On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands
In the past decade it became customary to relate the probability of appearance of extremely steep (the so-called freak, or rogue waves) to the value of the Benjamin-Feir Index (BFI) that represents the ratio of wave nonlinearity to the spectral width. This ratio appears naturally in the cubic Schröd...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2010-11-01
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| Series: | Natural Hazards and Earth System Sciences |
| Online Access: | http://www.nat-hazards-earth-syst-sci.net/10/2421/2010/nhess-10-2421-2010.pdf |
| _version_ | 1811246416638509056 |
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| author | L. Shemer |
| author_facet | L. Shemer |
| author_sort | L. Shemer |
| collection | DOAJ |
| description | In the past decade it became customary to relate the probability of appearance of extremely steep (the so-called freak, or rogue waves) to the value of the Benjamin-Feir Index (BFI) that represents the ratio of wave nonlinearity to the spectral width. This ratio appears naturally in the cubic Schrödinger equation that describes evolution of unidirectional narrow-banded wave field. The notion of this index stems from the Benjamin-Feir linear stability analysis of Stokes wave. The application of BFI to evaluate the evolution of wave fields, with non-vanishing amplitudes of sideband disturbances, is investigated using the Zakharov equation as the theoretical model. The present analysis considers a 3-wave system for which the exact analytical solution of the model equations is available. |
| first_indexed | 2024-04-12T14:53:14Z |
| format | Article |
| id | doaj.art-3c47749d16fb42ec99b23d32cb64e32f |
| institution | Directory Open Access Journal |
| issn | 1561-8633 1684-9981 |
| language | English |
| last_indexed | 2024-04-12T14:53:14Z |
| publishDate | 2010-11-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Natural Hazards and Earth System Sciences |
| spelling | doaj.art-3c47749d16fb42ec99b23d32cb64e32f2022-12-22T03:28:20ZengCopernicus PublicationsNatural Hazards and Earth System Sciences1561-86331684-99812010-11-0110112421242710.5194/nhess-10-2421-2010On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebandsL. ShemerIn the past decade it became customary to relate the probability of appearance of extremely steep (the so-called freak, or rogue waves) to the value of the Benjamin-Feir Index (BFI) that represents the ratio of wave nonlinearity to the spectral width. This ratio appears naturally in the cubic Schrödinger equation that describes evolution of unidirectional narrow-banded wave field. The notion of this index stems from the Benjamin-Feir linear stability analysis of Stokes wave. The application of BFI to evaluate the evolution of wave fields, with non-vanishing amplitudes of sideband disturbances, is investigated using the Zakharov equation as the theoretical model. The present analysis considers a 3-wave system for which the exact analytical solution of the model equations is available.http://www.nat-hazards-earth-syst-sci.net/10/2421/2010/nhess-10-2421-2010.pdf |
| spellingShingle | L. Shemer On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands Natural Hazards and Earth System Sciences |
| title | On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands |
| title_full | On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands |
| title_fullStr | On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands |
| title_full_unstemmed | On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands |
| title_short | On Benjamin-Feir instability and evolution of a nonlinear wave with finite-amplitude sidebands |
| title_sort | on benjamin feir instability and evolution of a nonlinear wave with finite amplitude sidebands |
| url | http://www.nat-hazards-earth-syst-sci.net/10/2421/2010/nhess-10-2421-2010.pdf |
| work_keys_str_mv | AT lshemer onbenjaminfeirinstabilityandevolutionofanonlinearwavewithfiniteamplitudesidebands |