Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LANNES, David | |
| hal.structure.identifier | Environnements et Paléoenvironnements OCéaniques [EPOC] | |
| dc.contributor.author | BONNETON, Philippe | |
| dc.date.accessioned | 2024-04-04T03:06:15Z | |
| dc.date.available | 2024-04-04T03:06:15Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193319 | |
| dc.description.abstractEn | A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \cite{matsuno3} and Choi \cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equations with the fully nonlinear shallow water Green-Naghdi equations represents a relevant model for describing ocean wave propagation from deep to shallow waters. | |
| dc.language.iso | en | |
| dc.title.en | Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Physique [physics]/Physique [physics]/Physique Atmosphérique et Océanique [physics.ao-ph] | |
| dc.identifier.arxiv | 0710.1349 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00177251 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00177251v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=LANNES,%20David&BONNETON,%20Philippe&rft.genre=preprint |
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