Karhunen-Loève analysis of spatiotemporal flame patterns

The ability of Karhunen-Loève ~KL! decomposition to identify, extract, and separate the spatial features that characterize a spatiotemporal system is demonstrated using video images from a combustion experiment and nonstationary states from a phenomenological model. Cellular flames on a circular porous plug burner exhibit a variety of stationary and nonstationary patterns. KL decomposition is used to analyze the spatiotemporal dynamics of four experimental states: oneand two-cell rotating states, two counterrotating rings, a standingwave state, and two one-cell rotating states from numerical simulations of a phenomenological model designed to study pattern formation in a circular domain. The KL technique optimally captures the dynamics of the states by producing a linear subspace on which the reconstructed dynamics has a minimum truncation error. It identifies the dominant spatial structures whose coupling produces the observed patterns and distinguishes between uniform and nonuniform rotational motion. The implementation of this technique using video images as input is explained and the implications of symmetry in interpreting the KL analysis of the dynamics are described. @S1063-651X~98!07105-0#