The magnetorotational instability prefers three dimensions

Taylor-Couette flow for astrophysical purposes

A concise review is given of astrophysically motivated experimental and theoretical research on Taylor-Couette flow. The flows of interest rotate differentially with the inner cylinder faster than the outer, but are linearly stable against Rayleigh's inviscid centrifugal instability. At shear Reynolds numbers as large as [Formula: see text], hydrodynamic flows of this type (quasi-Keplerian) appear to be nonlinearly stable: no turbulence is seen that cannot be attributed to interaction with the axial boundaries, rather than the radial shear itself. Direct numerical simulations agree, although they cannot yet reach such high Reynolds numbers. This result indicates that accretion-disc turbulence is not purely hydrodynamic in origin, at least insofar as it is driven by radial shear. Theory, however, predicts linear magnetohydrodynamic (MHD) instabilities in astrophysical discs: in particular, the standard magnetorotational instability (SMRI). MHD Taylor-Couette experiments aimed at SMRI are challenged by the low magnetic Prandtl numbers of liquid metals. High fluid Reynolds numbers and careful control of the axial boundaries are required. The quest for laboratory SMRI has been rewarded with the discovery of some interesting inductionless cousins of SMRI, and with the recently reported success in demonstrating SMRI itself using conducting axial boundaries. Some outstanding questions and near-future prospects are discussed, especially in connection with astrophysics. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Observation of Axisymmetric Standard Magnetorotational Instability in the Laboratory

We report the first direct evidence for the axisymmetric standard magnetorotational instability (SMRI) from a combined experimental and numerical study of a magnetized liquid-metal shear flow in a Taylor-Couette cell with independently rotating and electrically conducting end caps. When a uniform vertical magnetic field B_{i} is applied along the rotation axis, the measured radial magnetic field B_{r} on the inner cylinder increases linearly with a small magnetic Reynolds number Rm due to the magnetization of the residue Ekman circulation. Onset of the axisymmetric SMRI is identified from the nonlinear increase of B_{r} beyond a critical Rm in both experiments and nonlinear numerical simulations. The axisymmetric SMRI exists only at sufficiently large Rm and intermediate B_{i}, a feature consistent with theoretical predictions. Our simulations further show that the axisymmetric SMRI causes the velocity and magnetic fields to contribute an outward flux of axial angular momentum in the bulk region, just as it should in accretion disks.

Identification of a non-axisymmetric mode in laboratory experiments searching for standard magnetorotational instability

The standard magnetorotational instability (SMRI) is a promising mechanism for turbulence and rapid accretion in astrophysical disks. It is a magnetohydrodynamic (MHD) instability that destabilizes otherwise hydrodynamically stable disk flow. Due to its microscopic nature at astronomical distances and stringent requirements in laboratory experiments, SMRI has remained unconfirmed since its proposal, despite its astrophysical importance. Here we report a nonaxisymmetric MHD instability in a modified Taylor-Couette experiment. To search for SMRI, a uniform magnetic field is imposed along the rotation axis of a swirling liquid-metal flow. The instability initially grows exponentially, becoming prominent only for sufficient flow shear and moderate magnetic field. These conditions for instability are qualitatively consistent with SMRI, but at magnetic Reynolds numbers below the predictions of linear analyses with periodic axial boundaries. Three-dimensional numerical simulations, however, reproduce the observed instability, indicating that it grows linearly from the primary axisymmetric flow modified by the applied magnetic field.

Magnetohydrodynamic instabilities are related to different characteristics and behavior of fluids. Here the authors report an experiment and simulation combined study of a global non-axisymmetric MHD instability that exists at sufficiently large rotation rates and intermediate magnetic field strengths.