Persistent localized states for a chaotically mixed bistable reaction

Abstract

We describe the evolution of a bistable chemical reaction in a closed two-dimensional chaotic laminar flow, from a localized initial disturbance. When the fluid mixing is sufficiently slow, the disturbance may spread and eventually occupy the entire fluid domain. By contrast, rapid mixing tends to dilute the initial state and so extinguish the disturbance. Such a dichotomy is well known. However, we report here a hitherto apparently unremarked intermediate case, a persistent highly localized disturbance. Such a localized state arises when the Damkoehler number is great enough to sustain a hotspot, but not so great as to lead to global spread. We show that such a disturbance is located in the neighborhood of an unstable periodic orbit of the flow, and we describe some limited aspects of its behavior using a reduced, lamellar model.

6 pages, 6 figures

References in corpus (5)

• Chaotic mixing induced transitions in reaction-diffusion systems
• Excitable media in open and closed chaotic flows
• On propagation failure in 1 and 2 dimensional excitable media
• A bistable reaction--diffusion system in a stretching flow
• Filament bifurcations in a one-dimensional model of reacting excitable fluid flow