Chaotic phenomena in the interaction of vortex rings

The problem of interaction of several coaxial vortex rings in an inviscid fluid is investigated numerically. It is assumed that the core shape of the vortex rings remain circular. At the initial time the rings are located at the same distance ρ0 from the center of the system. This distance is a control parameter of the problem. The cases of interaction of three, four, and five vortex rings are studied. It is shown, that in spite of the nonintegrability of the problem, there are certain domains of values ρ0 where the motion of the vortex rings is quasiperiodical. The transition from one such domain to another occurs always through a domain of chaotic interaction. The results of the interaction of the vortex rings are compared with the interaction of their plane analogies–vortex pairs.