Transport in an oscillating/drifting vortex chain and L\'evy networks

We present numerical studies of diffusive and superdiffusive transport in a chain of alternating vortices. If the chain oscillates laterally (with velocity amplitude $v_o$), mixing is chaotic and transport is diffusive with mixing predominately between adjacent vortices. If the vortices drift as well with drift velocity $v_d$, transport can be superdiffusive (if $v_d > v_o$), characterized by L{\'e}vy flights that allow fluid to travel several vortices in a short period of time. We investigate in detail the transition between normal and superdiffusive transport in this system, studying in particular the statistics of the flights. We also determine the relative coupling strengths (due to mixing) between vortices as time increases. Ultimately, our goal is to develop a model of a ``L\'evy network'' for oscillatory process occurring in extended fluid systems.