The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.
La théorie classique des vagues repose sur la théorie des écoulements non-visqueux. Cependant il est important d'inclure les effets visqueux dans certaines applications. Deux modèles sont ainsi proposés pour rajouter des effets dissipatifs dans le contexte des équations de Boussinesq, qui incluent les effets de faible dispersion et faible nonlinéarité dans le cadre des équations en eau peu profonde. Les équations de Boussinesq dissipatives sont ensuite intégrées numériquement.
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Mots-clés : Mécanique des fluides numérique, Équations de Boussinesq, Dissipation, Viscosité, Approximation onde longue, Propagation de tsunami
Denys Dutykh 1; Frédéric Dias 1
@article{CRMECA_2007__335_9-10_559_0,
author = {Denys Dutykh and Fr\'ed\'eric Dias},
title = {Dissipative {Boussinesq} equations},
journal = {Comptes Rendus. M\'ecanique},
pages = {559--583},
publisher = {Elsevier},
volume = {335},
number = {9-10},
year = {2007},
doi = {10.1016/j.crme.2007.08.003},
language = {en},
}
Denys Dutykh; Frédéric Dias. Dissipative Boussinesq equations. Comptes Rendus. Mécanique, Joseph Boussinesq, a Scientist of bygone days and present times, Volume 335 (2007) no. 9-10, pp. 559-583. doi : 10.1016/j.crme.2007.08.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.08.003/
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