Fully nonlinear simulations of unidirectional extreme waves provoked by strong depth transitions: The effect of slope

Abstract

Recent studies of surface gravity waves propagating over a sloping bottom have shown that an increase in the probability of extreme waves can be triggered by depth variations in sufficiently shallow waters. A boundary element method is used to show that this increase in probability is greatest when the slope is steepest, i.e., for a step. A harmonic separation technique shows that the second-order terms in wave steepness are responsible for the change in the statistical properties near the depth transition.