Oscillations and spatiotemporal chaos of one-dimensional fluid fronts

Abstract

The bifurcations to time-dependent and chaotic one-dimensional fluid fronts are investigated in the flow of a fluid inside a partially filled rotating horizontal cylinder. A primary cellular pattern undergoes a variety of secondary transitions, depending on the filling fraction. We document three types of transitions to time dependence which are shown to be qualitatively distinct by space-time Fourier analysis. We focus particularly on a highly symmetric transition to spatially subharmonic oscillations that is well represented by model equations. A subsequent transition of the oscillatory state to spatiotemporal chaos is explored quantitatively through the use of spectral analysis and complex demodulation to extract slowly varying amplitudes and phases. Many features of this chaotic state are at least qualitatively described by the model, including propagating compressions that are related to a locally depressed 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 this method is shown to work well for numerically generated data, experimental noise limits its use with experimental data.