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Dynamics of the large-scale circulation in high-Prandtl-number turbulent thermal convection

Published online by Cambridge University Press:  01 February 2013

Yi-Chao Xie ,
Ping Wei  and
Ke-Qing Xia
Yi-Chao Xie
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
Ping Wei
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
Ke-Qing Xia*
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
*
†Email address for correspondence: [email protected]
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Abstract

We report experimental investigations of the dynamics of the large-scale circulation (LSC) in turbulent Rayleigh–Bénard convection at high Prandtl number $\mathit{Pr}= 19. 4$ (and also $\mathit{Pr}= 7. 8$) and Rayleigh number $\mathit{Ra}$ varying from $8. 3\times 1{0}^{8} $ to $2. 9\times 1{0}^{11} $ in a cylindrical convection cell with aspect ratio unity. The dynamics of the LSC is measured using the multithermal probe technique. Both the sinusoidal-fitting (SF) and the temperature-extrema-extraction (TEE) methods are used to analyse the properties of the LSC. It is found that the LSC in high-$\mathit{Pr}$ regime remains a single-roll structure. The azimuthal motion of the LSC is a diffusive process, which is the same as those for $\mathit{Pr}$ around 1. However, the azimuthal diffusion of the LSC, characterized by the angular speed $\Omega $ is almost two orders of magnitude smaller when compared with that in water. The non-dimensional time-averaged amplitude of the angular speed $\langle \vert \Omega \vert \rangle {T}_{d} $ (${T}_{d} = {L}^{2} / \kappa $ is the thermal diffusion time) of the LSC at the mid-height of the convection cell increases with $\mathit{Ra}$ as a power law, which is $\langle \vert \Omega \vert \rangle {T}_{d} \propto {\mathit{Ra}}^{0. 36\pm 0. 01} $. The $\mathit{Re}$ number based on the oscillation frequency of the LSC is found to scale with $\mathit{Ra}$ as $\mathit{Re}= 0. 13{\mathit{Ra}}^{0. 43\pm 0. 01} $. It is also found that the normalized flow strength $\langle \delta \rangle / \mrm{\Delta} T\times \mathit{Ra}/ \mathit{Pr}\propto {\mathit{Re}}^{1. 5\pm 0. 1} $, with the exponent in good agreement with that predicted by Brown & Ahlers (Phys. Fluids, vol. 20, 2008, p. 075101). A wealth of dynamical features of the LSC, such as the cessations, flow reversals, flow mode transitions, torsional and sloshing oscillations are observed in the high-$\mathit{Pr}$ regime as well.

JFM classification

Convection: Plumes/thermals Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 717 , 25 February 2013 , pp. 322 - 346
Copyright
©2013 Cambridge University Press

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