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Hydromagnetic screw dynamo

Published online by Cambridge University Press:  21 April 2006

Alexander Ruzmaikin ,
Dmitry Sokoloff  and
Anvar Shukurov
Alexander Ruzmaikin
Affiliation:
Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Academy of Sciences, Troitsk, Moscow Region, USSR
Dmitry Sokoloff
Affiliation:
Physics Department, Moscow State University, Lenin Hills, Moscow, USSR
Anvar Shukurov
Affiliation:
Space Research Institute, Academy of Sciences, Moscow, USSR
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Abstract

We solve the problem of magnetic field generation by a laminar flow of conducting fluid with helical (screw-like) streamlines for large magnetic Reynolds numbers, Rm. Asymptotic solutions are obtained with help of the singular perturbation theory. The generated field concentrates within cylindrical layers whose position, the magnetic field configuration and the growth rate are determined by the distribution of the angular, Ω, and longitudinal, Vz, velocities along the radius. The growth rate is proportional to Rm−½. When Ω and Vz are identically distributed along the radius, the asymptotic forms are of the WKB type; for different distributions, singular-layer asymptotics of the Prandtl type arise. The solutions are qualitatively different from those obtained for solid-body screw motion. The generation threshold strongly depends on the velocity profiles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 197 , December 1988 , pp. 39 - 56
Copyright
© 1988 Cambridge University Press

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