A reduced model for a self-accelerating expanding flame subjected to the Darrieus-Landau and Rayleigh-Taylor instabilities: Transition to detonation

A weakly nonlinear model for a self-accelerating outward propagating corrugated flame is formulated and explored. The self-acceleration is sustained by the intrinsic Darrieus-Landau and Rayleigh-Taylor instabilities until the Deshaies-Joulin deflagrability threshold is reached, followed by an abrupt transition to detonation. Emergence of the threshold is caused by positive feedback between the accelerating flame and the flame-driven pressure shock that results in the thermal runaway when the flame speed reaches a critical level. The model offers a simple mechanism that may be responsible for the transition to detonation in thermonuclear supernovae.