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Transition to the ultimate regime in a radiatively driven convection experiment

Published online by Cambridge University Press:  04 January 2019

Vincent Bouillaut ,
Simon Lepot ,
Sébastien Aumaître  and
Basile Gallet Open the ORCID record for Basile Gallet [Opens in a new window]
Vincent Bouillaut
Affiliation:
Service de Physique de l’État Condensé, CEA, CNRS UMR 3680, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
Simon Lepot
Affiliation:
Service de Physique de l’État Condensé, CEA, CNRS UMR 3680, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
Sébastien Aumaître
Affiliation:
Service de Physique de l’État Condensé, CEA, CNRS UMR 3680, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
Basile Gallet*
Affiliation:
Service de Physique de l’État Condensé, CEA, CNRS UMR 3680, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France
*
†Email address for correspondence: [email protected]
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Abstract

We report on the transition between two regimes of heat transport in a radiatively driven convection experiment, where a fluid gets heated up within a tunable heating length $\ell$ in the vicinity of the bottom of the tank. The first regime is similar to that observed in standard Rayleigh–Bénard experiments, the Nusselt number $Nu$ being related to the Rayleigh number $Ra$ through the power law $Nu\sim Ra^{1/3}$. The second regime corresponds to the ‘ultimate’ or mixing-length scaling regime of thermal convection, where $Nu$ varies as the square root of $Ra$. Evidence for these two scaling regimes has been reported in Lepot et al. (Proc. Natl Acad. Sci. USA, vol. 115, 2018, pp. 8937–8941), and we now study in detail how the system transitions from one to the other. We propose a simple model describing radiatively driven convection in the mixing-length regime. It leads to the scaling relation $Nu\sim (\ell /H)Pr^{1/2}Ra^{1/2}$, where $H$ is the height of the cell and $Pr$ is the Prandtl number, thereby allowing us to deduce the values of $Ra$ and $Nu$ at which the system transitions from one regime to the other. These predictions are confirmed by the experimental data gathered at various $Ra$ and $\ell$. We conclude by showing that boundary layer corrections can persistently modify the Prandtl number dependence of $Nu$ at large $Ra$, for $Pr\gtrsim 1$.

JFM classification

Turbulent Flows: Turbulent convection
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , R5
Copyright
© 2019 Cambridge University Press 

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