Invariant manifolds and the geometry of front propagation in fluid flows

Abstract

Recent theoretical and experimental work has demonstrated the existence of one-sided, invariant barriers to the propagation of reaction-diffusion fronts in quasi-two-dimensional periodically-driven fluid flows. These barriers were called burning invariant manifolds (BIMs). We provide a detailed theoretical analysis of BIMs, providing criteria for their existence, a classification of their stability, a formalization of their barrier property, and mechanisms by which the barriers can be circumvented. This analysis assumes the sharp front limit and negligible feedback of the front on the fluid velocity. A low-dimensional dynamical systems analysis provides the core of our results.

14 pages, 11 figures. To appear in Chaos Focus Issue: Chemo-Hydrodynamic Patterns and Instabilities (2012)

References in corpus (3)

• Invariant barriers to reactive front propagation in fluid flows
• Biological activity in the wake of an island close to a coastal upwelling
• Demonstration of Turnstiles as a Chaotic Ionization Mechanism in Rydberg Atoms

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• Mode-locking in advection-reaction-diffusion systems: an invariant manifold perspective