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

• The effect of fast and slow pumping on nonlinear wave statistics is examined.
• Slow pumping results in selective enhancement of the solitary part of the wave ensemble.
• An interruption of strong wind input results in occurrence of extreme wave conditions.
• The relation between wave statistics and BFI is ambiguous for non-Gaussian processes.

Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrödinger (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.