Ratcheting Motion of Concentric Rings in Cellular Flames

Ordered states of cellular flames consist of concentric rings of luminous cells. These states are observed to bifurcate to ratcheting states in which one or more rings drift $(\sim 1\mathrm{deg}/\sec )$ in a circular path, speeding up and slowing down in a characteristic manner. Experimental results from three ratcheting states are presented: one in which two rings of cells ratchet together; one in which an outer ring ratchets, locked with the inner ring through an angle, until the inner ring unlocks and snaps back to its original position; and one in which an outer ring ratchets and an inner ring remains fixed. These results are discussed in the context of bifurcations in symmetric systems.