Diffusion and reaction-diffusion in fast cellular flows

Cellular structures, as the rolls generated by Rayleigh-Benard instability, have always been an important topic in nonlinear science. The diffusion of a passive scalar in a given steady cellular flow becomes an interesting question in the limit of a large Peclet number, often realistic. The main result there is that the effective diffusion is somewhere in between the molecular diffusion and the "turbulent" diffusion. A new added twist to this is the reaction-diffusion case, where the front speed is the laminar propagation velocity (without flow) times the Peclet number to the power 1/4. I refine this last result and give the behavior of the prefactor in the Zel'dovich limit of a narrow reaction zone. (C) 2004 American Institute of Physics.