The minimal speeds (c * ) of the Kolmogorov-Petrovsky-Piskunov (KPP) fronts at small diffusion (ǫ ≪ 1) in a class of time-periodic cellular flows with chaotic streamlines is investigated in this paper. The variational principle of c * reduces the computation to that of a principal eigenvalue problem on a periodic domain of a linear advection-diffusion operator with space-time periodic coefficients and small diffusion. To solve the advection dominated time-dependent eigenvalue problem efficiently over large time, a combination of finite element and spectral methods, as well as the associated fast solvers, are utilized to accelerate computation. In contrast to the scaling c * = O(ǫ 1/4 ) in steady cellular flows, a new relation c * = O(1) as ǫ ≪ 1 is revealed in the time-periodic cellular flows due to the presence of chaotic streamlines. Residual propagation speed emerges from the Lagrangian chaos which is quantified as a sub-diffusion process.
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