STRUCTURE AND DYNAMICS OF MODULATED TRAVELING WAVES IN CELLULAR FLAMES

We describe the formation and evolution of spatial and temporal patter ns in cylindrical premixed flames. We consider the cellular regime, Le < 1, where the Lewis number Le is the ratio of thermal to mass diffus ivity of a deficient component of the combustible mixture. A transitio n from stationary, axisymmetric flames to stationary cellular flames i s predicted analytically if Le is decreased below a critical value. We present the results of numerical computations to show that as Le is f urther decreased, with all other parameters fixed, traveling waves (TW s) along the flame front arise via an infinite-period bifurcation whic h breaks the reflection symmetry of the cellular array. Upon further d ecreasing Le we find the development of different kinds of periodicall y modulated traveling waves (MTWs) as well as a branch of quasiperiodi cally modulated traveling waves (QPMTWs). These transitions are accomp anied by the development of different spatial and temporal symmetries including period doublings and period halvings in appropriate coordina te systems. We also observe the apparently chaotic temporal behavior o f a disordered cellular pattern involving creation and annihilation of cells. We analytically describe the stability of the TW solution near its onset using suitable phase-amplitude equations. Within this frame work one of the MTWs can be identified as a localized wave traveling t hrough an underlying stationary, spatially periodic structure.