Extreme dynamics of wave groups on jet currents

TL;DR

This paper investigates the behavior of long-lived, localized wave patterns on jet currents, demonstrating their robustness, interactions, and potential to generate rogue waves through numerical simulations and nonlinear theory.

Contribution

It provides a detailed numerical and theoretical analysis of trapped wave solitons on jet currents, highlighting their stability, interactions, and role in rogue wave formation.

Findings

Solitary waves remain localized for hundreds of wave periods.

Soliton collisions are nearly elastic.

Solitons can generate extreme waves upon collision.

Abstract

Rogue waves are known to be much more common on jet currents. A possible explanation was put forward in [ [V. Shrira and A. Slunyaev, Nonlinear dynamics of trapped waves on jet currents and rogue waves, Phys. Rev. E 89, 041002, 2014]]: for the waves trapped on a current robust long-lived envelope solitary waves localized in both horizontal directions become possible, such wave patterns cannot exist in the absence of the current. In this work we investigate interactions between envelope solitons of essentially nonlinear trapped waves by means of the direct numerical simulation of the Euler equations. The solitary waves remain localized in both horizontal directions for hundreds of wave periods. We also demonstrate a high efficiency of the developed analytic nonlinear mode theory for description of the long-lived solitary patterns up to remarkably steep waves. We show robustness of the solitons in the course of interactions, and the possibility of extreme wave generation as a result of solitons' collisions. Their collisions are shown to be nearly elastic. These robust solitary waves obtained from the Euler equations without weak nonlinearity assumptions are viewed as a plausible model of rogue waves on jet currents.