Thin front propagation in steady and unsteady cellular flows

Front propagation in two-dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. For the steady flow, a simplified model allows for an analytical prediction of the front speed v f dependence on the stirring intensity U , which is in good agreement with numerical estimates. In particular, at large U , the behavior v f;U/log(U) is predicted. By adding small scales to the velocity field we found that their main effect is to renormalize the flow intensity. In the unsteady ~time-periodic! flow, we found that the front speed locks to the flow frequency and that, despite the chaotic nature of the Lagrangian dynamics, the front evolution is chaotic only for a transient. Asymptotically the front evolves periodically and chaos manifests only in its spatially wrinkled structure. © 2003 American Institute of Physics. @DOI: 10.1063/1.1541668#