Caustics and clustering in the vicinity of a vortex

We study the formation of caustics in vortex-dominated \flows. We \find that only particles starting within a critical distance of a vortex which scales as the square roots of the particle inertia and the circulation can form sling caustics. We show that particles starting in an annular region around this critical radius contribute the densest clusters in the \flow. The large density spikes occurring for such particles, even at small inertia, are indicative that these particles will experience large collision rates.