Cellular structures, as the rolls generated by Rayleigh–Bénard 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 Péclet 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 Péclet 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.
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2004
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