On upward propagating flames

The premixed flame propagating through a vertical channel and subject to buoyancy effects is analyzed. In the limit of strong thermal expansion of the burned gas and small normal flame speed, assuming the channel to be wide enough, the problem transpires to be closely related to the classical Rayleigh-Taylor problem for a long bubble rising through a vertical tube. The important distinction between the two systems occurs near the channel walls where the flame interface acquires a long skirt. The skirt length is found to be inversely proportional to the normal flame speed. Similar to the Rayleigh-Taylor problem there is a one-parameter family of propagation modes. The multiplicity is resolved by a natural selection principle.