# Non-diffusive angular momentum transport in rotating $\bf z$-pinches

## TL;DR

This paper investigates how magnetic fields in rotating z-pinch configurations cause non-diffusive angular momentum transport, challenging traditional diffusion-based models and suggesting a new form of angular momentum flux driven by magnetohydrodynamic instabilities.

## Contribution

It reveals the existence of a nondiffusive b5 effect in z-pinch flows, providing a new perspective on angular momentum transport in magnetized rotating fluids.

## Key findings

- Angular momentum flux exists even in rigid rotation due to the b5 effect.
- The instability-induced eddy viscosity scales linearly with the Reynolds number.
- Results support a modified Shakura-Sunyaev viscosity model incorporating nondiffusive effects.

## Abstract

The stability of conducting Taylor-Couette flows under the presence of toroidal magnetic background fields is considered. For strong enough magnetic amplitudes such magnetohydrodynamic flows are unstable against nonaxisymmetric perturbations which may also transport angular momentum. In accordance with the often used diffusion approximation one expects the angular momentum transport vanishing for rigid rotation. In the sense of a nondiffusive $\Lambda$ effect, however, even for {\em rigidly} rotating $z$-pinches an axisymmetric angular momentum flux appears which is directed outward (inward) for large (small) magnetic Mach numbers. The internal rotation in a magnetized rotating tank can thus never be uniform. Those particular rotation laws are used to estimate the value of the instability-induced eddy viscosity for which the nondiffusive $\Lambda$ effect and the diffusive shear-induced transport compensate each other. The results provide the Shakura-Sunyaev viscosity ansatz leading to numerical values linearly growing with the Reynolds number of rotation.