Pattern formation and wave-number selection by Rayleigh-Benard convection in a cylindrical container

Rayleigh-Benard convection in a cylindrical layer of water with radius/height ratio L = 7.5 and Prandtl number sigma = 6.1 is investigated experimentally, using direct heat-transfer measurements (at resolution 0.1 percent) and computer-enhanced shadowgraph visualizations to observe the evolution of patterns and wave numbers (k) at values of epsilon = R/Rc - 1 (where R and Rc are the Rayleigh number and the critical Rayleigh number, respectively) as low as 0.01. The results are presented in graphs, diagrams, and flow patterns and characterized. When heating from below is increased to a supercritical level, cylindrical flow patterns due to dynamic sidewall forcing are observed and found to be stable for epsilon = 0.16-8.0, with a discontinuous decrease (by hysteretic changes) in k and a loss of cylindrical symmetry as epsilon is increased. At epsilon less than 0.16, the same k adjustment process is found, but the cylindrical patterns decay to defective rolls perpendicular to the sidewalls which persist even when epsilon is subsequently increased.