Note on dust trapping in point vortex pairs with unequal strengths

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 centrifuged away from vortices. It is observed that they can have various equilibrium positions in the reference frame rotating with the vortices, provided that 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 that the vortex strength ratio is different from 0 (single vortex) and -1 (translating symmetrical vortices). Trapping exists for both corotating and contrarotating vortex pairs. In the latter case, particle trapping on a limit cycle is also observed and confirmed by using the method of Sapsis and Haller ["Clustering criterion for inertial particles in 2D time-periodic and 3D steady flows," Chaos20, 017515 (2010)] generalized to noninertial reference frames. © 2010 American Institute of Physics.