Model flames in the Boussinesq limit: the case of pulsating fronts

We extend earlier work on the nonlinear behavior of premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation, in two dimensions. The main result is that the nature of the traveling burning front is largely determined by the form of the adopted boundary conditions on the side walls: while symmetric boundary conditions lead to stably scalloped traveling wave solutions, loss of symmetry leads to the development of pulsating fronts. However, despite differences in geometrical features, the symmetric and asymmetric systems obey the same scaling behavior for the average effective flame speed.