The effects of superdiffusive transport on front

We present experimental studies of the propagation of chemical fronts in an annular chain of alternating vortices. The vortex chain can be controlled to both drift (with velocity $v_d$) and oscillate (with velocity amplitude $v_o$) in the azimuthal direction. Transport in this flow is diffusive if $v_d < v_o$ and superdiffusive if $v_d > v_o$. The chemical front is produced using the excitable state of the Ruthenium-catalyzed Belousov-Zhabotinsky reaction. Previous experiments\footnote{Europhys. Lett. {\bf 69}, 819 (2005); Phys. Rev. E {\bf 72}, 046204 (2005).} have shown that the fronts often mode-lock to the external forcing for pure oscillatory time dependence ($v_d = 0$). We investigate the limits of this mode-locking behavior as the drift is increased, studying in particular any changes that occur when the transport becomes superdiffusive. An important parameter in these studies is the ratio $\eta = U/v_{rd}$ between the maximum flow velocity $U$ and the reaction-diffusion (no-flow) front velocity $v_{rd}$. We investigate changes in the observed behavior as $\eta$ is increased, increasing the relative importance of fluid advection in the advection-reaction-diffusion process.