Gellert, M, Rüdiger, G, Schultz, M et al. (2 more authors) (2016) Nonaxisymmetric MHD Instabilities of Chandrasekhar States in Taylor-Couette Geometry. Astrophysical Journal, 823 (2). 99. ISSN 0004-637X
Abstract
We consider axially periodic Taylor-Couette geometry with insulating boundary conditions. The imposed basic states are so-called Chandrasekhar states, where the azimuthal flow U and magnetic field B have the same radial profiles. Mainly three particular profiles are considered: the Rayleigh limit, quasi-Keplerian, and solid-body rotation. In each case we begin by computing linear instability curves and their dependence on the magnetic Prandtl number Pm. For the azimuthal wavenumberm = 1 modes, the instability curves always scale with the Reynolds number and the Hartmann number. For sufficiently small Pm these modes therefore only become unstable for magnetic Mach numbers less than unity, and are thus not relevant for most astrophysical applications. However, modes with m > 1 can behave very differently. For sufficiently flat profiles, they scale with the magnetic Reynolds number and the Lundquist number, thereby allowing instability also for the large magnetic Mach numbers of astrophysical objects. We further compute fully nonlinear, three-dimensional equilibration of these instabilities, and investigate how the energy is distributed among the azimuthal (m) and axial (k) wavenumbers. In comparison spectra become steeper for large m, reflecting the smoothing action of shear. On the other hand kinetic and magnetic energy spectra exhibit similar behavior: if several azimuthal modes are already linearly unstable they are relatively flat, but for the rigidly rotating case where m = 1 is the only unstable mode they are so steep that neither Kolmogorov nor Iroshnikov-Kraichnan spectra fit the results. The total magnetic energy exceeds the kinetic energy only for large magnetic Reynolds numbers Rm > 100.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, American Astronomical Society. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | stars: magnetic field; stars: rotation; instabilities; magnetohydrodynamics (MHD) |
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: | 20 Apr 2016 11:17 |
Last Modified: | 05 Nov 2016 16:41 |
Published Version: | http://dx.doi.org/10.3847/0004-637X/823/2/99 |
Status: | Published |
Publisher: | American Astronomical Society |
Identification Number: | 10.3847/0004-637X/823/2/99 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:98703 |