  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.
