Front Propagation in Stirred Media

• Published in: Milan journal of mathematics 2011-12, Vol.79 (2), p.497-520
• Main Authors: Vergni, D., Vulpiani, A.
• Format: Article
• Language: English
• Subjects: Analysis; Mathematics; Mathematics and Statistics
• ISSN: 1424-9286; 1424-9294
• DOI: 10.1007/s00032-011-0162-7

The problem of asymptotic features of front propagation in stirred media is addressed for laminar and turbulent velocity fields. In particular we consider the problem in two dimensional steady and unsteady cellular flows in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case we provide an analytical approximation for the front speed, v f , as a function of the stirring intensity, U , in good agreement with the numerical results. In the unsteady (time-periodic) case, albeit the Lagrangian dynamics is chaotic, chaos in the front dynamics is relevant only for a transient. Asymptotically the front evolves periodically and chaos manifests only in the spatially wrinkled structure of the front. In addition we study front propagation of reactive fields in systems whose diffusive behavior is anomalous. The features of the front propagation depend, not only on the scaling exponent ν , which characterizes the diffusion properties, , but also on the detailed shape of the probability distribution of the diffusive process.