2021, Rüdiger, G., Schultz, M., Hollerbach, R.

In an earlier paper we showed that the combination of azimuthal magnetic fields and super-rotation in Taylor–Couette flows of conducting fluids can be unstable against non-axisymmetric perturbations if the magnetic Prandtl number of the fluid is Pm≠1. Here we demonstrate that the addition of a weak axial field component allows axisymmetric perturbation patterns for Pm of order unity depending on the boundary conditions. The axisymmetric modes only occur for magnetic Mach numbers (of the azimuthal field) of order unity, while higher values are necessary for the non-axisymmetric modes. The typical growth time of the instability and the characteristic time scale of the axial migration of the axisymmetric mode are long compared with the rotation period, but short compared with the magnetic diffusion time. The modes travel in the positive or negative z direction along the rotation axis depending on the sign of BϕBz. We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if |Bϕ|≫|Bz|, independent of the form of the rotation law. Within a short-wave approximation for thin gaps it is also shown (in an appendix) that for ideal fluids the considered helical magnetorotational instability only exists for rotation laws with negative shear.

2007, Stefani, F., Gundrum, T., Gerbeth, G., Rüdiger, G., Szklarski, J., Hollerbach, R.

The magnetorotational instability (MRI) plays a key role in the formation of stars and black holes, by enabling outward angular momentum transport in accretion discs. The use of combined axial and azimuthal magnetic fields allows the investigation of this effect in liquid metal flows at moderate Reynolds and Hartmann numbers. A variety of experimental results is presented showing evidence for the occurrence of the MRI in a Taylor-Couette flow using the liquid metal alloy GaInSn. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.