CONVECTION NEAR-THRESHOLD FOR PRANDTL NUMBERS NEAR 1

Rayleigh-Benard convection in two cylindrical geometries with different sidewalls and with radius-to-height ratios Gamma=41 and 43 was studied with shadowgraph imaging and heat-transport measurements. The working fluid was CO2 at 25.3 bar with a Prandtl number sigma=0.93. For one of the cells (Gamma=43), axisymmetric convection rolls were stable above onset up to epsilon=Delta T/Delta T-c -1=0.19, where Delta T-c is the critical temperature difference. The amplitude of the center of the concentric patterns, the umbilicus, much larger near onset than that of the outlying region, grew as epsilon(beta 1), with beta(1) =O.27+/-0.04. Outside the umbilicus, the amplitude grew as epsilon(beta 2), with beta(2)=0.48+/-0.04. For Gamma=41, axisymmetric convection rolls, coexisting with an annular cross-roll state confined near the sidewall, were the preferred patterns above onset and remained stable up to an epsilon of 0.08. The umbilicus of the concentric convection pattern shifted slightly off center as epsilon was increased, but the shift never exceeded 50% of the cell depth. For epsilon > 0. 10, the patterns were unstable and evolved over many horizontal thermal diffusion times to straight-roll patterns with defects and grain boundaries. The process involved the umbilicus moving toward the sidewall, accompanied by radially traveling waves emitted by the umbilicus. While the umbilicus emitted, the crossrolls adjacent to the sidewall traveled parallel to the wan, and rolls were created and destroyed at a source and sink, respectively, presumably owing to large-scale flows generated by the off-centered position of the umbilicus.