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.
Highlights
The magnetorotational instability (MRI) is of great importance in astrophysics
In this work we address these points for the azimuthal MRI (AMRI)
We showed that the AMRI in Taylor–Couette flow manifests itself as a wave rotating in the azimuthal direction and standing in the axial direction, thereby preserving the reflection symmetry in the latter
Summary
The magnetorotational instability (MRI) is of great importance in astrophysics. First discovered by Velikhov [1] in 1959, it remained unnoticed until 1991 when Balbus and Hawley [2] realized its application to accretion disc theory. Hollerbach and Rüdiger [7] proposed instead a combination of axial and azimuthal magnetic fields, giving rise to the helical MRI (HMRI) at much lower Re ~ 103 for Hartmann numbers Ha ~ 10 (see table 1 for the definition of Ha) This was successfully observed [15, 16] in the Potsdam-ROssendorf magnetic instability experiment (PROMISE) facility. Of the practical impossibility of generating a purely azimuthal magnetic field experimentally, it is challenging to identify the AMRI modes in the experimental data unambiguously (see [17]) Despite this recent experimental progress in realizing magnetorotational instabilities in the laboratory, little is known about their bifurcation scenario, transition to turbulence and transport properties as Re increases. The results are in good qualitative agreement with the PROMISE observations [17] and substantially extend the parameter range explored experimentally
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