Chaotic mixing in vortex-dominated flows

We present experimental studies of chaotic mixing in time-periodic, two-dimensional (2D) arrays of vortices. The flows are formed from the superposition of two vortex arrays shifted by half a vortex width in both directions. Flows generated by this method show both diffusive and superdiffusive transport, depending on the relative strengths and nature of the time dependence of the currents producing the two vortex arrays. Experimentally, we track the motion of tracer particles moving with the flow. From these tracks, we can determine the growth of the variance of a distribution of tracers. We are also applying algorithms based on braiding analysis \footnote{J.-L. Thiffeault, preprint} to determine the topological entropy for mixing in these flows. We are also initiating studies of chaotic mixing in a 3D, time-independent flow (composed of nested vortices) with the goal of studying advection-reaction-diffusion processes in a 3D system.