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Rayleigh-Benard convection in elliptic and stadium-shaped containers Worawat Meevasana and Guenter Ahlers
 

Summary: Rayleigh-BeŽnard convection in elliptic and stadium-shaped containers
Worawat Meevasana and Guenter Ahlers
Department of Physics and iQUEST, University of California, Santa Barbara, California 93106
Received 20 June 2002; published 30 October 2002
We report on defect formation in convection patterns of stadium-shaped and elliptical horizontal layers of
fluid heated from below Rayleigh-BeŽnard convection . The fluid was ethanol with a Prandtl number
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 i Di/2d, i 1, 2 (Di 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 Ls 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 Ls
decreased with increasing T/ Tc 1, consistent with a prediction for wave-number selection by curved
rolls in an infinite system. At large , 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

  

Source: Ahlers, Guenter - Department of Physics, University of California at Santa Barbara

 

Collections: Physics