Trapping and extreme clustering of finitely-dense inertial particles near a rotating vortex pair

Abstract

Small heavy particles cannot get attracted into a region of closed streamlines in a non-accelerating frame (Sapsis & Haller 2010). In a rotating system, however, particles can get trapped (Angilella 2010) near vortices. We perform numerical simulations examining trapping of inertial particles in a prototypical rotating flow: an identical pair of rotating Lamb-Oseen vortices, without gravity. Our parameter space includes the particle Stokes number $St$, measuring the particle's inertia, and a density parameter $R$, measuring the particle-to-fluid relative density. We focus on inertial particles that are finitely denser than the fluid. Particles can get indefinitely trapped near the vortices and display extreme clustering into smaller dimensional objects: attracting fixed-points, limit cycles and chaotic attractors. As $St$ increases for a given $R$, we may have an incomplete or complete period-doubling route to chaos, as well as an unusual period-halving route back to a fixed-point attractor. The fraction of trapped particles can vary non-monotonically with $St$. We may even have windows in $St$ for which no particle trapping occurs. At $St$ larger than a critical value, beyond no trapping occurs, significant fractions of particles can spend long but finite times in the vortex vicinity. The inclusion of the Basset-Boussinesq history (BBH) force is imperative in our study due to particle's finite density. BBH force significantly increases the basin of attraction as well as the range of $St$ where trapping can occur. Extreme clustering can be physically significant in planetesimal formation by dust aggregation in protoplanetary disks, phytoplankton aggregation in oceans, etc.