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

TL;DR

This paper uses numerical simulations to show that extreme deep water waves can be asymmetrical, with deeper troughs more likely on the rear slopes, affecting rogue wave probability estimates.

Contribution

It reveals a nonlinear harmonic effect causing wave asymmetry, which influences rogue wave probability assessments, distinct from Benjamin-Feir instability.

Findings

Deep troughs are more likely on wave rear slopes.

Asymmetry is caused by nonlinear harmonic interactions.

Impacts rogue wave probability estimation methods.

Abstract

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.