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Front propagation in two dimensional steady and unsteady cellular flows isinvestigated in the limit of very fast reaction and sharp front, i.e., in thegeometrical 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 goodagreement with the numerical results and, for large $U$, the behavior$v_{{\scriptsize{f}}}\sim U/\log(U)$ is predicted. The large scale of thevelocity field mainly rules the front speed behavior even in the presence ofsmaller scales. In the unsteady (time-periodic) case, the front speed displaysa phase-locking on the flow frequency and, albeit the Lagrangian dynamics ischaotic, chaos in front dynamics only survives for a transient. Asymptoticallythe front evolves periodically and chaos manifests only in the spatiallywrinkled structure of the front.Comment: 12 pages, 13 figure

Thin front propagation in steady and unsteady cellular flows