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Patterns in rotating Rayleigh–Bénard convection at high rotation rates

Published online by Cambridge University Press:  30 June 2010

J. D. SCHEEL ,
P. L. MUTYABA  and
T. KIMMEL
J. D. SCHEEL*
Affiliation:
Department of Physics, Occidental College, 1600 Campus Road, M21, Los Angeles, CA 90041, USA
P. L. MUTYABA
Affiliation:
Department of Physics, California Lutheran University, 3750, Thousand Oaks, CA 91360, USA
T. KIMMEL
Affiliation:
Department of Physics, California Lutheran University, 3750, Thousand Oaks, CA 91360, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present the results from numerical and theoretical investigations of rotating Rayleigh–Bénard convection for relatively large dimensionless rotation rates, 170 < Ω < 274, and a Prandtl number of 6.4. Unexpected square patterns were found experimentally by Bajaj et al. (Phys. Rev. Lett., vol. 81, 1998, p. 806) in this parameter regime and near threshold for instability in the bulk. These square patterns have not yet been understood theoretically. Sánchez-Álvarez et al. (Phys. Rev. E, vol. 72, 2005, p. 036307) have found square patterns in numerical simulations for similar parameters when only the Coriolis force is included. We performed detailed numerical studies of rotating Rayleigh–Bénard convection for the same parameters as the experiments and simulations. To better understand these patterns, we compared the effects of the Coriolis force as well as the centrifugal force. We also computed the coefficients of the amplitude equation describing one-, two- and three-mode bulk solutions to rotating Rayleigh–Bénard convection. We find that squares are unstable, but we do find stable limit cycles consisting of three coupled oscillating amplitudes, which can superficially resemble squares, since one of the three amplitudes is rather small.

JFM classification

Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 659 , 25 September 2010 , pp. 24 - 42
Copyright
Copyright © Cambridge University Press 2010

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References

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