A nonlinear model for hydrodynamic instability of an expanding flame

Within the framework of a weakly nonlinear model that describes the front dynamics of a divergent cylindrical flame under the assumption of smallness of the gas-expansion coefficient, exact analytical solutions of the evolution equation for the disturbed-flame surface were constructed. These solutions are similar to those derived from the polar-decomposition method. Based on computer numerical simulation, a new approach for describing a self-accelerating expanding cylindrical flame is proposed.