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Dynamics of rigid bodies in a two dimensional incompressible perfect fluid

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Date
2019
Dewey
Analyse
Sujet
rigid bodies; Euler equations
Journal issue
Journal of Differential Equations
Volume
267
Number
6
Publication date
09-2019
Article pages
3561-3577
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.jde.2019.04.017
URI
https://basepub.dauphine.fr/handle/123456789/20376
Collections
  • CEREMADE : Publications
Metadata
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Author
Glass, Olivier
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lacave, Christophe
21 Institut Fourier [IF ]
Munnier, Alexandre
211251 Institut Élie Cartan de Lorraine [IECL]
Sueur, Franck
27730 Institut de Mathématiques de Bordeaux [IMB]
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider the motion of several rigid bodies immersed in a two-dimensional incompressible 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.

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