Structure and dynamics of Modulated Traveling Waves in cellular flames

We describe the formation and evolution of spatial and temporal patterns in cylindrical premixed flames. We consider the cellular regime, Le < 1, where the Lewis number Le is the ratio of thermal to mass diffusivity of a deficient component of the combustible mixture. A transition from stationary, axisymmetric flames to stationary cellular flames is predicted analytically if Le is decreased below a critical value. We present the results of numerical computations to show that as Le is further decreased, with all other parameters fixed, traveling waves (TWs) along the flame front arise via an infinite-period bifurcation which breaks the reflection symmetry of the cellular array. Upon further decreasing Le we find the development of different kinds of periodically modulated traveling waves (MTWs) as well as a branch of quasiperiodically modulated traveling waves (QPMTWs). These transitions are accompanied by the development of different spatial and temporal symmetries including period doublings and period halvings in appropriate coordinate systems. We also observe the apparently chaotic temporal behavior of 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 framework one of the MTWs can be identified as a localized wave traveling through an underlying stationary, spatially periodic structure.