Eddy viscosity and turbulent Schmidt number by kink-type instability of strong toroidal magnetic fields

The potential of the nonaxisymmetric magnetic instability to transport angular momentum and to mix chemicals is probed considering the stability of a nearly uniform toroidal field between conducting cylinders with different rotation rates. The fluid between the cylinders is assumed as incompressible and to be of uniform density. With a linear theory the neutral-stability maps for m = 1 are computed. Rigid rotation must be subAlfvénic to allow instability while for differential rotation with negative shear also an unstable domain with superAlfvénic rotation exists. The rotational quenching of the magnetic instability is strongest for magnetic Prandtl number Pm = 1 and becomes much weaker for Pm 6= 1. The effective angular momentum transport by the instability is directed outwards(inwards) for subrotation(superrotation). The resulting magnetic-induced eddy viscosities exceed the microscopic values by factors of 10–100. This is only true for superAlfvénic flows; in the strong-field limit the values remain much smaller. The same instability also quenches concentration gradients of chemicals by its nonmagnetic fluctuations. The corresponding diffusion coefficient remains always smaller than the magnetic-generated eddy viscosity. A Schmidt number of order 30 is found as the ratio of the effective viscosity and the diffusion coefficient. The magnetic instability transports much more angular momentum than that it mixes chemicals.