Abstract
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.
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