Front propagation in laminar flows - art. no. 046307

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. Pr oduction terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrheni us type are considered under the assumption of no feedback of the concentra tion 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 b y 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,dep ending on the topological properties of the flow, and on the ratio of react ive and advective time scales. For open-streamline flows we find always V-f similar to U, whereas for cellular flows we observe V-f similar to U-1/4 f or fast advection and V-f similar to U-3/4 for slow advection.