Thin front propagation in steady and unsteady cellular flows

Details Thin front propagation in steady and unsteady cellular flows Thin front propagation in steady and unsteady cellular flows

2002-01-10

arxiv.org/abs/nlin/0201015v3

Physics of Fluids 15, 679-688 (2003)

Nonlinear Sciences

Pattern Formation and Solitons

12 pages, 13 figures

Scientific paper

10.1063/1.1541668

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. In the steady case, by means of a simplified model, we provide an analytical approximation for the front speed, $v_{{\scriptsize{f}}}$, as a function of the stirring intensity, $U$, in good agreement with the numerical results and, for large $U$, the behavior $v_{{\scriptsize{f}}}\sim U/\log(U)$ is predicted. The large scale of the velocity field mainly rules the front speed behavior even in the presence of smaller scales. In the unsteady (time-periodic) case, the front speed displays a phase-locking on the flow frequency and, albeit the Lagrangian dynamics is chaotic, chaos in front dynamics only survives for a transient. Asymptotically the front evolves periodically and chaos manifests only in the spatially wrinkled structure of the front.

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