Stability of fronts in the Kuramoto-Sivashinsky equation advected by a Poiseuille flow

Abstract

We study reaction fronts described by the Kuramoto-Sivashinsky equation subject to a Poiseuille flow. The fronts propagate with or against the flow located inside a two-dimensional slab. Steady front profiles can be flat, axisymmetric, or nonaxisymmetric, depending on the gap between the plates and the average flow speed. We first obtain the steady front solutions, later executing a linear stability analysis to determine the stability of the fronts. Applying fluid flow can turn initially unstable fronts into stable fronts. Stable steady fronts propagating in the adverse direction of the Poiseuille flow are axisymmetric for slow fluid flows. However, for higher speeds an adverse flow can lead to stable nonaxisymmetric fronts. We also show regions of bistability where stable nonaxisymmetric and axisymmetric fronts can coexist.