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Pré-Publication, Document De Travail Année : 2014

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

Résumé

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.
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Dates et versions

hal-00950544 , version 1 (21-02-2014)
hal-00950544 , version 2 (22-04-2016)
hal-00950544 , version 3 (15-09-2017)

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Olivier Glass, Alexandre Munnier, Franck Sueur. Dynamics of a point vortex as limits of a shrinking solid in an irrotational fluid. 2014. ⟨hal-00950544v1⟩
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