Stability and the Fractal Structure of a Spherical Flame in a Self-Similar Regime

Stability of a discontinuous flame front propagating in a self-similar regime ${R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}At}^{\ensuremath{\alpha}}$ is considered. It is shown that the regime with $\ensuremath{\alpha}>1$ is more unstable compared to the flame propagating with a constant front velocity. The destabilizing effect is more pronounced for flames with the ratio of the fuel density to the density of the products of burning ${\ensuremath{\rho}}_{1}/{\ensuremath{\rho}}_{2}>2$ which is typical for usual laboratory flames. A formula for the velocity of a flame with a fractal structure of the front is discussed.