The transition from spinning to radial solid flame waves

Abstract

We describe computations of various propagating wave modes in a cylinder of radius R modeled by an array of interacting 1D rods in a reaction-diffusion model of solid flames. For sufficiently small and sufficiently large R, the model exhibits planar uniformly propagating combustion waves. Spin modes, characterized by hot spots spinning periodically around the cylinder, occur for small R, and radial modes, periodically oscillating solutions independent of the cylindrical angle occur for larger R. We describe the transition from spin to radial modes via a family of quasi-periodic modes.