On multiple routes to chaos in advection induced by point vortices

Chaotic advection induced by periodic motions of point vortices inside and outside of a circular domain and in the infinite plane is analyzed. Though simple, this model flow captures multiple routes to chaos and gives a good qualitative picture of advection in more complicated domains such as rectangle and ellipse. Different scenarios of chaotic advection depend on the topology of unperturbed phase portraits and type of perturbations. In addition to the typical KAM cases, we find scenarios accounting for inherent singularity of the velocity field.