scholarly journals Rayleigh–Bénard convection in non-Newtonian fluids: Experimental and theoretical investigations

2021 ◽  
Vol 33 (11) ◽  
pp. 114112
Author(s):  
Mondher Bouteraa ◽  
Thomas Varé ◽  
Chérif Nouar ◽  
Simon Becker ◽  
Jamal Ouhajjou
Keyword(s):  
Newtonian Fluids ◽  
Bénard Convection ◽  
Benard Convection ◽  
Theoretical Investigations ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Patterns in rotating Rayleigh–Bénard convection at high rotation rates

2010 ◽  
Vol 659 ◽  
pp. 24-42 ◽  
Author(s):  
J. D. SCHEEL ◽  
P. L. MUTYABA ◽  
T. KIMMEL
Keyword(s):  
Coriolis Force ◽  
Stable Limit ◽  
Rotation Rates ◽  
Numerical Studies ◽  
Bénard Convection ◽  
Benard Convection ◽  
Theoretical Investigations ◽  
Rayleigh Benard Convection ◽  
Bulk Solutions ◽  
Rayleigh Benard

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.

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