Rayleigh-Benard Convection in Large-Aspect-Ratio Domains
by
Mark Paul
California Institute of Technology

Pattern formation in an extended, driven, and far-from-equilibrium system is studied by performing large scale numerical simulations of Rayleigh-Benard Convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. The coarsening of striped states, originating from initial random thermal perturbations, are explored and various diagnostic measures and correlation lengths are used to quantify the pattern dynamics. Our results indicate the presence of at least two length scales as the domains of stripes become larger. The contrast with our results and with what is seen in equilibrium or undriven systems (such as the cylindrical block copolymer work) are also discussed. Lastly, the pattern selection process, or wavenumber selection, in Rayleigh-Benard has received much attention over the years and many wavenumber selection mechanisms have been identified. However, the wavenumber selected in a large aspect ratio system is still not yet fully understood. Our results suggest that in large aspect ratios the pattern selects the wavenumber at which isolated dislocations become motionless and the implications of this are discussed.

Date received: October 27, 2003