Guervilly, C, Wood, TS and Brummell, NH (2013) Effect of metallic walls on dynamos generated by laminar boundary-driven flow in a spherical domain. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 88 (5). 053010. ISSN 1539-3755
Abstract
We present a numerical study of dynamo action in a conducting fluid encased in a metallic spherical shell. Motions in the fluid are driven by differential rotation of the outer metallic shell, which we refer to as "the wall." The two hemispheres of the wall are held in counter-rotation, producing a steady, axisymmetric interior flow consisting of differential rotation and a two-cell meridional circulation with radial inflow in the equatorial plane. From previous studies, this type of flow is known to maintain a stationary equatorial dipole by dynamo action if the magnetic Reynolds number is larger than about 300 and if the outer boundary is electrically insulating. We vary independently the thickness, electrical conductivity, and magnetic permeability of the wall to determine their effect on the dynamo action. The main results are the following: (a) Increasing the conductivity of the wall hinders the dynamo by allowing eddy currents within the wall, which are induced by the relative motion of the equatorial dipole field and the wall. This processes can be viewed as a skin effect or, equivalently, as the tearing apart of the dipole by the differential rotation of the wall, to which the field lines are anchored by high conductivity. (b) Increasing the magnetic permeability of the wall favors dynamo action by constraining the magnetic field lines in the fluid to be normal to the wall, thereby decoupling the fluid from any induction in the wall. (c) Decreasing the wall thickness limits the amplitude of the eddy currents, and is therefore favorable for dynamo action, provided that the wall is thinner than the skin depth. We explicitly demonstrate these effects of the wall properties on the dynamo field by deriving an effective boundary condition in the limit of vanishing wall thickness.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | ©2013 American Physical Society. This is an author produced version of a paper published in Physical Review E: statistical, nonlinear, and soft matter physics. Uploaded in accordance with the publisher's self-archiving policy |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Nov 2015 11:30 |
Last Modified: | 17 Jan 2018 17:25 |
Published Version: | http://dx.doi.org/10.1103/PhysRevE.88.053010 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevE.88.053010 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85253 |