UC Irvine

We studied the minimal speed (c∗) of the Kolmogorov-Petrovsky-Piskunov (KPP) fronts at small diffusion (ε ≪ 1) in a class of time-periodic cellular flows with chaotic streamlines. 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 pe- riodic coefficients and small diffusion. To solve the advection dominated time-dependent eigenvalue problem efficiently over large time, a combination of spectral methods and finite element, as well as the associated fast solvers, are utilized to accelerate computation. In con- trast to the scaling c∗ = O(ε1/4) in steady cellular flows, a new relation c∗ = O(1) as ε ≪ 1 is revealed in the time-periodic cellular flows due to the presence of chaotic streamlines. In the meantime, we found that residual propagation speed emerges from the Lagrangian chaos which is quantified as a sub-diffusion process. The challenging part of obtaining the asymptotic behavior of traveling front is that requires computation in a long time interval. By taking advantage of the fact that numerical solution under time periodic cellular flows will preserve the layers structure, a new method of using global basis trained from samples under spectral method is introduced to obtain the minimal speed quickly.