Dynamics of a small rigid body in a perfect incompressible fluid

Glass, Olivier

Journées équations aux dérivées partielles (2014), article no. 3, 20 p.

We consider a solid in a perfect incompressible fluid in dimension two. The fluid is driven by the classical Euler equation, and the solid evolves under the influence of the pressure on its surface. We consider the limit of the system as the solid shrinks to a point. We obtain several different models in the limit, according to the asymptotics for the mass and the moment of inertia, and according to the geometrical situation that we consider. Among the models that we get in the limit, we find Marchioro and Pulvirenti’s vortex-wave system and a variant of this system where the vortex, placed in the point occupied by the shrunk body, is accelerated by a lift force similar to the Kutta-Joukowski force. These results are obtained in collaboration with Christophe Lacave (Paris-Diderot), Alexandre Munnier (Nancy) and Franck Sueur (Bordeaux).

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