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| HAL : hal-00456891, version 5 |
| arXiv : 1002.3019 |
| DOI : 10.1016/j.physd.2011.09.015 |
| Fiche détaillée |  Récupérer au format |
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| Physica D: Nonlinear Phenomena 241, 1 (2012) 25-36 |
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| Versions disponibles : | v1 (16-02-2010) | v2 (16-02-2010) | v3 (21-07-2010) | v4 (04-03-2011) | v5 (21-07-2011) |
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| Practical use of variational principles for modeling water waves |
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Didier Clamond 1Denys Dutykh 2 |
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| (01/01/2012) |
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| This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a 'relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is particularly suitable for the construction of approximate water wave models, since it allows more freedom while preserving the variational structure. The advantages of this relaxed formulation are illustrated with various examples in shallow and deep waters, as well as arbitrary depths. Using subordinate constraints (e.g., irrotationality or free surface impermeability) in various combinations, several model equations are derived, some being well-known, other being new. The models obtained are studied analytically and exact travelling wave solutions are constructed when possible. |
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| 1 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS) |
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| 2 : | Laboratoire de Mathématiques (LAMA) |
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CNRS : UMR5127 – Université de Savoie |
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| Domaine | : | Physique/Mécanique/Mécanique des fluides Sciences de l'ingénieur/Mécanique/Mécanique des fluides Mathématiques/Equations aux dérivées partielles Planète et Univers/Océan, Atmosphère Science non linéaire/Formation de Structures et Solitons Science non linéaire/Systèmes Solubles et Intégrables Physique/Physique/Dynamique des Fluides Physique/Physique/Physique Atmosphérique et Océanique Physique/Physique/Physique Classique |
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| water waves – variational principles – Lagrangian – Hamiltonian – shallow water – deep water |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00456891, version 5 | |
| http://hal.archives-ouvertes.fr/hal-00456891 | |
| oai:hal.archives-ouvertes.fr:hal-00456891 | |
| Contributeur : Denys Dutykh | |
| Soumis le : Jeudi 21 Juillet 2011, 07:45:12 | |
| Dernière modification le : Mercredi 16 Novembre 2011, 09:41:15 | |
