Imperial College London
Alternate

Prof Jonathan Mestel

Faculty of Natural Sciences, Department of Mathematics

Senior Consul & Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8513j.mestel Website

 
 
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Location

 

746Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Arslan:2021:10.1080/03091929.2020.1867123,
author = {Arslan, A and Mestel, A},
doi = {10.1080/03091929.2020.1867123},
journal = {Geophysical and Astrophysical Fluid Dynamics},
pages = {710--727},
title = {Dynamo action between two rotating discs},
url = {http://dx.doi.org/10.1080/03091929.2020.1867123},
volume = {115},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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>Rc100. 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 Rem0.7Rc. 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.
AU  - Arslan,A
AU  - Mestel,A
DO  - 10.1080/03091929.2020.1867123
EP  - 727
PY  - 2021///
SN  - 0309-1929
SP  - 710
TI  - Dynamo action between two rotating discs
T2  - Geophysical and Astrophysical Fluid Dynamics
UR  - http://dx.doi.org/10.1080/03091929.2020.1867123
UR  - https://www.tandfonline.com/doi/full/10.1080/03091929.2020.1867123
UR  - http://hdl.handle.net/10044/1/86322
VL  - 115
ER  -
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