Front propagation in cellular flows for fast reaction and small diffusivity.

We investigate the influence of fluid flows on the propagation of chemical fronts arising in Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type models. We develop an asymptotic theory for the front speed in a cellular flow in the limit of small molecular diffusivity and fast reaction, i.e., large Peclet (Pe) and Damkohler (Da) numbers. The front speed is expressed in terms of a periodic path-an instanton-that minimizes a certain functional. This leads to an efficient procedure to calculate the front speed, and to closed-form expressions for (log Pe)(-1) << Da << Pe and for Da >> Pe. Our theoretical predictions are compared with (i) numerical solutions of an eigenvalue problem and (ii) simulations of the advection-diffusion-reaction equation.