Rayleigh-Bénard convection in elliptic and stadium-shaped containers

We report on defect formation in convection patterns of stadium-shaped and elliptical horizontal layers of fluid heated from below (Rayleigh-Bénard convection). The fluid was ethanol with a Prandtl number sigma=14.2. The outermost convection roll was forced to be parallel to the sidewall by a supplementary wall heater. The major- and minor-axis aspect ratios Gamma(i)=D(i)/2d, i=1, 2 (D(i) are the major and minor diameter and d the thickness) were 19.4 and 13.0, respectively. For the stadium shape, we found a stable pattern that was reflection-symmetric about the major diameter and had a downflow roll of length L(s) along a large part of this diameter. This roll terminated in two convex disclinations, as expected from theory. No other patterns with the outermost roll parallel to the sidewall were found. The wave numbers of the rolls in the curved sections and L(s) decreased with increasing epsilon identical with DeltaT/DeltaT(c)-1, consistent with a prediction for wave-number selection by curved rolls in an infinite system. At large epsilon, the roll adjacent to the sidewall became unstable due to the cross-roll instability. For the elliptical shape, wave-director frustration yielded a new defect structure predicted by Ercolani et al. Depending on the sample history, three different patterns with the outermost roll parallel to the wall were found. For one, the central downflow roll seen in the stadium was shortened to the point where it resembled a single convection cell. Along much of the major diameter there existed an upflow roll. The new defect structure occurred where the two downflow rolls surrounding the central upflow roll joined. This joint, instead of being smooth as in the stadium case, was angular and created a protuberance pointing outward along the major diameter. We also found a pattern with an upflow roll along the major diameter without the central downflow cell. A third pattern contained a downflow cell, but this cell was displaced by a roll width from the center along a minor diameter. As epsilon increased, the length L(e) between the two protuberances and the wave numbers along the outer parts of the major diameter decreased for all three patterns, analogous to what was found for the stadium. The upper stability limit of these patterns was also set by the cross-roll instability.