Front speed enhancement in cellular flows

The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the enhancement of front speed with respect to the nonstirred case. By means of numerical simulations and theoretical arguments we describe the behavior of front speed as a function of the stirring intensity, U. For slow reaction, the front propagates with a speed proportional to U^1/4, conversely for fast reaction the front speed is proportional to U^3/4. In the geometrical optics limit, the front speed asymptotically behaves as U/ln U.