Type of Document Master's Thesis Author Einarsson, Magnus Ingi Author's Email Address email@example.com URN etd-08062006-143058 Title Quantifying Spatio-Temporal Chaos in Rayleigh Benard Convection Degree Master of Science Department Mechanical Engineering Advisory Committee
Advisor Name Title Paul, Mark R. Committee Chair Tafti, Danesh K. Committee Member Vick, Brian L. Committee Member Keywords
- microextensive chaos
Date of Defense 2006-07-26 Availability unrestricted AbstractIn this project Rayleigh Benard 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 (gamma) has on the system dynamics (gamma = radius/depth for a cylindrical domain). Temperature fields were viewed for different gamma's and a transition to spiral defect chaos was observed for large gamma's. The temperature and thermal perturbation fields were inspected for gamma = 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.
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