Note on dust trapping in inviscid vortex pairs with unequal strengths

TL;DR

This paper theoretically analyzes how tiny heavy particles can be trapped in the flow of two point vortices, revealing conditions for stable trapping and potential dust traps in inviscid vortex pairs.

Contribution

It introduces a comprehensive analysis of particle trapping in inviscid vortex pairs, including stability conditions and trapping diagrams, extending previous understanding of vortex-particle interactions.

Findings

Particles can be stably trapped at equilibrium points in vortex flows.

Trapping occurs for vortex strength ratios other than 0 and -1.

Particle trapping on limit cycles is observed in contra-rotating vortex pairs.

Abstract

We investigate theoretically the motion of tiny heavy passive particles transported in a plane inviscid flow consisting of two point vortices, in order to understand particle dispersion and trapping during vortex interaction. In spite of their large density, particles are not necessarily centrifugated away from vortices. It is observed that they can have various equilibrium positions in the reference frame rotating with the vortices, provided the particle response time and the vortex strength ratio lie in appropriate ranges. A stability analysis reveals that some of these points can be asymptotically stable, and can therefore trap particles released in their basin of attraction. A complete trapping diagram is derived, showing that any vortex pair can potentially become a dust trap, provided the vortex strength ratio is different from 0 (single vortex) and -1 (translating symmetrical vortices). Trapping exists for both co-rotating or contra-rotating vortex pairs. In the latter case, particle trapping on a limit cycle is also observed, and confirmed by using Sapsis and Haller's method [Chaos, 20, 017515, 2010] generalized to non-inertial reference frames.