Grimshaw, R;
(2019)
Two-dimensional modulation instability of wind waves.
Journal of Ocean Engineering and Marine Energy
10.1007/s40722-019-00146-7.
(In press).
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Abstract
It is widely known that deep-water waves are modulationally unstable and that this can be modelled by a nonlinear Schrödinger equation. In this paper, we extend the previous studies of the effect of wind forcing on this instability to water waves in finite depth and in two horizontal space dimensions. The principal finding is that the instability is enhanced and becomes super-exponential and that the domain of instability in the modulation wavenumber space is enlarged. Since the outcome of modulation instability is expected to be the generation of rogue waves, represented within the framework of the nonlinear Schrödinger equation as a Peregrine breather, we also examine the effect of wind forcing on a Peregrine breather. We find that the breather amplitude will grow at twice the rate of a linear instability.
| Type: | Article |
|---|---|
| Title: | Two-dimensional modulation instability of wind waves |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s40722-019-00146-7 |
| Publisher version: | https://doi.org/10.1007/s40722-019-00146-7 |
| Language: | English |
| Additional information: | © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10090518 |
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