FLAME PROPAGATION IN CHANNELS: SECONDARY BIFURCATION TO QUASI-PERIODIC PULSATIONS.

Premixed flame propagation in long rectangular channels is considered. A steadily propagating planar flame is stable for Lewis numbers less than a critical value. For Lewis numbers exceeding this critical value a sequence of primary bifurcation states, corresponding to time-periodic pulsating cellular flames, emanates from the steadily propagating solution. The problem is analyzed in a neighborhood of a multiple primary bifurcation point. By varying the channel dimensions, the multiple bifurcation point is split, and it is shown that a stable quasi-periodic pulsating flame can arise as a secondary bifurcation from one of the primary bifurcation states. The phenomenon of mode-jumping, in which there is an exchange of stability between two primary states, is also exhibited.