Heavy inertial particles near two co-rotating vortices: Chaos, Entrapment and Collisions

Chaotic motion, collisions, clustering, mixing and entrainment of inertial particles is important for various natural and technological processes. To understand the origin of these, we study inertial particles with densities slightly higher than the background fluid near two co-rotating vortices. We find that heavy inertial particles can get entrapped indefinitely near fixed points, limit cycles or chaotic attractors, depending on the density ratio and Stokes number (St). As St is monotinically increased from zero, limit cycles can undergo period doubling bifurcations up to chaos, as well as period-doubling and then period-halving bifurcations back to a fixed point. The basin-of-attraction is generally large, and can persist even for St~O(1) for certain density ratios. Importantly, these behaviours cannot be predicted using a perturbative field description of particle velocity.