Extreme and rogue waves in directional wave fields

It is well established that modulational instability enhances the probability of occurrence for rogue waves if the wave field is long crested, narrow banded and sufficiently steep. As a result, a substantial deviation from commonly used second order theory-based distributions can be expected. However the spreading of the wave energy over a number of directional components can notably reduce the effect of modulational instability. In order to achieve a better understanding on the influence of wave directionality and its implication for design work, numerical simulations based on the truncated potential Euler equations were used. Results show the existence of a transition region between strongly and weakly non-Gaussian statistics as short crestedness increases.