MHD Taylor-Couette Flow for Small Magnetic Prandtl Number and With Hall Effect

Abstract

Rotating shear flows are very common in astrophysics. Rotation profiles of stars, accretion disks, and galaxies are shear flows. The Rayleigh criterion for stability of a given rotation profile requires an increasing specific angular momentum with distance from the rotation axis. This criterion is fulfilled in nearly all astrophysical objects. The rotation profile in accretion disks obeys roughly Ω ∼ r−3/2, where r is the axis distance. A powerful ingredient to rotating shear flows are magnetic fields, which excite a linear instability even if they are weak in terms of energy compared with the thermal energy. The magnetorotational instability (MRI) has been proven by analytical and numerical studies to be very efficient in generating turbulence. The turbulent flows emerging from the instability lead to outward transport of angular momentum (see e.g. [1], [2], [3]). This is a very promising finding for the problem of the formation of stars. The MRI had not yet been observed in the laboratory at the time of the Conference. Taylor-Couette (TC) experiments study the flow between two coaxial cylinders with one of them, or both, rotating. If the inner cylinder is rotating – by far the most often studied case in the laboratory – the rotation profile Ω = A + B/r2 looks similar to the Keplerian one, but is Rayleigh unstable whence not comparable to accretion disks. Nevertheless, the TC flow bears the chance to reproduce the MRI in an experiment.