Accumulation of Heavy Particles in Bounded Vortex Flow

Abstract

Much research has been done on the motion of heavy particles in simple vortex flows. In most of this work, particle motion is investigated under the influence of fixed vortices. In the context of astrophysics, the motion of heavy particles in rotating two-dimensional flows has been investigated; the rotation follows from the laws of Kepler. In the present paper, the motion of heavy particles in potential vortex flow in a circular domain is investigated. The vortex describes a circular trajectory due to the presence of the boundary, so that a steadily rotating flow is obtained. In order to isolate the effect of particle inertia, only Stokes drag is taken into account in the equation of motion. The numerical simulations are based on a oneway coupling. They show that small heavy particles accumulate in an ellitpic region of the flow, counterrotating with respect to the vortex. When the particle Stokes number exceeds a threshold, depending on the vortex configuration, particles are expelled from the circular domain. A stability criterion for this particle accumulation is derived analytically. These results are qualitatively comparable to those obtained by others in astrophysics.