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.
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