Taylor-Couette flow for astrophysical purposes

TL;DR

This paper reviews experimental and theoretical research on Taylor-Couette flow in astrophysics, highlighting the stability of quasi-keplerian flows, the role of magnetic instabilities, and recent laboratory advances in magnetorotational instability studies.

Contribution

It provides a comprehensive overview of hydrodynamic and magnetohydrodynamic stability in Taylor-Couette flows relevant to astrophysical disks, including recent experimental breakthroughs.

Findings

Quasi-keplerian flows are nonlinearly stable at high Reynolds numbers.

Laboratory experiments have demonstrated some forms of magnetorotational instability.

Hydrodynamic turbulence is unlikely to drive accretion in astrophysical disks.

Abstract

A concise review is given of astrophysically motivated experimental and theoretical research on Taylor-Couette flow. The flows of interest rotate differentially with inner cylinder faster than outer one but are linearly stable against Rayleigh's inviscid centrifugal instability. At shear Reynolds numbers as large as 10^6, 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 the recently reported success in demonstrating SMRI itself by taking advantage of conducting axial boundaries. Some outstanding questions and near-future prospects are discussed, especially in connection with astrophysics.