Disintegration of Nonlinear Long Waves over Even and Uneven Bathymetry

Nonlinear long waves may disintegrate into several small waves after traveling some distance, which can be observed both in tsunami and tidal waves. This disintegration can lead to a significant amplification of the wave height, causing serious disasters in coastal regions. In the present study, the disintegration of nonlinear long waves over even and uneven bathymetry is investigated numerically. For this purpose, a two-dimensional fully nonlinear numerical wave flume is developed based on a time-domain higher-order boundary element method. Fully nonlinear kinematic and dynamic boundary conditions are satisfied on the instantaneous free surface. With this developed model, it is found that the sinusoidal wave generated by the wavemaker can induce higher-order harmonic waves during propagation that are spatially modulated. The recurrence distance of higher-order components increases linearly with wavelength, as well as the higher-order amplitudes, which lead to the amplification of free-surface elevation. The investigation of long waves propagating on a step through a slope indicates that the topography contributes to the disintegration process.