Stratorotational instability in MHD Taylor-Couette flows

TL;DR

This paper investigates the stability of magnetohydrodynamic Taylor-Couette flows with axial density stratification, revealing how magnetic fields, rotation laws, and density gradients influence various nonaxisymmetric instabilities.

Contribution

It provides a comprehensive analysis of the combined effects of magnetic fields, density stratification, and differential rotation on flow stability, including the identification of new instability regimes and transition behaviors.

Findings

SRI is destabilized by Pm > 1 and suppressed by Pm ≤ 1.

Flat rotation laws are unstable against nonaxisymmetric SRI.

Density stratification significantly enlarges the stability domain against Tayler instability.

Abstract

The stability of dissipative Taylor-Couette flows with an axial stable density stratification and a prescribed azimuthal magnetic field is considered. Global nonaxisymmetric solutions of the linearized MHD equations with toroidal magnetic field, axial density stratification and differential rotation are found for both insulating and conducting cylinder walls. Flat rotation laws such as the quasi-Kepler law are unstable against the nonaxisymmetric stratorotational instability (SRI). The influence of a current-free toroidal magnetic field depends on the magnetic Prandtl number Pm: SRI is supported by Pm > 1 and it is suppressed by Pm \lsim 1. For too flat rotation laws a smooth transition exists to the instability which the toroidal magnetic field produces in combination with the differential rotation. This nonaxisymmetric azimuthal magnetorotational instability (AMRI) has been computed under the presence of an axial density gradient. If the magnetic field between the cylinders is not current-free then also the Tayler instability occurs and the transition from the hydrodynamic SRI to the magnetic Tayler instability proves to be rather complex. Most spectacular is the `ballooning' of the stability domain by the density stratification: already a rather small rotation stabilizes magnetic fields against the Tayler instability. An azimuthal component of the resulting electromotive force only exists for density-stratified flows. The related alpha-effect for magnetic SRI of Kepler rotation appears to be positive for negative d\rho/dz <0.