Invariant manifolds and the geometry of front propagation in fluid flows

TL;DR

This paper offers a comprehensive theoretical analysis of burning invariant manifolds (BIMs), which act as barriers to reaction front propagation in fluid flows, elucidating their existence, stability, and how they can be bypassed.

Contribution

It introduces formal criteria and classifications for BIMs, advancing understanding of their role in fluid flow reaction dynamics.

Findings

BIMs serve as invariant barriers to front propagation.

Criteria for the existence and stability of BIMs are established.

Mechanisms for circumventing BIMs are identified.

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.