A computational study of residual KPP front speeds in time-periodic cellular flows in the small diffusion limit

Abstract

The minimal speeds (c∗) of the Kolmogorov–Petrovsky–Piskunov (KPP) fronts at small diffusion (ϵ≪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 principle 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 spectral methods and finite element, as well as the associated fast solvers, are utilized to accelerate computation. In contrast 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. Residual propagation speed emerges from the Lagrangian chaos which is quantified as a sub-diffusion process.