Flame Propagation in Channels: Secondary Bifurcation to Quasi-Periodic Pulsations

We consider premixed flame propagation in long rectangular channels. 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. We analyze the problem in a neighborhood of a multiple primary bifurcation point. By varying the channel dimensions, we split the multiple bifurcation point and show that a stable quasi-periodic pulsating flame can arise as a secondary bifurcation from one of the primary bifurcation states. We also exhibit the phenomenon of mode-jumping, in which there is an exchange of stability between two primary states.