An Elementary Model for a Self-Accelerating Outward Propagating Flame Subject to the Rayleigh–Taylor Instability: Transition to Detonation

Within the Boussinesq approximation, an elementary model for the deflagration-to- detonation transition triggered by self-acceleration of an expanding flame is formulated and explored. The self-acceleration is sustained by the intrinsic Rayleigh–Taylor instability 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.