Competition between curvature and chemistry in a spherically expanding detonation

The methods of bifurcation theory and asymptotic analysis are used to study curvilinear perturbations of a plane detonation wave. An asymptotic model is derived for the small curvature limit. The nonlinear competition between curvature and chemistry is manifested by a highly degenerate critical point in the state space of the model equations. Computer simulations are presented showing agreement of this model with the reactive Euler equations in the small curvature limit. In particular, we find that the leading order correction to the wave speed due to the curvature of the detonation front depends on the order of the chemical reaction to leading order in curvature.