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On the spin-up of an electrically conducting fluid Part 2. Hydromagnetic spin-up between infinite flat insulating plates

Published online by Cambridge University Press:  29 March 2006

David E. Loper  and
Edward R. Benton
David E. Loper
Affiliation:
Florida State University
Edward R. Benton
Affiliation:
University of Colorado
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Abstract

The linear spin-up of a homogeneous electrically conducting fluid confined between infinite flat insulating plates is analyzed for the case in which a uniform magnetic field is applied normal to the boundaries. As in part 1 (Benton & Loper 1969), complete hydromagnetic interaction is embraced even within linearized equations. Approximate inversion of the exact Laplace transform solution reveals the presence of several flow structures: two thin Ekman–Hartmann boundary layers (one on each plate), which are quasi-steady on the time scale of spin-up, two thicker continuously growing magnetic diffusion regions, and an essentially inviscid, current-free core, which may or may not be present on the spin-up time scale, depending upon the growth rate of the magnetic diffusion regions. When a current-free core exists, it is found to spin-up at the same rate as the fluid within magnetic diffusion regions, although different physical mechanisms are at play. As a result, a single hydromagnetic spin-up time is derived, independently of the thickness of magnetic diffusion regions; this time is shorter than in the non-magnetic problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 43 , Issue 4 , 2 October 1970 , pp. 785 - 799
Copyright
© 1970 Cambridge University Press

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References

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Loper, D. E. & Benton, E. R. 1970 On the spin-up of an electrically conducting fluid. Part 2. Hydromagnetic spin-up between infinite flat, insulating plates. Geophysical Fluid Dynamics Institute, Florida State University, Technical Report, no. 26.