Pattern formation in a rotating coating flow

Highly symmetric patterns form spontaneously in a one-dimensional front of fluid inside a rotating horizontal cylinder (rimming flow). The stability and evolution of these patterns can be understood in part by comparing them to generic models of bifurcations from highly ordered states. The range of behavior which has been documented in parameter space is extended beyond previous studies of rimming flow. Several important highly symmetric bifurcations are investigated, including a cellular instability of a flat front (primary bifurcation), and a number of secondary bifurcations of this cellular state. A novel spatially subharmonic oscillatory bifurcation of the cellular pattern is observed, which undergoes a subsequent transition to spatiotemporal chaos as the bifurcation parameter is increased. This transition is characterized through comparison with amplitude equations derived from symmetry. A battery of experiments measure several of the coefficients in the equations independently. In addition, a least squares method is presented that attempts to determine the appropriate coefficients by directly fitting the equations to the chaotic state. This fitting method is successful on synthetic data, but implementation to experimental data does not yet yield satisfactory results. The transition to chaos is characterized further using standard statistical tests. Three distinct chaotic states are presented and compared