct numerical simulations, based on the nonlinear shallow water equations. The bathymetry consists of the section of a constant depth, which is matched with the beach of constant slope. To address different levels of nonlinearity, the time series with five different significant wave heights are considered. The selected wave parameters allow also seeing the effects of wave breaking on wave statistics. The total physical time of each simulated time-series is 1000 hours (~360000 wave periods). The statistics of calculated wave runup heights are discussed with respect to the wave nonlinearity, wave breaking and the bandwidth of the incoming wave field. The conditional Weibull distribution is suggested as a model for the description of extreme runup heights and assessment of extreme inundations.

中文翻译：

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复合海滩的极端淹没统计

基于非线性浅水方程，使用直接数值模拟研究了初始高斯窄带和宽带波场的上升及其统计特性。测深由一定深度的部分组成，与一定坡度的海滩相匹配。为了解决不同程度的非线性，考虑了具有五个不同有效波高的时间序列。选定的波浪参数还允许查看波浪破碎对波浪统计的影响。每个模拟时间序列的总物理时间为 1000 小时（~360000 波周期）。从波浪非线性、波浪破碎和入射波场的带宽方面讨论了计算出的波浪爬高高度的统计数据。