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Electromagnetically driven zonal flows in a rapidly rotating spherical shell

Published online by Cambridge University Press:  14 May 2013

Rainer Hollerbach ,
Xing Wei ,
Jérõme Noir  and
Andrew Jackson
Rainer Hollerbach*
Affiliation:
Institute of Geophysics, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Xing Wei
Affiliation:
Institute of Geophysics, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland Geophysics Institute, University of Göttingen, D-37077 Göttingen, Germany
Jérõme Noir
Affiliation:
Institute of Geophysics, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland
Andrew Jackson
Affiliation:
Institute of Geophysics, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland
*
†Email address for correspondence: rh@maths.leeds.ac.uk
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Abstract

We consider the flow of an electrically conducting fluid confined in a rotating spherical shell. The flow is driven by a directly imposed electromagnetic body force, created by the combination of an electric current flowing from the inner sphere to a ring-shaped electrode around the equator of the outer sphere and a separately imposed predominantly axial magnetic field. We begin by numerically computing the axisymmetric basic states, which consist of a strong zonal flow. We next compute the linear onset of non-axisymmetric instabilities, and fully three-dimensional solutions up to ten times supercritical. We demonstrate that an experimental liquid-sodium device 50 cm in diameter could achieve and exceed these parameter values.

JFM classification

Boundary Layers: Free shear layers MHD and Electrohydrodynamics: High-Hartmann-number flows MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 428 - 445
Copyright
©2013 Cambridge University Press 

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