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New results for the Herzenberg dynamo: Steady and oscillatory solutions

Lookup NU author(s): Professor Axel Brandenburg, Professor Andrew Soward

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Abstract

The Herzenberg dynamo, consisting of two rotating electrically conducting spheres with non-parallel spin axes, immersed in a finite spherical conducting medium, is simulated numerically for a variety of parameters not accessible to the original asymptotic theory. Our model places the spheres in a spatially periodic box. The largest growth rate is obtained when the angle, between the spin axes is somewhat larger than 125°. In agreement with the asymptotic analysis, it is found that the critical dynamo number is approximately proportional to the cube of the ratio of the common radius of the spheres and their separation. The asymptotic prediction, strictly valid only in the limit of small spheres, remains approximately valid even when the diameter of the spheres becomes comparable to their separation. For <90° we also find oscillatory solutions, which were not predicted by Herzenberg's analysis. To understand such solutions we present a modified asymptotic analysis in which the separation of the two spheres is essentially replaced by the skin depth which, in turn, depends on the diameter of the spheres. The magnetic field consists of magnetic flux rings wrapped around the two spheres. Applications to local models of turbulent dynamos and to dynamo action in binary stars are discussed. © 1998 The Royal Society.


Publication metadata

Author(s): Brandenburg A, Moss D, Soward AM

Publication type: Article

Publication status: Published

Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Year: 1998

Volume: 454

Issue: 1973

Pages: 1283-1300

Print publication date: 08/05/1998

ISSN (print): 1364-5021

ISSN (electronic): 1471-2946

Publisher: The Royal Society Publishing

URL: http://dx.doi.org/10.1098/rspa.1998.0207

DOI: 10.1098/rspa.1998.0207


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