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Parametric resonance in low-frequency magnetic stirring

Published online by Cambridge University Press:  26 April 2006

J. M. Galpin,
Y. Fautrelle and
A. D. Sneyd
J. M. Galpin
Affiliation:
INPG-MADYLAM, B.P. 95X, 38402 St Martin d'Hères Cedex, FrancePresent address: IRSID, Station d'Essais, 57210 Maizières-les-Metz, France.
Y. Fautrelle
Affiliation:
INPG-MADYLAM, B.P. 95X, 38402 St Martin d'Hères Cedex, France
A. D. Sneyd
Affiliation:
University of Waikato, Private Bag, Hamilton, New Zealand
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Abstract

This paper analyses the effect of an alternating magnetic field of low frequency ω on a cylindrical tank of liquid metal. Previous work with higher-frequency fields has focused attention on the mean recirculating motion, but in the low-frequency limit periodic motion and surface waves become important. We show that a system of forced standing axisymmetric waves of frequency 2ω is established, and that the growth of non-axisymmetric modes is governed by a coupled system of Mathieu-type equations. The stability regions associated with this system are discussed and it is shown that the most easily excited transition to a non-axisymmetric mode is subharmonic, with frequency ω. Comparison with experiment shows that the theory gives qualitatively correct predictions.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 239 , June 1992, pp. 409 - 427
Copyright
© 1992 Cambridge University Press

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