Markus Abel, A. Celani, D. Vergeni, A. Vulpiani

• 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 <i>V_<i>f depends on the typical flow velocity <i>U asa 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<i>V_<i>f~<i>U, whereas for cellular flows we observe <i>V<sub><i>f</ sub>~<i>U^1/4 for fastThe 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 <i>V_<i>f depends on the typical flow velocity <i>U asa 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<i>V_<i>f~<i>U, whereas for cellular flows we observe <i>V<sub><i>f</ sub>~<i>U^1/4 for fast advection and <i>V_<i>f~<i>U^3/4 for slow advection.…