Coherent structures in reacting flows*

Our goal is to characterize the nature of reacting flows by identifying important ``coherent'' structures. We follow the recent work by Haller, Beron-Vera, and Farazmand which formalized the the notion of lagrangian coherent structures (LCSs) in fluid flows. In this theory, LCSs were derived from the Cauchy-Green strain tensor. We adapt this perspective to analogously define coherent structures in \emph{reacting} flows. By this we mean a fluid flow with a reaction front propagating through it such that the propagation does not affect the underlying flow. A reaction front might be chemical (Belousov-Zhabotinsky, flame front, etc.) or some other type of front (electromagnetic, acoustic, etc.). While the recently developed theory of burning invariant manifolds (BIMs) describes barriers to front propagation in time-periodic flows, this current work provides an important complement by extending to the aperiodic setting.