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 vf dependence on the stirring intensity U, which is in good agreement with numerical estimates. In particular, at large U, the behavior vf∼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.