Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrodinger equation-based model
This paper sets out an approximate analytical model describing the nonlinear evolution of a Gaussian wave group in deep water. The model is derived using the conserved quantities of the cubic nonlinear Schrödinger equation (NLSE). The key parameter for describing the evolution is the amplitude-to-wa...
| Auteurs principaux: | , |
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| Format: | Journal article |
| Langue: | English |
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2009
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| _version_ | 1826273921433862144 |
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| author | Adcock, T Taylor, P |
| author_facet | Adcock, T Taylor, P |
| author_sort | Adcock, T |
| collection | OXFORD |
| description | This paper sets out an approximate analytical model describing the nonlinear evolution of a Gaussian wave group in deep water. The model is derived using the conserved quantities of the cubic nonlinear Schrödinger equation (NLSE). The key parameter for describing the evolution is the amplitude-to-wavenumber bandwidth ratio, a quantity analogous to the Benjamin-Feir index for random sea-states. For smaller values of this parameter, the group is wholly dispersive, whereas for more nonlinear cases, solitons are formed. Our model predicts the characteristics and the evolution of the groups in both regimes. These predictions are found to be in good agreement with numerical simulations using the NLSE and are in qualitative agreement with numerical results from a fully nonlinear potential flow solver and experimental results. This journal is © 2009 The Royal Society. |
| first_indexed | 2024-03-06T22:35:35Z |
| format | Journal article |
| id | oxford-uuid:59c58e0c-3b12-4583-8c30-8a9bca15c63f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:35:35Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:59c58e0c-3b12-4583-8c30-8a9bca15c63f2022-03-26T17:11:46ZFocusing of unidirectional wave groups on deep water: an approximate nonlinear Schrodinger equation-based modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:59c58e0c-3b12-4583-8c30-8a9bca15c63fEnglishSymplectic Elements at Oxford2009Adcock, TTaylor, PThis paper sets out an approximate analytical model describing the nonlinear evolution of a Gaussian wave group in deep water. The model is derived using the conserved quantities of the cubic nonlinear Schrödinger equation (NLSE). The key parameter for describing the evolution is the amplitude-to-wavenumber bandwidth ratio, a quantity analogous to the Benjamin-Feir index for random sea-states. For smaller values of this parameter, the group is wholly dispersive, whereas for more nonlinear cases, solitons are formed. Our model predicts the characteristics and the evolution of the groups in both regimes. These predictions are found to be in good agreement with numerical simulations using the NLSE and are in qualitative agreement with numerical results from a fully nonlinear potential flow solver and experimental results. This journal is © 2009 The Royal Society. |
| spellingShingle | Adcock, T Taylor, P Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrodinger equation-based model |
| title | Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrodinger equation-based model |
| title_full | Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrodinger equation-based model |
| title_fullStr | Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrodinger equation-based model |
| title_full_unstemmed | Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrodinger equation-based model |
| title_short | Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrodinger equation-based model |
| title_sort | focusing of unidirectional wave groups on deep water an approximate nonlinear schrodinger equation based model |
| work_keys_str_mv | AT adcockt focusingofunidirectionalwavegroupsondeepwateranapproximatenonlinearschrodingerequationbasedmodel AT taylorp focusingofunidirectionalwavegroupsondeepwateranapproximatenonlinearschrodingerequationbasedmodel |