Guenther Ruediger, Marcus Gellert, Manfred Schultz, Klaus G. Strassmeier, Frank Stefani, Thomas Gundrum, Martin Seilmayer, Gunter Gerbeth
The Tayler instability (TI) is experimentally realized in a liquid-metal flow
confined in a columnar container with an insulating outer cylinder. To predict
the critical electrical current and the expected growth rates, simulations with
MHD codes are used for a container with an inner cylinder whose radius is small
or even zero. The very small magnetic Prandtl number of the gallium alloy
(Pm\simeq 10^{-6}) only influences the growth rates rather than the critical
field amplitudes. It is thus allowed to calculate the critical Hartmann numbers
for marginal instability also with direct numerical simulations. The
theoretical value of the critical electric current of 2.8 kA, resulting from
both linear theory and simulations, is well confirmed by the experiment. Also
the predicted (small) growth rates of the nonaxisymmetric kink-type
perturbations are certified by the observed data. Due to the rather long growth
times of order of minutes, the resulting Joule heating might excite convective
modes forming a saturation mechanism of the observed TI.
View original:
http://arxiv.org/abs/1201.2318
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