Ruediger, G, Schultz, M, Stefani, F et al. (1 more author) (2018) Magnetorotational instability in Taylor-Couette flows between cylinders with finite electrical conductivity. Geophysical and Astrophysical Fluid Dynamics, 112 (4). pp. 301-320. ISSN 0309-1929
Abstract
The nonaxisymmetric azimuthal magnetorotational instability is studied for hydromagnetic Taylor-Couette flows between cylinders of finite electrical conductivity. We find that the magnetic Prandtl number Pm determines whether perfectly conducting or insulating boundary conditions lead to lower Hartmann numbers for the onset of instability. Regardless of the imposed rotation profile, for small Pm the solutions for perfectly conducting cylinders become unstable for weaker magnetic fields than the solutions for insulating cylinders. The critical Hartmann and Reynolds numbers form monotonic functions of the ratio σˆ of the electrical conductivities of the cylinders and the fluid, such that σˆ=O(10) provides a very good approximation to perfectly conducting cylinders, and σˆ=O(0.1) a very good approximation to insulating cylinders. These results are of particular relevance for the super-rotating case where the outer cylinder rotates faster than the inner one; in this case the critical onset values are substantially different for perfectly conducting versus insulating boundary conditions. An experimental realisation of the super-rotating instability, with liquid sodium as the fluid and cylinders made of copper, would need an electric current of at least 33.5 kA running along the central axis.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Informa UK Limited, trading as Taylor & Francis Group. This is an author produced version of a paper published in Geophysical & Astrophysical Fluid Dynamics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Astrophysical fluid dynamics; Taylor-Couette flow; magnetic boundary conditions |
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: | 19 Feb 2019 16:21 |
Last Modified: | 24 Aug 2019 00:42 |
Status: | Published |
Publisher: | Taylor and Francis |
Identification Number: | 10.1080/03091929.2018.1508575 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:142677 |