Interacting nonlinear wave envelopes and rogue wave formation in deep water

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.

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• Deterministic Vector Freak Waves
• Capillary rogue waves
• Rogue waters
• Nonlinear stage of the Benjamin-Feir instability: Three-dimensional coherent structures and rogue waves
• Modulational instability in asymmetric coupled wave functions

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• Electrostatic wave interaction via asymmetric vector solitons as precursor to rogue wave formation in non-Maxwellian plasmas
• Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory
• Domain Walls and Vector Solitons in the Coupled Nonlinear Schrodinger Equation
• The Modulation of Multiple Phases Leading to the Modified KdV Equation
• Spatially quasi-periodic solutions of the Euler equation
• Numerical study of the transverse stability of the Peregrine solution