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Tristable flow states and reversal of the large-scale circulation in two-dimensional circular convection cells

Published online by Cambridge University Press:  15 January 2021

Ao Xu Open the ORCID record for Ao Xu [Opens in a new window] ,
Xin Chen Open the ORCID record for Xin Chen [Opens in a new window]  and
Heng-Dong Xi Open the ORCID record for Heng-Dong Xi [Opens in a new window]
Ao Xu
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
Xin Chen
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
Heng-Dong Xi*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi'an 710072, PR China
*
†Email address for correspondence: [email protected]
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Abstract

We present a numerical study of the flow states and reversals of the large-scale circulation (LSC) in a two-dimensional circular Rayleigh–Bénard cell. Long-time direct numerical simulations are carried out in the Rayleigh number ($Ra$) range $10^{7} \leqslant Ra \leqslant 10^{8}$ and Prandtl number ($Pr$) range $2.0 \leqslant Pr \leqslant 20.0$. We found that a new, long-lived, chaotic flow state exists, in addition to the commonly observed circulation states (the LSC in the clockwise and counterclockwise directions). The circulation states consist of one primary roll in the middle and two secondary rolls near the top and bottom circular walls. The primary roll becomes stronger and larger, while the two secondary rolls diminish, with increasing $Ra$. Our results suggest that the reversal of the LSC is accompanied by the secondary rolls growing, breaking the primary roll and then connecting to form a new primary roll with reversed direction. We mapped out the phase diagram of the existence of the LSC and the reversal in the $Ra\text{--}Pr$ space, which reveals that the flow is in the circulation states when $Ra$ is large and $Pr$ is small. The reversal of the LSC can only occur in a limited $Pr$ range. The phase diagram can be understood in terms of competition between the thermal and viscous diffusions. We also found that the internal flow states manifested themselves into global properties such as Nusselt and Reynolds numbers.

JFM classification

Convection: Plumes/thermals Turbulent Flows: Turbulent convection
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JFM Papers
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Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A33
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© The Author(s), 2021. Published by Cambridge University Press

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