Modal decomposition of hopping states in cellular flames

We use Karhunen-Loeve (KL) decomposition of video images from an experiment to analyze a spatiotemporal dynamic state, unique to cellular flames, refe rred to as a "hopping state." Ordered states of cellular flames on a circul ar burner consist of one or two concentric rings of luminous cells. The hop ping states correspond to the motions of individual cells in a ring sequent ially executing abrupt changes in their angular position, while the other c ells in the ring remain symmetric and at rest. KL decomposition separates t he spatial and temporal characteristics of the hopping motion. The underlyi ng symmetries of the experiment allow us to deduce a set of normal form equ ations that describe the formation of these states. We find that they resul t from secondary bifurcations connecting two primary branches of traveling waves. The solutions corresponding to hopping states exist as mixed-mode so lutions away from the secondary bifurcations. (C) 1999 American Institute o f Physics. [S1054-1500(99)02503-3].