Particle dynamics and mixing in an oscillating viscous vortex pair

A model of a viscous vortex pair, based on a solution of the Stokes equation, is applied for studying particle dynamics and mixing in vortex-pair-like structures. The perturbed flow field and dynamics of small spherical particles, contained in this flow, are studied on the basis of this solution. The particle-path equations and well-established techniques, such as computing of Poincaré maps, is used. It is shown that the flow inside the vortex pair can behave chaotically when a relatively thick pair (core size of the pair comparable with its radius) is under the influence of a periodic perturbation. This is expected to lead to better mixing of the fluid. However, an increase of the perturbation frequency causes the appearance of regions where a bounded quasi-periodic motion occurs. These regions behave like barriers in the phase space, reducing mixing and transport processes in the fluid. Introduction of the perturbation causes changes in the trajectories of the spherical aerosol-type particles. For a certain range of Stokes numbers (St < 10), long-term accumulation inside the vortex pair is observed for these particles, while the same particles in the unperturbed flow are forced out of the pair into the ambient flow