Generation of extreme waves with flexible features in fully nonlinear wave models

We consider the generation of extreme waves of flexible features in deep-water surface gravity waves, in the context of the fully nonlinear wave model, i.e. Euler equations of the free surface. This is achieved through a recently developed GenWave approach, coupled with the high-order spectral method to solve the Euler equations. Through an iterative refinement procedure, GenWave progressively refines the initial phases associated with a given wave spectrum, which leads to extreme-wave generation at specified design time and location, with their probability of exceedance quantified. In this study, we consider two types of extreme waves, enabled by the flexibility of GenWave. The first type is a spatially and temporally localised rogue wave, and second is a spatially localised extreme-wave group propagating at a constant speed. The two generated extreme-wave profiles are compared with their prototypes – the Peregrine soliton and regular soliton (or bright soliton) in the context of the nonlinear Schrödinger equation (NLS), with reasonable agreement. For the persistent group, comparison with linear evolution and the NLS identifies nonlinear persistence, faster propagation and bound-wave content beyond the leading-order NLS description.