Wind-wave amplification mechanisms: possible models for steep wave events in finite depth
We extend the Miles mechanism of wind-wave generation to finite depth. A β-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth <i>h</i>. The evolution...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2013-11-01
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| Series: | Natural Hazards and Earth System Sciences |
| Online Access: | http://www.nat-hazards-earth-syst-sci.net/13/2805/2013/nhess-13-2805-2013.pdf |
| _version_ | 1819025951141396480 |
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| author | P. Montalvo R. Kraenkel M. A. Manna C. Kharif |
| author_facet | P. Montalvo R. Kraenkel M. A. Manna C. Kharif |
| author_sort | P. Montalvo |
| collection | DOAJ |
| description | We extend the Miles mechanism of wind-wave generation to finite
depth. A β-Miles linear growth rate depending on the depth
and wind velocity is derived and allows the study of linear growth
rates of surface waves from weak to moderate winds in finite depth
<i>h</i>. The evolution of β is plotted, for several values of the
dispersion parameter <i>kh</i> with <i>k</i> the wave number. For
constant depths we find that no matter what the values of wind
velocities are, at small enough wave age the β-Miles linear
growth rates are in the known deep-water limit. However winds of
moderate intensities prevent the waves from growing beyond
a critical wave age, which is also constrained by the water depth
and is less than the wave age limit of deep water. Depending on
wave age and wind velocity, the Jeffreys and Miles mechanisms are
compared to determine which of them dominates. A wind-forced
nonlinear Schrödinger equation is derived and the Akhmediev,
Peregrine and Kuznetsov–Ma breather solutions for weak wind inputs
in finite depth <i>h</i> are obtained. |
| first_indexed | 2024-12-21T05:18:50Z |
| format | Article |
| id | doaj.art-066d3e68a46646d690bb748f21dbc4db |
| institution | Directory Open Access Journal |
| issn | 1561-8633 1684-9981 |
| language | English |
| last_indexed | 2024-12-21T05:18:50Z |
| publishDate | 2013-11-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Natural Hazards and Earth System Sciences |
| spelling | doaj.art-066d3e68a46646d690bb748f21dbc4db2022-12-21T19:14:51ZengCopernicus PublicationsNatural Hazards and Earth System Sciences1561-86331684-99812013-11-0113112805281310.5194/nhess-13-2805-2013Wind-wave amplification mechanisms: possible models for steep wave events in finite depthP. Montalvo0R. Kraenkel1M. A. Manna2C. Kharif3Université Montpellier 2, Laboratoire Charles Coulomb, UMR5221, 34095, Montpellier, FranceInstituto de Física Téorica, UNESP – Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 27, Bloco II, 01140-070, São Paulo, BrazilUniversité Montpellier 2, Laboratoire Charles Coulomb, UMR5221, 34095, Montpellier, FranceEcole Centrale Marseille, 38 rue Frédéric Joliot-Curie, 13451 Marseille cedex 20, FranceWe extend the Miles mechanism of wind-wave generation to finite depth. A β-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth <i>h</i>. The evolution of β is plotted, for several values of the dispersion parameter <i>kh</i> with <i>k</i> the wave number. For constant depths we find that no matter what the values of wind velocities are, at small enough wave age the β-Miles linear growth rates are in the known deep-water limit. However winds of moderate intensities prevent the waves from growing beyond a critical wave age, which is also constrained by the water depth and is less than the wave age limit of deep water. Depending on wave age and wind velocity, the Jeffreys and Miles mechanisms are compared to determine which of them dominates. A wind-forced nonlinear Schrödinger equation is derived and the Akhmediev, Peregrine and Kuznetsov–Ma breather solutions for weak wind inputs in finite depth <i>h</i> are obtained.http://www.nat-hazards-earth-syst-sci.net/13/2805/2013/nhess-13-2805-2013.pdf |
| spellingShingle | P. Montalvo R. Kraenkel M. A. Manna C. Kharif Wind-wave amplification mechanisms: possible models for steep wave events in finite depth Natural Hazards and Earth System Sciences |
| title | Wind-wave amplification mechanisms: possible models for steep wave events in finite depth |
| title_full | Wind-wave amplification mechanisms: possible models for steep wave events in finite depth |
| title_fullStr | Wind-wave amplification mechanisms: possible models for steep wave events in finite depth |
| title_full_unstemmed | Wind-wave amplification mechanisms: possible models for steep wave events in finite depth |
| title_short | Wind-wave amplification mechanisms: possible models for steep wave events in finite depth |
| title_sort | wind wave amplification mechanisms possible models for steep wave events in finite depth |
| url | http://www.nat-hazards-earth-syst-sci.net/13/2805/2013/nhess-13-2805-2013.pdf |
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