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| HAL : hal-00334440, version 3 |
| arXiv : 0810.4697 |
| DOI : 10.1016/j.physleta.2009.07.029 |
| Fiche détaillée |  Récupérer au format |
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| Physics Letters A 373, 36 (2009) 3212-3216 |
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| Versions disponibles : | v1 (26-10-2008) | v2 (02-05-2009) | v3 (05-07-2009) |
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| Group and phase velocities in the free-surface visco-potential flow: new kind of boundary layer induced instability |
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Denys Dutykh 1 |
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| (01/09/2009) |
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| Water wave propagation can be attenuated by various physical mechanisms. One of the main sources of wave energy dissipation lies in boundary layers. The present work is entirely devoted to thorough analysis of the dispersion relation of the novel visco-potential formulation. Namely, in this study we relax all assumptions of the weak dependence of the wave frequency on time. As a result, we have to deal with complex integro-differential equations that describe transient behaviour of the phase and group velocities. Using numerical computations, we show several snapshots of these important quantities at different times as functions of the wave number. Good qualitative agreement with previous study [Dutykh2009] is obtained. Thus, we validate in some sense approximations made anteriorly. There is an unexpected conclusion of this study. According to our computations, the bottom boundary layer creates disintegrating modes in the group velocity. In the same time, the imaginary part of the phase velocity remains negative for all times. This result can be interpreted as a new kind of instability which is induced by the bottom boundary layer effect. |
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| 1 : | 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 Physique/Physique/Physique Atmosphérique et Océanique Physique/Physique/Dynamique des Fluides Physique/Physique/Physique Numérique Physique/Physique/Physique Générale Physique/Physique/Géophysique Planète et Univers/Sciences de la Terre/Géophysique Sciences de l'environnement/Milieux et Changements globaux Mathématiques/Equations aux dérivées partielles Sciences de l'ingénieur/Milieux fluides et réactifs Mathématiques/Analyse numérique |
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| free-surface flows – visosity – dissipation – visco-potential flow – bottom boundary layer |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00334440, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00334440 | |
| oai:hal.archives-ouvertes.fr:hal-00334440 | |
| Contributeur : Denys Dutykh | |
| Soumis le : Dimanche 5 Juillet 2009, 14:42:00 | |
| Dernière modification le : Lundi 8 Novembre 2010, 21:23:16 | |
