  Front propagation in two dimensional steady and unsteady cellular flows is
investigated in the limit of very fast reaction and sharp front, i.e., in the
geometrical optics limit. In the steady case, by means of a simplified model,
we provide an analytical approximation for the front speed,
$v_{{\scriptsize{f}}}$, as a function of the stirring intensity, $U$, in good
agreement with the numerical results and, for large $U$, the behavior
$v_{{\scriptsize{f}}}\sim U/\log(U)$ is predicted. The large scale of the
velocity field mainly rules the front speed behavior even in the presence of
smaller scales. In the unsteady (time-periodic) case, the front speed displays
a phase-locking on the flow frequency and, albeit the Lagrangian dynamics is
chaotic, chaos in front dynamics only survives for a transient. Asymptotically
the front evolves periodically and chaos manifests only in the spatially
wrinkled structure of the front.
