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On the hydromagnetic stability of a rotating fluid annulus

Published online by Cambridge University Press:  29 March 2006

D. J. Acheson
D. J. Acheson
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich Present address: Geophysical Fluid Dynamics Laboratory, Meteorological Office, Bracknell, Berkshire.
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Abstract

A non-dissipative fluid rotates uniformly in the annular region between two infinitely long cylinders and is permeated by a magnetic field varying with distance from the axis of rotation. The hydromagnetic stability of this system is examined theoretically. When the magnetic field is azimuthal the system can always be rendered stable to axisymmetric disturbances by sufficiently rapid rotation (Michael 1954). Unless the magnetic field everywhere decreases with radius, however, the system may be unstable to non-axisymmetric disturbances even when the rotation speed exceeds a typical Alfvén speed by many orders of magnitude. ‘Slow’ hydromagnetic waves, akin to those invoked in a recent theory of the geomagnetic secular variation (Hide 1966), may then be generated by the spatial variations of the magnetic field. All unstable waves so generated propagate against the basic rotation, i.e. ‘westward’, when the field is azimuthal, and this property is in fact remarkably insensitive to variations in both magnitude and direction of the imposed field.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 52 , Issue 3 , 11 April 1972 , pp. 529 - 541
Copyright
© 1972 Cambridge University Press

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