Evolution of Nonlinear Directional Random Wave Train from Deep to Shallow Water

Abstract

 In the evolution of nonlinear wave trains, four-wave interaction plays an important role in the wave envelope dynamics, which is related to the modulational instability and potentially leads to the occurrence of freak wave. This research conducts a Monte Carlo simulation based on two-dimensional modified NLS equation considering spatial inhomogeneity, and discusses the evolution of weakly nonlinear wave trains in random directional sea states considering the water depth change from the offshore to the onshore. The numerical result concentrates on the influence from the directional dispersion effect on the fourth-order cumulant in the evolution of the wave field in different bottom topography.