Front propagation in laminar flows

Abstract

The problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius type are considered under the assumption of no feedback of the concentration on the velocity. Numerical simulations of advection-reaction-diffusion equations have been performed by an algorithm based on discrete-time maps. The results show a generic enhancement of the speed of front propagation by the underlying flow. For small molecular diffusivity, the front speed $V_f$ depends on the typical flow velocity $U$ as a power law with an exponent depending on the topological properties of the flow, and on the ratio of reactive and advective time-scales. For open-streamline flows we find always $V_f\sim U$, whereas for cellular flows we observe $V_f\sim U^{1/4}$ for fast advection, and $V_f\sim U^{3/4}$ for slow advection.

Enlarged, revised version, 37 pages, 14 figures

References in corpus (1)

• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts

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