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Generation of Wave Groups by Shear Layer Instability

Department of Mathematics, University College London, London WC1E 6BT, UK
Fluids 2019, 4(1), 39; https://doi.org/10.3390/fluids4010039
Received: 23 January 2019 / Revised: 21 February 2019 / Accepted: 25 February 2019 / Published: 2 March 2019
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Abstract

The linear stability theory of wind-wave generation is revisited with an emphasis on the generation of wave groups. The outcome is the fundamental requirement that the group move with a real-valued group velocity. This implies that both the wave frequency and the wavenumber should be complex-valued, and in turn this then leads to a growth rate in the reference frame moving with the group velocity which is in general different from the temporal growth rate. In the weakly nonlinear regime, the amplitude envelope of the wave group is governed by a forced nonlinear Schrödinger equation. The effect of the wind forcing term is to enhance modulation instability both in terms of the wave growth and in terms of the domain of instability in the modulation wavenumber space. Also, the soliton solution for the wave envelope grows in amplitude at twice the linear growth rate. View Full-Text
Keywords: wind waves; wave groups; modulation instability wind waves; wave groups; modulation instability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Grimshaw, R. Generation of Wave Groups by Shear Layer Instability. Fluids 2019, 4, 39.

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