Propagation of a chemical wave front in a quasi-two-dimensional superdiffusive flow

Pattern formation in reaction-diffusion systems is an important self-organizing mechanism in nature. Dynamics of systems with normal diffusion do not always reflect the processes that take place in real systems when diffusion is enhanced by a fluid flow. In such reaction-diffusion-advection systems diffusion might be anomalous for certain time and length scales. We experimentally study the propagation of a chemical wave occurring in a Belousov-Zhabotinsky reaction subjected to a quasi-two-dimensional chaotic flow created by the Faraday experiment. We present a novel analysis technique for the local expansion of the active wave front and find evidence of its superdiffusivity. In agreement with these findings the variance σ(2)(t)∝t(γ) of the reactive wave grows supralinear in time with an exponent γ>2. We study the characteristics of the underlying flow with microparticles. By statistical analysis of particle trajectories we derive flight time and jump length distributions and find evidence that tracer-particles undergo complex trajectories related to Lévy statistics. The propagation of active and passive media in the flow is compared.