The applicability of dispersive and nondispersive wave models for describing long-wave propagation and run-up on a beach in the case of composite bottom topography is investigated: a plane beach transforms into a zone of constant depth. Numerical simulations are performed in the framework of two models: (1) nonlinear shallow-water theory and (2) the dispersive model in the Boussinesq approximation based on modified Peregrine equations. Simulations are compared with the data of a laboratory experiment for different types of waves: regular waves, biharmonic signals, and “vessel-like” wave trains strongly modulated by frequency and amplitude. Conclusions about the applicability of the corresponding theories for describing considered types of waves are drawn based on this comparison.

中文翻译：

---

海滩上波浪爬升的色散和非色散模型的比较

研究了色散和非色散波模型在复合底部地形情况下描述长波在海滩上传播和爬升的适用性：平面海滩转变为恒定深度的区域。数值模拟在两个模型的框架内进行：(1) 非线性浅水理论和 (2) 基于修正 Peregrine 方程的 Boussinesq 近似中的色散模型。将模拟与实验室实验的不同类型波的数据进行比较：规则波、双谐波信号和由频率和幅度强烈调制的“船状”波列。基于这种比较得出关于描述所考虑的波浪类型的相应理论的适用性的结论。