Transition to magnetorotational turbulence in Taylor--Couette flow with imposed azimuthal magnetic field

TL;DR

This paper investigates the transition to turbulence in magnetorotational instability within Taylor--Couette flow with azimuthal magnetic fields, revealing bifurcation sequences and turbulent behavior through numerical simulations.

Contribution

It provides the first detailed numerical analysis of the MRI transition with azimuthal magnetic fields, extending experimental findings and exploring turbulence development.

Findings

Flow becomes unstable via a supercritical Hopf bifurcation.

Transition to turbulence involves a subcritical subharmonic Hopf bifurcation.

Momentum transport scales weakly with increasing Reynolds number.

Abstract

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence and momentum transport in astrophysical accretion discs, but obtaining observational evidence of its operation is challenging. Recently, laboratory experiments of Taylor--Couette flow with externally imposed axial and azimuthal magnetic fields have revealed the kinematic and dynamic properties of the MRI close to the instability onset. While good agreement was found with linear stability analyses, little is known about the transition to turbulence and transport properties of the MRI. We here report on a numerical investigation of the MRI with an imposed azimuthal magnetic field. We show that the laminar Taylor--Couette flow becomes unstable to a wave rotating in the azimuthal direction and standing in the axial direction via a supercritical Hopf bifurcation. Subsequently, the flow features a catastrophic transition to spatio-temporal defects which is mediated by a subcritical subharmonic Hopf bifurcation. Our results are in qualitative agreement with the PROMISE experiment and dramatically extend their realizable parameter range. We find that as the Reynolds number increases defects accumulate and grow into turbulence, yet the momentum transport scales weakly.