Clustering and chaotic motion of inertial particles in an isolated vortex

Inertial particles sample a flow field preferentially, getting centrifuged away from vortical regions and accumulating in strain-dominated regions. The dynamics of heavy particles in an axisymmetric vortex monopole are along expected lines - particles spirally migrate to infinity. We show that a deviation from axisymmetry for the vorticity profile can lead to intriguing clustering dynamics for inertial particles. We consider the Kirchhoff vortex, an elliptical patch of uniform vorticity that rotates with a constant angular velocity, and show that four fixed points exist for heavy particles in the irrotational exterior. They appear as saddles and stable spirals, and we investigate their stability as a function of the Stokes number. A background shear often strains elliptical vortices - the Kida vortex is an example. Beyond a critical shear rate, the Kida vortex is known to exhibit Lagrangian chaos; the tracer pathlines are chaotic. We study the dynamics of heavy inertial particles in a Kida vortex, investigating how particle inertia can compete with background shear to suppress the occurrence of chaotic trajectories.