| The modulational instability is a fundamental mechanism for nonlinear exchanges of
energy between carrier and sideband waves. It is one of the processes at the origin of
rogue-wave formation in deep-water. Since the wind is the energy source in surface wave
propagation, accurate modelling of the wind is critical for understanding rogue-wave
phenomenon.
We describe how different forcing terms, due to different modelling of the wind action,
affect the band of positive gain of the modulational instability. In particular, we consider the
wind-forced nonlinear Schrödinger equation obtained in the potential flow framework when
the Miles growth rate is of the order of the wave steepness [1]. 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 [2]. This regime is characterised by the fact that the
ratio between wave momentum and norm is not a constant of motion [2], in contrast to what
happens in the standard case where the Miles growth rate is of the order of the steepness
squared.
References
[1] M. Brunetti, N. Marchiando, N. Berti, J. Kasparian, 2014, Phys. Lett. A, 378,
1025-1030
[2] M. Brunetti, J. Kasparian, 2014, Phys. Lett. A, 378, 3626-3630 |