# Absolute versus convective helical magnetorotational instabilities in Taylor-Couette flows

## TL;DR

This study compares absolute and convective helical magnetorotational instabilities in Taylor-Couette flows, showing similar behaviors in linear and nonlinear regimes despite different magnetic field configurations.

## Contribution

It distinguishes between absolute and convective HMRI in Taylor-Couette flows using different magnetic field configurations, highlighting their similar linear and nonlinear behaviors.

## Key findings

- Both instabilities show similar linear onset.
- Nonlinear equilibration is similar for both.
- Magnetic field configuration influences wave propagation direction.

## Abstract

We study magnetic Taylor-Couette flow in a system having nondimensional radii $r_i=1$ and $r_o=2$, and periodic in the axial direction with wavelengths $h\ge100$. The rotation ratio of the inner and outer cylinders is adjusted to be slightly in the Rayleigh-stable regime, where magnetic fields are required to destabilize the flow, in this case triggering the axisymmetric helical magnetorotational instability (HMRI). Two choices of imposed magnetic field are considered, both having the same azimuthal component $B_\phi=r^{-1}$, but differing axial components. The first choice has $B_z=0.1$, and yields the familiar HMRI, consisting of unidirectionally traveling waves. The second choice has $B_z\approx0.1\sin(2\pi z/h)$, and yields HMRI waves that travel in opposite directions depending on the sign of $B_z$. The first configuration corresponds to a convective instability, the second to an absolute instability. The two variants behave very similarly regarding both linear onset as well as nonlinear equilibration.