# Effects of small-scale dynamo and compressibility on the $\Lambda$ effect

## TL;DR

This study investigates how small-scale magnetic fields and compressibility influence the $\Lambda$ effect, revealing that magnetic fields cause mild quenching while compressibility has negligible impact within certain Mach numbers.

## Contribution

It provides new insights into the sensitivity of the $\Lambda$ effect to small-scale magnetic fields and compressibility through turbulence simulations.

## Key findings

- Small-scale magnetic fields cause a milder quenching of the $\Lambda$ effect.
- Compressibility effects are negligible for Mach numbers 0.015 to 0.8.
- Density stratification induces anisotropy and a vertical $\Lambda$ effect.

## Abstract

The $\Lambda$ effect describes a rotation-induced non-diffusive contribution to the Reynolds stress. It is commonly held responsible for maintaining the observed differential rotation of the Sun and other late-type stars. Here the sensitivity of the $\Lambda$ effect to small-scale magnetic fields and compressibility is studied by means of forced turbulence simulations either with anisotropic forcing in fully periodic cubes or in density-stratified domains with isotropic forcing. Effects of small-scale magnetic fields are studied in cases where the magnetic fields are self-consistently generated by a small-scale dynamo. The results show that small-scale magnetic fields lead to a quenching of the $\Lambda$ effect which is milder than in cases where also a large-scale field is present. The effect of compressibility on the $\Lambda$ effect is negligible in the range of Mach numbers from 0.015 to 0.8. Density stratification induces a marked anisotropy in the turbulence and a vertical $\Lambda$ effect if the forcing scale is roughly two times larger than the density scale height.