Generation of Wave Groups by Shear Layer Instability
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,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-03-01
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| Series: | Fluids |
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| Online Access: | http://www.mdpi.com/2311-5521/4/1/39 |
| _version_ | 1818096424889352192 |
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| author | Roger Grimshaw |
| author_facet | Roger Grimshaw |
| author_sort | Roger Grimshaw |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T23:04:25Z |
| format | Article |
| id | doaj.art-1a0bbd680245446baa9a695cc517f8b9 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-12-10T23:04:25Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-1a0bbd680245446baa9a695cc517f8b92022-12-22T01:30:04ZengMDPI AGFluids2311-55212019-03-01413910.3390/fluids4010039fluids4010039Generation of Wave Groups by Shear Layer InstabilityRoger Grimshaw0Department of Mathematics, University College London, London WC1E 6BT, UKThe 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.http://www.mdpi.com/2311-5521/4/1/39wind waveswave groupsmodulation instability |
| spellingShingle | Roger Grimshaw Generation of Wave Groups by Shear Layer Instability Fluids wind waves wave groups modulation instability |
| title | Generation of Wave Groups by Shear Layer Instability |
| title_full | Generation of Wave Groups by Shear Layer Instability |
| title_fullStr | Generation of Wave Groups by Shear Layer Instability |
| title_full_unstemmed | Generation of Wave Groups by Shear Layer Instability |
| title_short | Generation of Wave Groups by Shear Layer Instability |
| title_sort | generation of wave groups by shear layer instability |
| topic | wind waves wave groups modulation instability |
| url | http://www.mdpi.com/2311-5521/4/1/39 |
| work_keys_str_mv | AT rogergrimshaw generationofwavegroupsbyshearlayerinstability |