A perturbation study of particle dynamics in a plane wake flow

We analyse the dynamics of small, rigid, dilute spherical particles in the far wake of a bluff body under the assumption that the background flow fiel d is approximated by a periodic array of Stuart vortices that can be consid ered to be a regularization of the von Karman vortex street. Using geometri c singular perturbation theory and numerical methods, we show that when ine rtia (measured by a dimensionless Stokes number) is not too large, there is a periodic attractor in the phase space of the dynamical system governing the particle motion. We argue that this provides a simple mechanism to expl ain the unexpected 'focusing' effect that has been observed both numericall y and experimentally in the far-wake flow past a bluff body by Tang et al. (1992). Their results show that over a range of Reynolds numbers and interm ediate values of the Stokes number, particles injected into the wake of a b luff body concentrate near the edges of the vortex structures downstream, t hus tending to 'demix' rather than disperse homogeneously.