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We consider a model that approximates vortex rings in the axisymmetric 3DEuler equation by the movement of almost rigid bodies described by Newtonianmechanics. We assume that the bodies have a circular cross-section and that thefluid is irrotational and interacts with the bodies through the pressureexerted at the boundary. We show that this kind of system can be describedthrough an ODE in the positions of the bodies and that in the limit, where thebodies shrink to massless filaments, the system converges to an ODE systemsimilar to the point vortex system. In particular, we can show that in asuitable set-up, the bodies perform a leapfrogging motion.

A model for the approximation of vortex rings by almost rigid bodies