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Scaling behaviour of small-scale dynamos driven by Rayleigh–Bénard convection

Published online by Cambridge University Press:  09 March 2021

M. Yan Open the ORCID record for M. Yan [Opens in a new window] ,
S.M. Tobias Open the ORCID record for S.M. Tobias [Opens in a new window]  and
M.A. Calkins
M. Yan*
Affiliation:
Department of Physics, University of Colorado, Boulder, CO80309, USA
S.M. Tobias
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
M.A. Calkins
Affiliation:
Department of Physics, University of Colorado, Boulder, CO80309, USA
*
†Email address for correspondence: ming.yan@colorado.edu
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Abstract

A numerical investigation of convection-driven dynamos is carried out in the plane layer geometry. Dynamos with different magnetic Prandtl numbers $Pm$ are simulated over a broad range of the Rayleigh number $Ra$. The heat transport, as characterized by the Nusselt number $Nu$, shows an initial departure from the heat transport scaling of non-magnetic Rayleigh–Bénard convection (RBC) as the magnetic field grows in magnitude; as $Ra$ is increased further, the data suggest that $Nu$ grows approximately as $Ra^{2/7}$, but with a smaller prefactor in comparison with RBC. Viscous ($\epsilon _u$) and ohmic ($\epsilon _B$) dissipation contribute approximately equally to $Nu$ at the highest $Ra$ investigated; both ohmic and viscous dissipation approach a Reynolds-number-dependent scaling of the form $Re^a$, where $a \approx 2.8$. The ratio of magnetic to kinetic energy approaches a $Pm$-dependent constant as $Ra$ is increased, with the constant value increasing with $Pm$. The ohmic dissipation length scale depends on $Ra$ in such a way that it is always smaller, and decreases more rapidly with increasing $Ra$, than the viscous dissipation length scale for all investigated values of $Pm$.

JFM classification

MHD and Electrohydrodynamics: Dynamo theory MHD and Electrohydrodynamics: Magneto convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A15
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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