Interacting nonlinear wave envelopes and rogue wave formation in deep water

TL;DR

This paper introduces a mechanism for rogue wave formation in deep water through the interaction of two waves modeled by a coupled nonlinear Schrödinger system, highlighting the role of oblique angles and vector soliton solutions.

Contribution

It proposes a rogue wave formation mechanism based on coupled nonlinear Schrödinger equations and introduces a rogue condition linking interaction angle and wave velocities, revealing enhanced rogue events.

Findings

Coupled system exhibits more extreme waves than scalar models.

Rogue events are well approximated by hyperbolic secant functions.

Crossing states significantly contribute to rogue wave generation.

Abstract

A rogue wave formation mechanism is proposed within the framework of a coupled nonlinear Schrodinger (CNLS) system corresponding to the interaction of two waves propagating in oblique directions in deep water. A rogue condition is introduced that links the angle of interaction with the group velocities of these waves: different angles of interaction can result in a major enhancement of rogue events in both numbers and amplitude. For a range of interacting directions it is found that the CNLS system exhibits significantly more extreme wave amplitude events than its scalar counterpart. Furthermore, the rogue events of the coupled system are found to be well approximated by hyperbolic secant functions; they are vectorial soliton-type solutions of the CNLS system, typically not considered to be integrable. Overall, our results indicate that crossing states provide an important mechanism for the generation of rogue water wave events.