A perturbation study of particle dynamics in a plane wake flow

Abstract

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 field is approximated by a periodic array of Stuart vortices that can be considered to be a regularization of the von Kármán vortex street. Using geometric singular perturbation theory and numerical methods, we show that when inertia (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 explain the unexpected ‘focusing’ effect that has been observed both numerically 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 intermediate values of the Stokes number, particles injected into the wake of a bluff body concentrate near the edges of the vortex structures downstream, thus tending to ‘demix’ rather than disperse homogeneously.