Caustics and clustering in the vicinity of a vortex

TL;DR

This paper investigates how particles form dense clusters and caustics near vortices, revealing critical initial positions that lead to high collision rates, relevant for understanding particle dynamics in turbulent flows.

Contribution

It identifies the critical initial distance from a vortex for caustic formation and shows how particles in this region create dense clusters, advancing understanding of particle-vortex interactions.

Findings

Particles within a critical radius form sling caustics.

Densest clusters originate from particles in an annular region around the critical radius.

Large density spikes imply high collision rates even at small inertia.

Abstract

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.