GLASS, Olivier; LACAVE, Christophe; MUNNIER, Alexandre; SUEUR, Franck

doi:10.1016/j.jde.2019.04.017

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GLASS, Olivier
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

LACAVE, Christophe
Institut Fourier [IF ]

MUNNIER, Alexandre
Institut Élie Cartan de Lorraine [IECL]
Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization [SPHINX]

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Article de revue

Ce document a été publié dans

Journal of Differential Equations. 2019-09, vol. 267, n° 6, p. 3561-3577

Elsevier

Résumé en anglais

We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler equations and the motion of the rigid bodies is given by Newton's laws with forces due to the fluid pressure. We prove that, for smooth solutions, Newton's equations can be recast as a second-order ODE for the degrees of freedom of the rigid bodies with coefficients depending on the fluid vorticity and on the circulations around the bodies, but not anymore on the fluid pressure. This reformulation highlights geodesic aspects linked to the added mass effect, gyroscopic features generalizing the Kutta-Joukowski-type lift force, including body-body interactions through the potential flows induced by the bodies' motions, body-body interactions through the irrotational flows induced by the bodies' circulations, and interactions between the bodies and the fluid vorticity.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192912

DOI

http://dx.doi.org/10.1016/j.jde.2019.04.017

Project ANR

Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation - ANR-15-CE40-0010
Ecoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure - ANR-18-CE40-0027
Bords, oscillations et couches limites dans les systèmes différentiels - ANR-16-CE40-0027

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251