Paul, M. R. and Cross, M. C. and Fischer, P. F. (2002) Rayleigh-Bénard convection with a radial ramp in plate separation. Physical Review E, 66 (4). Art. No. 046210. ISSN 1063-651X http://resolver.caltech.edu/CaltechAUTHORS:PAUpre02
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Pattern formation in Rayleigh-Bénard convection in a large-aspect-ratio cylinder with a radial ramp in the plate separation is studied analytically and numerically by performing numerical simulations of the Boussinesq equations. A horizontal mean flow and a vertical large scale counterflow are quantified and used to understand the pattern wave number. Our results suggest that the mean flow, generated by amplitude gradients, plays an important role in the roll compression observed as the control parameter is increased. Near threshold, the mean flow has a quadrupole dependence with a single vortex in each quadrant while away from threshold the mean flow exhibits an octupole dependence with a counterrotating pair of vortices in each quadrant. This is confirmed analytically using the amplitude equation and Cross-Newell mean flow equation. By performing numerical experiments, the large scale counterflow is also found to aid in the roll compression away from threshold but to a much lesser degree. Our results yield an understanding of the pattern wave numbers observed in experiment away from threshold and suggest that near threshold the mean flow and large scale counterflow are not responsible for the observed shift to smaller than critical wave numbers.
|Additional Information:||©2002 The American Physical Society. Received 28 May 2002; published 21 October 2002. We are grateful to H. S. Greenside and G. Ahlers for helpful discussions. This research was supported by the US Department of Energy, Grant No. DE-FT02-98ER14892, and the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, US Department of Energy, under Contract No. W-31-109-Eng-38. We also acknowledge the Caltech Center for Advanced Computing Research and the North Carolina Supercomputing Center.|
|Subject Keywords:||SPIRAL DEFECT CHAOS; WAVENUMBER SELECTION; WAVELENGTH SELECTION; PATTERN SELECTION; THRESHOLD; DYNAMICS; NUMBERS; EQUILIBRIUM; EQUATIONS; BEHAVIOR|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Lindsay Cleary|
|Deposited On:||09 Oct 2006|
|Last Modified:||26 Dec 2012 09:04|
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