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.

References in corpus (16)

• Heavy particle concentration in turbulence at dissipative and inertial scales
• Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R^2
• Caustic activation of rain showers
• Particle Aggregation in a turbulent Keplerian flow
• On the role of the history force for inertial particles in turbulence
• Accurate solution method for the Maxey-Riley equation, and the effects of Basset history
• Influence of the history force on inertial particle advection: Gravitational effects and horizontal diffusion
• Caustics and clustering in the vicinity of a vortex
• Memory effects in chaotic advection of inertial particles
• Dust trapping in inviscid vortex pairs
• Attracting fixed points for heavy particles in the vicinity of a vortex pair
• Inertial particle trapping in an open vortical flow
• Surface tension as the destabiliser of a vortical interface
• Note on dust trapping in inviscid vortex pairs with unequal strengths
• Clusters of heavy particles in two-dimensional Keplerian turbulence
• Explicit Runge-Kutta algorithm to solve non-local equations with memory effects: case of the Maxey-Riley-Gatignol equation

Cited by in corpus (1)

• Caustics of finitely dense inertial particles