Particle paths in wavy vortices

We study the paths of individual fluid particles moving in velocity fields which model Taylor vortices close to the onset of the wavy instability. In particular, we consider the possibility of particle transport between vortices. By studying the flow in the context of dynamical systems theory, we show that this arises through the destruction of invariant surfaces which form the vortex boundaries in the absence of the wave. Particles able to pass between vortices follow chaotic trajectories (in the sense of showing sensitive dependence on initial conditions). This results in a mixing process that has some properties in common with diffusion.