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) approximately U, whereas for cellular flows we observe V(f) approximately U(1/4) for fast advection and V(f) approximately U(3/4) for slow advection.