On the adjustment to the Bondi-Gold theorem in a spherical-shell fast dynamo
作者:
R. Hollerbach,
D.J. Galloway,
M.R. E. Proctor,
期刊:
Geophysical & Astrophysical Fluid Dynamics
(Taylor Available online 1998)
卷期:
Volume 87,
issue 1-2
页码: 111-132
ISSN:0309-1929
年代: 1998
DOI:10.1080/03091929808208996
出版商: Taylor & Francis Group
关键词: Kinematic fast dynamos;Bondi-Gold theorem
数据来源: Taylor
摘要:
We present a numerical solution of the magnetic induction equation in a spherical fluid shell, with an insulator inside and outside. Prescribing an axisymmetric, time-dependent, chaotic flow, we find that the magnetic field appears to grow on the fast advective, rather than on the slow diffusive time scale. We demonstrate how this may be reconciled with the theorem of Bondi and Gold (1950), that the potential field in these insulators inside and outside the shell cannot be amplified on the fast time scale, by having the field become increasingly contained within the shell with increasing magnetic Reynolds number. Thus, as the Bondi-Gold theorem becomes more and more applicable, there is indeed less and less external field being amplified. This is in precise agreement with the conjecture of Rädler (1982) that the resolution would be to have an “invisible dynamo,” one having no external field. Finally, we consider some of the implications of this adjustment for the different symmetries of the field (dipolar versus quadrupolar) and the flow (uversus—u).
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