@article{AbelCelaniVergenietal.2001,
  author    = {Abel, Markus and Celani, A. and Vergeni, D. and Vulpiani, A.},
  title     = {Front propagation in laminar flows},
  year      = {2001},
  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 <i>V<sub><i>f</sub> depends on the typical flow velocity <i>U as<sup> </sup>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<sup> </sup><i>V<sub><i>f</sub>~<i>U, whereas for cellular flows we observe <i>V<sub><i>f</ sub>~<i>U<sup>1/4</sup> for fast advection and <i>V<sub><i>f</sub>~<i>U<sup>3/4</sup> for slow advection.},
  language  = {en}
}