Assessing the effect of finite water depth on the occurrence of extreme waves using a direct numerical simulation method

Provided waves are long crested, narrow banded and sufficiently steep, third-order nonlinearity is responsible for increasing the probability of occurrence of extreme wave events in deep water conditions. A notably reduction of third-order effects is however expected for short crested (directional) wave fields. In water of arbitrary depth, on the other hand, third-order nonlinearity is suppressed by finite depth effects if waves are long crested, while it can be triggered by transverse perturbation in short crested seas. Numerical simulations of the Euler equations are here used to address the combined effect of directionality and finite depth on the statistical properties of surface gravity waves. Results show that random directional wave fields in intermediate water depths, i.e. kh = O(1), weakly deviate from Gaussian statistics despite the degree of directional spreading of the wave energy.