Frozen reaction fronts in steady flows: a burning-invariant-manifold perspective

TL;DR

This paper investigates the structure and formation of frozen reaction fronts in steady fluid flows, revealing they are composed of burning invariant manifolds and analyzing bifurcations leading to their emergence, supported by experiments and simulations.

Contribution

It demonstrates that frozen fronts are made of burning invariant manifolds and provides a bifurcation analysis for their formation and topological changes in steady flows.

Findings

Frozen fronts are composed of segments of burning invariant manifolds.

Bifurcations can lead from nonfrozen to frozen states.

Experimental and numerical evidence supports the theoretical framework.

Abstract

The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the reacted domain is static, and the front appears "frozen". Our central result is that these frozen fronts in the two-dimensional fluid are composed of segments of burning invariant manifolds---invariant manifolds of front-element dynamics in $xy\theta$-space, where $\theta$ is the front orientation. Burning invariant manifolds (BIMs) have been identified previously as important local barriers to front propagation in fluid flows. The relevance of BIMs for frozen fronts rests in their ability, under appropriate conditions, to form global barriers, separating reacted domains from nonreacted domains for all time. The second main result of this paper is an understanding of bifurcations that lead from a nonfrozen state to a frozen state, as well as bifurcations that change the topological structure of the frozen front. Though the primary results of this study apply to general fluid flows, our analysis focuses on a chain of vortices in a channel flow with an imposed wind. For this system, we present both experimental and numerical studies that support the theoretical analysis developed here.