Model Flames in the Boussinesq Limit: The Effects of Feedback
  We have studied the fully nonlinear behavior of pre-mixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. Key results include the establishment of criterion for when such flames propagate as simple planar flames; elucidation of scaling laws for the effective flame speed; and a study of the stability properties of these flames. The simplicity of some of our scalings results suggests that analytical work may further advance our understandings of buoyant flames. 
N. Vladimirova and R. Rosner