Quantifying Spatio-Temporal Chaos in Rayleigh Bénard Convection

Abstract

In this project Rayleigh Bénard convection (RBC) in a cylindrical domain with experimentally realistic boundaries was investigated numerically. The results were obtained using large-scale parallel calculations. The flow field was determined as well as its linearized solutions in order to obtain Lyapunov diagnostics. The emphasis is on the effects that the domain size Γ (gamma) has on the system dynamics (Γ = radius/depth for a cylindrical domain). Temperature fields were viewed for different Γ's) and a transition to spiral defect chaos was observed for large Γ's. The temperature and thermal perturbation fields were inspected for Γ = 10 and large perturbations were found to be very localized and caused by small defects in the temperature field. The azimuthal average of thermal perturbations indicate that the perturbations are largest at the boundaries for small domains and largest at the center for large domains. This suggests that small to intermediate aspect ratio RBC should not be thought of as a set of weakly correlated regions in space. The leading order Lyapunov exponent was positive over a range of conditions indicating that the system is truly chaotic. The fractal dimension was calculated for several domain sizes and the system was found to be extensive even though the system dynamics change significantly.