Persistent localized states for a chaotically mixed bistable reaction

Cox, Stephen M.

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 "hot spot," 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.

Copyright American Physical Society (APS) 2006.

Citation

Cox, S. M. (2006). Persistent localized states for a chaotically mixed bistable reaction. Physical Review E, 74(5),

• Journal Article Type: Article
• Publication Date: Nov 1, 2006
• Deposit Date: May 10, 2007
• Publicly Available Date: Oct 9, 2007
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 74
• Issue: 5
• Keywords: chaotic advection, sine flow, localized hotspot
• Public URL: https://nottingham-repository.worktribe.com/output/1018166