On the pulsating instability of two-dimensional flames

We consider a well-known thermo-diffusive model for the propagation of a premixed, adiabatic flame front in the large-activation-energy limit. That model depends only on one nondimensional parameter β, the reduced Lewis number. Near the pulsating instability limit, as β↓β 0 = 32/3, we obtain an asymptotic model for the evolution of a quasi-planar flame front, via a multi-scale analysis. The asymptotic model consists of two complex Ginzburg–Landau equations and a real Burgers equation, coupled by non-local terms. The model is used to analyse the nonlinear stability of the flame front.