FKPP fronts in cellular flows: the large-Péclet regime

Alexandra Tzella
University of Birmingham

(Joint work with Jacques Vanneste) We investigate the influence of cellular flows on the propagation of chemical fronts arising in Fisher– Kolmogorov–Petrovskii–Piskunov (FKPP) type models. In the long-time limit, a steadily propagating pulsating front is established. Its speed can be obtained by solving an eigenvalue problem closely related to large-deviation theory. We use matched-asymptotics to solve this eigenvalue problem in the limit of small molecular diffusivity (large Péclet number) and arbitrary reaction rate (arbitrary Damkohler number). We identify three distinguished regimes that, together, provide a complete description of the front speed in terms of non-trivial functions of the Peclet and Damkohler numbers. Earlier results, characterised by power-law dependences on these numbers, are recovered as limiting cases. The theoretical results are illustrated by a number of numerical simulations.

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