SIMULATION OF ROGUE WAVE FORMATION IN FINITE DEPTH IRREGULAR WAVES WITH A FULLY NONLINEAR MODEL

The formation of rogue waves in coastal areas can be triggered by modulational instability (MI, known also as Benjamin-Feir instability), especially in deep water. The analysis of rogue wave generation and statistical characteristics of irregular waves in finite depth has predominantly focused on low-order (third-order) nonlinear interactions. In the present study, we conduct numerical simulations using a fully nonlinear, spectrally accurate water wave model (Klahn et al. 2021) to explore the statistical properties of irregular, uni-directional wave fields initially described by a TMA spectrum (Holthuijsen 2010). The numerical model is initially validated through the simulation of modulational instability in nonlinear plane wave trains in deep water. Subsequently, a series of random uni-directional wave fields, spanning a broad spectrum of water depths, is examined. This investigation encompasses various aspects of wave statistics, and discusses the relationship between the occurrence probability of extreme waves (rogue waves) with full nonlinearity. The significance of fully nonlinear behavior, as opposed to third-order nonlinearity, is also assessed.