Wave amplification in the framework of forced nonlinear Schrodinger equation: the rogue wave context

TL;DR

This study investigates how external forcing affects wave amplification in the nonlinear Schrödinger equation, revealing that slow forcing enhances rogue wave likelihood while rapid forcing causes quick statistical changes.

Contribution

It provides a numerical analysis of wave amplification under external forcing, highlighting the effects of different forcing time scales on rogue wave formation.

Findings

Slow forcing increases kurtosis and large wave probability.

Rapid forcing causes quick statistical adjustments.

Approximate solutions help understand coherent wave group roles.

Abstract

Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrodinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much longer than the nonlinear time scale) results in selective enhancement of the solitary part of the wave ensemble. The slow forcing provides eventually wider wavenumber spectra, larger values of kurtosis and higher probability of large waves. In the opposite case of rapid forcing the nonlinear waves readjust passing through the stage of fast surges of statistical characteristics. Single forced envelope solitons are considered with the purpose to better identify the role of coherent wave groups. An approximate description on the basis of solutions of the integrable NLS equation is provided. Applicability of the Benjamin - Feir Index to forecasting of conditions favourable for rogue waves is discussed.