Patterns in rotating Rayleigh–B´enard convection at high rotation rates
Loading...
Date
2010-06-30
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Journal of fluid mechanics
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.
Description
Keywords
Citation
Scheel, J. D., Mutyaba, P. L., & Kimmel, T. (2010). Patterns in rotating Rayleigh–Bénard convection at high rotation rates. Journal of fluid mechanics, 659, 24-42.