Dynamics of Nearly Extinguished Non-Adiabatic Premixed Flames in a Gravitation Field

A nonlinear stability analysis of a uniformly propagating plane flame subject to gravitational forces and small volumetric heat loss is presented. A nonlinear partial differential equation describing the evolution and structure of the flame near the extinction point (i.e., the point beyond which a uniformly propagating plane flame cannot be sustained) is derived. It is shown that this equation admits nontrivial solutions beyond the extinction point. The solutions represent steady wrinkled flames, which are spatially periodic in the direction transverse to the direction of propagation of the flame.