The rotor-oscillator flow : searching for coherence amidst chaos

Abstract

Chaotic mixing of highly viscous fluids is common in many biological and industrial processes. This study aims to gain insight about the properties of such common processes by examining one particular case of viscous, chaotic mixing: the rotor-oscillator flow. For some couplings of the rotor motion with its oscillation, this flow has been shown to have coherent islands of fluid parcels surrounded by a sea of chaos. Through finite-time Lyapunov exponent (FTLE) analysis, a roughly optimal coupling was found. The parameters that describe this coupling are the nondimensional oscillation amplitude [epsilon] = 0.125 and frequency [lambda] = 0.4[pi]. In order to understand more about the mixing of slow-moving, highly viscous fluids, these values can and will be explored experimentally and through braid theory to further examine the regions of coherence in this generally chaotic flow.