Nonlinear stage of Benjamin-Feir instability in forced/damped deep water waves
Abstract
We study a three-wave truncation of a recently proposed damped/forced high-order nonlinear Schr\"odinger equation for deep-water gravity waves under the effect of wind and viscosity. The evolution of the norm (wave-action) and spectral mean of the full model are well captured by the reduced dynamics. Three regimes are found for the wind-viscosity balance: we classify them according to the attractor in the phase-plane of the truncated system and to the shift of the spectral mean. A downshift can coexist with both net forcing and damping, i.e., attraction to period-1 or period-2 solutions. Upshift is associated with stronger winds, i.e., to a net forcing where the attractor is always a period-1 solution. The applicability of our classification to experiments in long wave-tanks is verified.
Keywords
Cite
@article{arxiv.1709.07850,
title = {Nonlinear stage of Benjamin-Feir instability in forced/damped deep water waves},
author = {Andrea Armaroli and Debbie Eeltink and Maura Brunetti and Jérôme Kasparian},
journal= {arXiv preprint arXiv:1709.07850},
year = {2018}
}
Comments
8 pages, 4 figures