Chaotic dynamics of a body–vortex pair

Abstract

We study an idealized model of body–vortex interaction in two dimensions. The fluid is incompressible and inviscid and assumed to occupy the entire unbounded plane except for a simply connected region representing a rigid body. There may be a constant circulation around the body. The fluid also contains a finite number of point vortices of constant circulation but is otherwise irrotational. We assign a mass distribution to the body and let it move and rotate freely in response to the force and torque exerted by the fluid. Conversely, the fluid moves in response to the body motion. We study the occurrence of chaos in the system of ODEs emerging from these assumptions. It is well-known that the system consisting of a circular body with uniform mass distribution interacting with a single point vortex is integrable. Here we investigate how this integrability breaks down when the body center-of-mass is displaced from its geometrical center. We find two distinct regions of chaos and discuss how they relate to the topology of the trajectories of body and vortex.