Modulational instability in wind-forced waves
arXiv:1410.4070 · doi:10.1016/j.physleta.2014.10.017
Abstract
We consider the wind-forced nonlinear Schroedinger (NLS) equation obtained in the potential flow framework when the Miles growth rate is of the order of the wave steepness. In this case, the form of the wind-forcing terms gives rise to the enhancement of the modulational instability and to a band of positive gain with infinite width. This regime is characterised by the fact that the ratio between wave momentum and norm is not a constant of motion, in contrast to what happens in the standard case where the Miles growth rate is of the order of the steepness squared.
5 pages, 2 figures, accepted for publication in Physics Letters A, few misprints corrected
References in corpus (5)
- Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions
- Approximate rogue wave solutions of the forced and damped Nonlinear Schrödinger equation for water waves
- Experiments on wind-perturbed rogue wave hydrodynamics using the Peregrine breather model
- Nonlinear fast growth of water waves under wind forcing
- Enhancement of the Benjamin-Feir instability with dissipation
Cited by in corpus (8)
- Spectral up- and downshifting of Akhmediev breathers under wind forcing
- Frequency downshift in a viscous fluid
- Nonlinear stage of Benjamin-Feir instability in forced/damped deep water waves
- Recurrence in the high-order nonlinear Schrödinger equation: a low dimensional analysis
- A Comparison of Frequency Downshift Models of Wave Trains on Deep Water
- Wind-Induced Changes to Surface Gravity Wave Shape in Deep to Intermediate Water
- Impurity induced Modulational instability in Bose-Einstein condensates
- Modelling of ocean waves with the Alber equation: application to non-parametric spectra and generalization to crossing seas