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Reynolds number scaling in cryogenic turbulent Rayleigh–Bénard convection in a cylindrical aspect ratio one cell

Published online by Cambridge University Press:  26 October 2017

Věra Musilová Open the ORCID record for Věra Musilová [Opens in a new window] ,
Tomáš Králík ,
Marco La Mantia Open the ORCID record for Marco La Mantia [Opens in a new window] ,
Michal Macek ,
Pavel Urban  and
Ladislav Skrbek
Věra Musilová*
Affiliation:
The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, Brno, Czech Republic
Tomáš Králík
Affiliation:
The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, Brno, Czech Republic
Marco La Mantia
Affiliation:
Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague, Czech Republic
Michal Macek
Affiliation:
The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, Brno, Czech Republic
Pavel Urban
Affiliation:
The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, Brno, Czech Republic
Ladislav Skrbek
Affiliation:
Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague, Czech Republic
*
†Email address for correspondence: vera@isibrno.cz
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Abstract

We perform an experimental study of turbulent Rayleigh–Bénard convection up to very high Rayleigh number, $10^{8}<Ra<10^{14}$, in a cylindrical aspect ratio one cell, 30 cm in height, filled with cryogenic helium gas. We monitor temperature fluctuations in the convective flow with four small (0.2 mm) sensors positioned in pairs 1.5 cm from the sidewalls and 2.5 cm vertically apart and symmetrically around the mid-height of the cell. Based on one-point and two-point correlations of the temperature fluctuations, we determine different types of Reynolds numbers, $\mathit{Re}$, associated with the large-scale circulation (LSC). We observe a transition between two types of $\mathit{Re}(\mathit{Ra})$ scaling around $\mathit{Ra}=10^{10}{-}10^{11}$, which is accompanied by a scaling change of the skewness of the probability distribution functions (PDFs) of the temperature fluctuations. The $\mathit{Re}(\mathit{Ra})$ dependencies measured near the sidewall at Prandtl number $\mathit{Pr}\sim 1$ are consistent with the $\mathit{Ra}^{4/9}\mathit{Pr}^{-2/3}$ scaling above the transition, while for $\mathit{Ra}<10^{10}$, the $\mathit{Re}(\mathit{Ra})$ dependencies are steeper. It seems likely that this change in $\mathit{Re}(\mathit{Ra})$ scaling is linked to the previously reported change in the Nusselt number $\mathit{Nu}(\mathit{Ra})$ scaling. This behaviour is in agreement with independent cryogenic laboratory experiments with $\mathit{Pr}\sim 1$, but markedly different from the $\mathit{Re}$ scaling obtained in water experiments ($\mathit{Pr}\sim 3.3{-}5.6$). We discuss the results in comparison with different versions of the Grossmann–Lohse theory.

JFM classification

Turbulent Flows: Turbulent convection Turbulent Flows: Turbulent Flows
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Papers
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Journal of Fluid Mechanics , Volume 832 , 10 December 2017 , pp. 721 - 744
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© 2017 Cambridge University Press 

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