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Freely Floating Objects on a Fluid Governed by the Boussinesq Equations

hal.structure.identifierDépartement de Mathématiques et Applications - ENS Paris [DMA]
dc.contributor.authorBECK, Geoffrey
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLANNES, David
dc.date.accessioned2024-04-04T02:41:40Z
dc.date.available2024-04-04T02:41:40Z
dc.date.created2021-01-27
dc.date.issued2022-03-11
dc.identifier.issn0294-1449
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191171
dc.description.abstractEnWe investigate here the interactions of waves governed by a Boussinesq system with a partially immersed body allowed to move freely in the vertical direction. We show that the whole system of equations can be reduced to a transmission problem for the Boussinesq equations with transmission conditions given in terms of the vertical displacement of the object and of the average horizontal discharge beneath it; these two quantities are in turn determined by two nonlinear ODEs with forcing terms coming from the exterior wave-field. Understanding the dispersive contribution to the added mass phenomenon allows us to solve these equations, and a new dispersive hidden regularity effect is used to derive uniform estimates with respect to the dispersive parameter. We then derive an abstract general Cummins equation describing the motion of the solid in the return to equilibrium problem and show that it takes an explicit simple form in two cases, namely, the nonlinear non dispersive and the linear dispersive cases; we show in particular that the decay rate towards equilibrium is much smaller in the presence of dispersion. The latter situation also involves an initial boundary value problem for a nonlocal scalar equation that has an interest of its own and for which we consequently provide a general analysis.
dc.description.sponsorshipEcoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure - ANR-18-CE40-0027
dc.description.sponsorshipFrontières numériques et couplages - ANR-17-CE40-0025
dc.language.isoen
dc.publisherEMS
dc.subject.enFluid structure Interaction
dc.subject.enBoussinesq equations
dc.subject.enDispersive boundary layer
dc.subject.enReturn to equilibrium
dc.subject.enNonlocal transport equations
dc.subject.enFree surface
dc.title.enFreely Floating Objects on a Fluid Governed by the Boussinesq Equations
dc.typeArticle de revue
dc.identifier.doi10.4171/AIHPC/15
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
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]
bordeaux.journalAnnales de l'Institut Henri Poincaré C, Analyse non linéaire
bordeaux.pagehttps://ems.press/journals/aihpc/articles/5300753
bordeaux.volume39
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03122615
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03122615v1
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