Numerical simulation of the Tayler instability in liquid metals

TL;DR

This paper presents a 3D numerical simulation of the Tayler instability in liquid metals, validating growth rates against experiments and demonstrating applications to liquid metal batteries.

Contribution

Developed a fully three-dimensional numerical code to simulate the Tayler instability in liquid metals, matching experimental growth rates and enabling realistic battery geometry studies.

Findings

Numerical growth rates agree with experimental data.

Code effectively simulates Tayler instability in realistic geometries.

Demonstrated potential for liquid metal battery applications.

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.