OSCILLATIONS AND SPATIOTEMPORAL CHAOS OF ONE-DIMENSIONAL FLUID FRONTS

The bifurcations to time-dependent and chaotic one-dimensional fluid f ronts are investigated in the flow of a fluid inside a partially rotat ing horizontal cylinder. A primary cellular pattern undergoes a variet y of secondary transitions, depending on the filling fraction. We docu ment three types of transitions to time dependence which are shown to be qualitatively distinct by space-time Fourier analysis. We focus par ticularly on a highly symmetric transition to spatially subharmonic os cillations that is well represented by model equations. A subsequent t ransition of the oscillatory state to spatiotemporal chaos is explored quantitatively through the use of spectral analysis and complex demod ulation to extract slowly varying amplitudes and phases. Many features of this chaotic state are at least qualitatively described by the mod el, including propagating compressions that are related to a locally d epressed amplitude of oscillation. We are able to measure some of the parameters of the model directly. We also attempt to determine all of them by a least squares fitting method in the chaotic regime. Though t his method is shown to work well for numerically generated data, exper imental noise limits its use with experimental data.