Freak wave in a two-dimensional directional wavefield with bottom topography change. Part 1. Normal incidence wave

In the propagation and evolution of sea waves, previous studies pointed out that the occurrence of the freak wave height is significantly related to the quasi-resonant four-wave interaction in the modulated waves. From numerical--experimental study over an uneven bottom, the nonlinear effect caused by the bathymetry change also contributes to the occurrence of extreme events in unidirectional waves. To comprehensively analyse the two-dimensional wavefield, this study develops an evolution model for a directional random wavefield based on the depth-modified nonlinear Schrödinger equation, which considers the nonlinear resonant interactions and the wave shoaling the shallow water. Through Monte Carlo simulation, we discuss the directional effect on the four-wave interaction in the wave train and the maximum wave height distribution from deep to shallow water with a slow varying slope. The numerical result indicates that the directional spreading has a dispersion effect on the freak wave height. In a shallow-water environment, this effect becomes weak, and the bottom topography change is the main influencing factor in the wave evolution.