Lifetime Characterization of Extreme Wave Localizations in Crossing Seas

TL;DR

This paper investigates the unique lifetime and dynamics of extreme rogue waves in crossing seas, revealing a novel nonlinear focusing mechanism that produces long-lived, localized wave events distinct from classical models.

Contribution

It introduces a new understanding of rogue wave formation in crossing seas, highlighting a distinct nonlinear focusing mechanism with prolonged lifespans, supported by numerical simulations and theoretical analysis.

Findings

Crossing seas can produce long-lived rogue waves through a unique nonlinear focusing mechanism.

Localized rogue waves in crossing seas exhibit dual bimodality and recurrent focusing.

The new focusing dynamics can be modeled by both fully nonlinear simulations and weakly nonlinear equations.

Abstract

Rogue waves (RWs) can form on the ocean surface due to quasi-four wave resonant interaction or superposition principle. Both mechanisms have been acutely studied. The first of the two is known as the nonlinear focusing mechanism and leads to an increased probability of rogue waves when wave conditions are favourable, i.e., when unidirectionality and high narrowband energy of the wave field are satisfied. This work delves into the dynamics of extreme wave focusing in crossing seas, revealing a distinct type of nonlinear RWs, characterized by a decisive longevity compared to those generated by the dispersive focusing mechanism. In fact, through fully nonlinear hydrodynamic numerical simulations, we show that the interactions between two crossing unidirectional wave beams can trigger fully localized and robust development of RWs. These coherent structures, characterized by a typical spectral broadening then spreading in the form of dual bimodality and recurrent wave group focusing, not only defy the weakening expectation of quasi-four wave resonant interaction in directionally spread wave fields, but also differ from classical focusing mechanisms already mentioned. This has been determined following a rigorous lifespan-based statistical analysis of extreme wave events in our fully nonlinear simulations. Utilizing the coupled nonlinear Schr\"odinger framework, we also show that such intrinsic focusing dynamics can also be captured by weakly nonlinear wave evolution equations. This opens new research avenues for further explorations of these complex and intriguing wave phenomena in hydrodynamics as well as other nonlinear and dispersive multi-wave systems.