Numerical simulation of the Tayler instability in liquid metals

Abstract

The electrical current through an incompressible, viscous and resistive liquid conductor produces an azimuthal magnetic field that becomes unstable when the corresponding Hartmann number exceeds a critical value in the order of 20. This Tayler instability, which is not only discussed as a key ingredient of a non-linear stellar dynamo model (Tayler-Spruit dynamo), but also as a limiting factor for the maximum size of large liquid metal batteries, was recently observed experimentally in a column of a liquid metal (Seilmayer et al., Phys. Rev. Lett. 108, 244501, 2012}. On the basis of an integro-differential equation approach, we have developed a fully three-dimensional numerical code, and have utilized it for the simulation of the Tayler instability at typical viscosities and resistivities of liquid metals. The resulting growth rates are in good agreement with the experimental data. We illustrate the capabilities of the code for the detailed simulation of liquid metal battery problems in realistic geometries.

19 pages, 16 figures

References in corpus (8)

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• Evolution of massive population III stars with rotation and magnetic fields
• White dwarf spins from low mass stellar evolution models
• Experimental evidence for Tayler instability in a liquid metal column
• Kink instabilities in jets from rotating magnetic fields
• How to circumvent the size limitation of liquid metal batteries due to the Tayler instability
• Breakdown of chiral symmetry during saturation of the Tayler instability
• Critical fields and growth rates of the Tayler instability as probed by a columnar gallium experiment

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