Modulational instability and wave amplification in finite water depth
The modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts e...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2014-03-01
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| Series: | Natural Hazards and Earth System Sciences |
| Online Access: | http://www.nat-hazards-earth-syst-sci.net/14/705/2014/nhess-14-705-2014.pdf |
| _version_ | 1818610711531618304 |
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| author | L. Fernandez M. Onorato J. Monbaliu A. Toffoli |
| author_facet | L. Fernandez M. Onorato J. Monbaliu A. Toffoli |
| author_sort | L. Fernandez |
| collection | DOAJ |
| description | The modulational instability of a uniform wave train to side band
perturbations is one of the most plausible mechanisms for the generation of
rogue waves in deep water. In a condition of finite water depth, however, the
interaction with the sea floor generates a wave-induced current that
subtracts energy from the wave field and consequently attenuates the
instability mechanism. As a result, a plane wave remains stable under the
influence of collinear side bands for relative depths <i>kh</i> ≤ 1.36 (where <i>k</i>
is the wavenumber of the plane wave and <i>h</i> is the water depth), but it can
still destabilise due to oblique perturbations. Using direct numerical
simulations of the Euler equations, it is here demonstrated that oblique side
bands are capable of triggering modulational instability and eventually
leading to the formation of rogue waves also for <i>kh</i> ≤ 1.36. Results,
nonetheless, indicate that modulational instability cannot sustain a
substantial wave growth for <i>kh</i> < 0.8. |
| first_indexed | 2024-12-16T15:18:47Z |
| format | Article |
| id | doaj.art-47772b3ed9894681b76eff72c4b218c1 |
| institution | Directory Open Access Journal |
| issn | 1561-8633 1684-9981 |
| language | English |
| last_indexed | 2024-12-16T15:18:47Z |
| publishDate | 2014-03-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Natural Hazards and Earth System Sciences |
| spelling | doaj.art-47772b3ed9894681b76eff72c4b218c12022-12-21T22:26:43ZengCopernicus PublicationsNatural Hazards and Earth System Sciences1561-86331684-99812014-03-0114370571110.5194/nhess-14-705-2014Modulational instability and wave amplification in finite water depthL. Fernandez0M. Onorato1J. Monbaliu2A. Toffoli3Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40 box 2448, 3001 Heverlee, BelgiumDipartimento di Fisica, Universita' di Torino, Via P. Giuria, Turin, 10125, ItalyDepartment of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40 box 2448, 3001 Heverlee, BelgiumCentre for Ocean Engineering Science and Technology, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC., 3122, AustraliaThe modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates the instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative depths <i>kh</i> ≤ 1.36 (where <i>k</i> is the wavenumber of the plane wave and <i>h</i> is the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for <i>kh</i> ≤ 1.36. Results, nonetheless, indicate that modulational instability cannot sustain a substantial wave growth for <i>kh</i> < 0.8.http://www.nat-hazards-earth-syst-sci.net/14/705/2014/nhess-14-705-2014.pdf |
| spellingShingle | L. Fernandez M. Onorato J. Monbaliu A. Toffoli Modulational instability and wave amplification in finite water depth Natural Hazards and Earth System Sciences |
| title | Modulational instability and wave amplification in finite water depth |
| title_full | Modulational instability and wave amplification in finite water depth |
| title_fullStr | Modulational instability and wave amplification in finite water depth |
| title_full_unstemmed | Modulational instability and wave amplification in finite water depth |
| title_short | Modulational instability and wave amplification in finite water depth |
| title_sort | modulational instability and wave amplification in finite water depth |
| url | http://www.nat-hazards-earth-syst-sci.net/14/705/2014/nhess-14-705-2014.pdf |
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