The unsteady evolution of localized unidirectional deep water wave groups

TL;DR

This paper investigates how localized wave groups in unidirectional deep water evolve, revealing how additional terms in modified NLS equations induce a critical scale for rogue wave formation.

Contribution

It introduces a novel technique to reduce PDE dynamics to an ODE, analyzing the impact of spatial localization and scale-invariance breakdown on extreme wave emergence.

Findings

Spatial localization influences rogue wave development.

Scale-invariance breaks down with MNLS, creating a critical scale.

Reduced ODE model captures key dynamics of wave amplitude evolution.

Abstract

We study the evolution of localized wave groups in unidirectional water wave envelope equations (nonlinear Schrodinger (NLS) and modified NLS (MNLS)). These localizations of energy can lead to disastrous extreme responses (rogue waves). Previous studies have focused on the role of energy distribution in the frequency domain in the formation of extreme waves. We analytically quantify the role of spatial localization, introducing a novel technique to reduce the underlying PDE dynamics to a simple ODE for the wave packet amplitude. We use this reduced model to show how the scale- invariant symmetries of NLS break down when the additional terms in MNLS are included, inducing a critical scale for the occurrence of extreme waves.