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On the nonlinear behavior of Boussinesq type models: amplitude-velocity vs amplitude-flux forms

hal.structure.identifierParallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
dc.contributor.authorFILIPPINI, Andrea Gilberto
hal.structure.identifierParallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
dc.contributor.authorBELLEC, Stevan
hal.structure.identifierParallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
dc.contributor.authorCOLIN, Mathieu
hal.structure.identifierParallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
dc.contributor.authorRICCHIUTO, Mario
dc.date.accessioned2024-04-15T09:58:07Z
dc.date.available2024-04-15T09:58:07Z
dc.date.issued2014-07-29
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/198974
dc.description.abstractEnIn this paper we consider the modeling of nonlinear wave transformation by means of weakly nonlinear Boussinesq models. We show that for a given linear dispersion relation and linear shoaling parameter one can derive, within the same asymptotic truncation, two system of PDEs differing only in the form of the linear dispersive operators. In particular, these can either be formulated in terms of derivatives of the velocity, or in terms of derivatives of the flux. In the first case we speak of amplitude-velocity form of the model, in the second case of amplitude flux form. We show examples of these couples for several linear relations, including a new amplitude-flux variant of the model of Nwogu. We then show, both analytically and by numerical nonlinear shoaling tests, that while for small amplitude waves it is important to have accurate linear dispersion and shoaling characteristics, when approaching breaking conditions it is only the amplitude-velocity or amplitude-flux form of the equations which determines the behavior of the model, and in particular the shape and the height of the waves. This knowledge has tremendous importance when considering the use of these models in conjunction with wave breaking detection and dissipation mechanisms.
dc.language.isoen
dc.title.enOn the nonlinear behavior of Boussinesq type models: amplitude-velocity vs amplitude-flux forms
dc.typeRapport
dc.subject.halSciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph]
dc.subject.halSciences de l'environnement/Ingénierie de l'environnement
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.subject.halPhysique [physics]/Physique [physics]/Physique Atmosphérique et Océanique [physics.ao-ph]
dc.subject.halPhysique [physics]/Physique [physics]/Dynamique des Fluides [physics.flu-dyn]
dc.subject.halPlanète et Univers [physics]/Sciences de la Terre/Océanographie
dc.subject.halPlanète et Univers [physics]/Océan, Atmosphère
bordeaux.hal.laboratoriesLaboratoire Bordelais de Recherche en Informatique (LaBRI) - UMR 5800*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.type.institutionINRIA
bordeaux.type.reportrr
hal.identifierhal-01053036
hal.version1
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01053036v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2014-07-29&rft.au=FILIPPINI,%20Andrea%20Gilberto&BELLEC,%20Stevan&COLIN,%20Mathieu&RICCHIUTO,%20Mario&rft.genre=unknown


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