On the probability of down-crossing and up-crossing rogue waves

Physics of Fluids. 2023. Vol. 35. No. 11. Article 117109.

Slunyaev A., Kokorina A.

By means of the direct numerical simulation of directional waves on the surface of deep water, it is shown that extreme waves can exhibit
such asymmetry that the occurrence of deeper troughs is several times more likely on the wave rear slopes. This effect becomes most
pronounced in the case of steep short-crested waves. It is not related to the Benjamin–Feir instability but is a result of complex contribution
from nonlinear combination harmonics, mainly cubic in nonlinearity. The discovered asymmetry can lead to remarkably different estimates
of the rogue wave probability based on either down- or up-zero-crossing methods for individual wave selection, commonly used in the
oceanography.

Keywords: численное моделирование, hydrodynamics, уравнения гидродинамики, numerical simulation