Dynamo action between two rotating discs
File(s)
Accepted version
Author(s)
Arslan, Ali
Mestel, Andrew
Type
Journal Article
Abstract
Dynamo action is considered in the region between two differentially rotating infinite discs. The boundaries may be insulating, perfectly conducting or ferromagnetic. In the absence of a magnetic field, various well-known self-similar flows arise, generalising that of von Kármán. Magnetic field instabilities with the same similarity structure are sought. The kinematic eigenvalue problem is found to have growing modes for Rem>Rc≃100. The growth rate is real for the perfectly conducting and ferromagnetic cases, but may be complex for insulating boundaries. As Rem→∞ it is shown that the dynamo can be fast or slow, depending on the flow structure. In the slow case, the growth rate is governed by a magnetic boundary layer on one of the discs. The growing field saturates in a solution to the nonlinear dynamo problem. The bifurcation is found to be subcritical and nonlinear dynamos are found for Rem≳0.7Rc. Finally, the flux of magnetic energy to large r is examined, to determine which solutions might generalise to dynamos between finite discs. It is found that the fast dynamos tend to have inward energy flux, and so are unlikely to be realised in practice. Slow dynamos with outward flux are found. It is suggested that the average rotation rate should be non-zero in practice.
Date Issued
2021-05-01
Date Acceptance
2020-12-17
Citation
Geophysical and Astrophysical Fluid Dynamics, 2021, 115 (5-6), pp.710-727
ISSN
0309-1929
Publisher
Taylor and Francis
Start Page
710
End Page
727
Journal / Book Title
Geophysical and Astrophysical Fluid Dynamics
Volume
115
Issue
5-6
Copyright Statement
© 2021 Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Geophysical & Astrophysical Fluid Dynamics on 22 January 2021, available online: https://doi.org/10.1080/03091929.2020.1867123
Subjects
Science & Technology
Physical Sciences
Technology
Astronomy & Astrophysics
Geochemistry & Geophysics
Mechanics
Laminar dynamo
von Karman flow
Fluids & Plasmas
Publication Status
Published
Date Publish Online
2021-01-22