Destabilization of super-rotating Taylor-Couette flows by current-free helical magnetic fields

TL;DR

This paper investigates how adding a weak axial magnetic field component affects the stability of super-rotating Taylor-Couette flows with azimuthal magnetic fields, revealing conditions for axisymmetric and non-axisymmetric instabilities and their characteristics.

Contribution

It demonstrates that a weak axial field can enable axisymmetric instabilities in super-rotating flows for certain magnetic Prandtl numbers, extending understanding of magnetorotational instabilities.

Findings

Axisymmetric modes occur at magnetic Mach numbers of order unity.

Non-axisymmetric modes require higher magnetic Mach numbers.

Instability growth times are long compared to rotation periods but short relative to magnetic diffusion times.

Abstract

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 $Pm\neq 1$. Here we demonstrate that the addition of a weak axial field component may allow 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 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 $B_\phi B_z$. We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if $|B_\phi|\gg |B_z|$, 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 {\em ideal} fluids the considered helical magnetorotational instability (HMRI) only exists for rotation laws with negative shear.