The dynamics of a passive tracer in the velocity field of four identical point vortices,
moving under the influence of their self-induced advection, is investigated. Of interest
is the change in mixing and transport properties of the tracer for the three different
classes of vortex motion: periodic, quasi-periodic and chaotic. As a consequence of
conservation laws, the vortex motion is confined to a finite region of phase space;
therefore, the tracer phase space can be partitioned into an inner and an outer region.
We find that in the case of quasi-periodic vortex motion the tracer phase space
exhibits a well-defined barrier to transport between the central chaotic region and the
outer region, where the trajectories are regular. In the case of chaotic vortex motion
the barrier becomes permeable. The particle dynamics goes through an intermittent
behaviour, where forays into the central region alternate with trapping in outer
annular orbits. In the far field, an estimate of diffusion rates is made through a
multipole expansion of the tracer velocity field. We make use of a specific stochastic
model for the tracer velocity field which predicts no diffusion for the case of quasi-periodic vortex motion and, for the case of chaotic vortex motion, a diffusion rate
that goes to zero at large distances from the vortex cluster.