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Dynamics of a point vortex as limits of a shrinking solid in an irrotational fluid

Munnier, Alexandre; Glass, Olivier (2014), Dynamics of a point vortex as limits of a shrinking solid in an irrotational fluid. https://basepub.dauphine.fr/handle/123456789/12771

Type
Document de travail / Working paper
External document link
http://hal.archives-ouvertes.fr/hal-00950544
Date
2014
Publisher
Université Paris-Dauphine
Published in
Paris
Pages
83
Metadata
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Author(s)
Munnier, Alexandre
Glass, Olivier
Abstract (EN)
We consider the motion of a rigid body immersed in a two-dimensional perfect fluid. The fluid is assumed to be irrotational and confined in a bounded domain. We prove that when the body shrinks to a point wise massless particle with fixed circulation, its dynamics in the limit is given by the point vortex equation. As a byproduct of our analysis we also prove that when the body shrinks with a fixed mass the limit equation is a second-order differential equation involving a Kutta-Joukowski-type lift force, which extends the result of [Glass O., Lacave C., Sueur F., On the motion of a small body immersed in a two dimensional incompressible perfect fluid. {Preprint 2011}, to appear in Bull. Soc. Math. France. {\tt arXiv:1104.5404}] to the case where the domain occupied by the solid-fluid system is bounded.
Subjects / Keywords
Fluid dynamics; Dynamics of a point vortex

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