  Recent theoretical and experimental investigations have demonstrated the role
of certain invariant manifolds, termed burning invariant manifolds (BIMs), as
one-way dynamical barriers to reaction fronts propagating within a flowing
fluid. These barriers form one-dimensional curves in a two-dimensional fluid
flow. In prior studies, the fluid velocity field was required to be either
time-independent or time-periodic. In the present study, we develop an approach
to identify prominent one-way barriers based only on fluid velocity data over a
finite time interval, which may have arbitrary time-dependence. We call such a
barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian
coherent structures (LCSs) commonly used in passive advection. Our approach is
based on the variational formulation of LCSs using curves of stationary
"Lagrangian shear", introduced by Farazmand, Blazevski, and Haller [Physica D
278-279, 44 (2014)] in the context of passive advection. We numerically
validate our technique by demonstrating that the bLCS closely tracks the BIM
for a time-independent, double-vortex channel flow with an opposing "wind".
