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Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns

Published online by Cambridge University Press:  10 May 2018

Jonathan M. Aurnou Open the ORCID record for Jonathan M. Aurnou [Opens in a new window] ,
Vincent Bertin ,
Alexander M. Grannan ,
Susanne Horn Open the ORCID record for Susanne Horn [Opens in a new window]  and
Tobias Vogt
Jonathan M. Aurnou*
Affiliation:
Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, CA 90095, USA
Vincent Bertin
Affiliation:
Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, CA 90095, USA Department of Physics, École Normale Supérieure, Paris, France
Alexander M. Grannan
Affiliation:
Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, CA 90095, USA
Susanne Horn
Affiliation:
Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, CA 90095, USA
Tobias Vogt
Affiliation:
Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, PO Box 510119, 01314 Dresden, Germany
*
†Email address for correspondence: aurnou@ucla.edu
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Abstract

Earth’s magnetic field is generated by convective motions in its liquid metal core. In this fluid, the heat diffuses significantly more than momentum, and thus the Prandtl number $Pr$ is well below unity. The thermally driven convective flow dynamics of liquid metals are very different from moderate-$Pr$ fluids, such as water and those used in current dynamo simulations. In order to characterise rapidly rotating thermal convection in low-$Pr$ number fluids, we have performed laboratory experiments in a cylinder of aspect ratio $\unicode[STIX]{x1D6E4}=1.94$ using liquid gallium ($Pr\simeq 0.025$ ) as the working fluid. The Ekman number varies from $E\simeq 5\times 10^{-6}$ to $5\times 10^{-5}$ and the Rayleigh number varies from $Ra\simeq 2\times 10^{5}$ to $1.5\times 10^{7}$ . Using spectral analysis stemming from point-wise temperature measurements within the fluid and measurements of the Nusselt number $Nu$ , we characterise the different styles of low-$Pr$ rotating convective flow. The convection threshold is first overcome in the form of container-scale inertial oscillatory modes. At stronger forcing, sidewall-attached modes are identified for the first time in liquid metal laboratory experiments. These wall modes coexist with the bulk oscillatory modes. At $Ra$ well below the values where steady rotating columnar convection occurs, the bulk flow becomes turbulent. Our results imply that rotating convective flows in liquid metals do not develop in the form of quasisteady columns, as in moderate-$Pr$ fluids, but in the form of oscillatory convective motions. Thus, thermally driven flows in low-$Pr$ geophysical and astrophysical fluids can differ substantively from those occurring in $Pr\simeq 1$ models. Furthermore, our experimental results show that relatively low-frequency wall modes are an essential dynamical component of rapidly rotating convection in liquid metals.

JFM classification

Geophysical and Geological Flows: Geodynamo Geophysical and Geological Flows: Rotating flows

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JFM Papers
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Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 846 - 876
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© 2018 Cambridge University Press 

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