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Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field

Published online by Cambridge University Press:  02 September 2019

Ming Yan Open the ORCID record for Ming Yan [Opens in a new window] ,
Michael A. Calkins ,
Stefano Maffei ,
Keith Julien ,
Steven M. Tobias Open the ORCID record for Steven M. Tobias [Opens in a new window]  and
Philippe Marti
Ming Yan*
Affiliation:
Department of Physics, University of Colorado, Boulder, CO 80309, USA
Michael A. Calkins
Affiliation:
Department of Physics, University of Colorado, Boulder, CO 80309, USA
Stefano Maffei
Affiliation:
Department of Physics, University of Colorado, Boulder, CO 80309, USA
Keith Julien
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA
Steven M. Tobias
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Philippe Marti
Affiliation:
Department of Earth Science, ETH Zurich, 8092 Zurich, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

Numerical simulations of quasi-static magnetoconvection with a vertical magnetic field are carried out up to a Chandrasekhar number of $Q=10^{8}$ over a broad range of Rayleigh numbers $Ra$. Three magnetoconvection regimes are identified: two of the regimes are magnetically constrained in the sense that a leading-order balance exists between the Lorentz and buoyancy forces, whereas the third regime is characterized by unbalanced dynamics that is similar to non-magnetic convection. Each regime is distinguished by flow morphology, momentum and heat equation balances, and heat transport behaviour. One of the magnetically constrained regimes appears to represent an ‘ultimate’ magnetoconvection regime in the dual limit of asymptotically large buoyancy forcing and magnetic field strength; this regime is characterized by an interconnected network of anisotropic, spatially localized fluid columns aligned with the direction of the imposed magnetic field that remain quasi-laminar despite having large flow speeds. As for non-magnetic convection, heat transport is controlled primarily by the thermal boundary layer. Empirically, the scaling of the heat transport and flow speeds with $Ra$ appear to be independent of the thermal Prandtl number within the magnetically constrained, high-$Q$ regimes.

JFM classification

MHD and Electrohydrodynamics: Magneto convection MHD and Electrohydrodynamics: MHD turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 877 , 25 October 2019 , pp. 1186 - 1206
Copyright
© 2019 Cambridge University Press 

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