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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(2):137-147; doi:10.1093/qjmam/10.2.137
© 1957 by Oxford University Press
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MAGNETO-HYDRODYNAMICS OF A FINITE ROTATING DISK

K. STEWARTSON

( Department of Mathematics, The University Bristol )

The effect of a vertical magnetic field on the motion of a shallow dish of mercury, part of whose base is rotating while the rest is fixed, is considered. It is found that both in the absence of the field and when the field is large there is a steady solution in which the mercury is either uniformly rotating or at rest, there being a thin friction layer separating the two regions. A comparison with experiment suggests that the flow in the absence of the field is unstable but that the field stabilizes the motion while it is still not large enough to make substantial modiciations to the velocity field in the friction layer.


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