When tsunami waves propagate into shallow and gentle continental shelves, the effects of submarine topography and wave dispersion lead to the appearance of undular bore. This kind of wave is quite different from the initial tsunami wave in the waveform, and its amplitude is enhanced significantly. The undular bore will cause great and repeated runups on the beach, which brings larger destruction to the coastal region. In order to investigate the characteristics of the propagation of undular bore, this paper simulates the evolution from the sinusoidal long wave to the undular bore and analyzes the influencing factors. The beach slope has an important effect on the development of undular bores in terms of the undulation form, amplitude, wave length and occurrence time. The influence of bottom friction and submarine topography on the undulations and soliton fissions are discussed. These bottom conditions will lead to great change of the waveform and amplitude of undular bores.

中文翻译：

---

海岸带波状孔的演化：底坡、摩擦和特殊地形的影响

当海啸波传播到浅而平缓的大陆架时，受海底地形和波散的影响，会导致波状孔的出现。这种波在波形上与最初的海啸波有很大不同，其幅度明显增强。波状钻孔会在海滩上造成巨大且反复的隆起，给沿海地区带来更大的破坏。为研究波状孔的传播特性，本文模拟了正弦长波向波状孔的演化，并分析了影响因素。滩坡在起伏形式、波幅、波长和发生时间等方面对波状钻孔的发育具有重要影响。讨论了底部摩擦和海底地形对起伏和孤子裂变的影响。这些底部条件将导致波状孔的波形和幅度发生很大变化。