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

TL;DR

This paper investigates how kink-type magnetic instabilities in strong toroidal fields influence angular momentum transport and chemical mixing, revealing that magnetic effects dominate over chemical diffusion with a high Schmidt number.

Contribution

It provides a linear stability analysis of nonaxisymmetric magnetic instabilities in toroidal fields, quantifies eddy viscosities, and compares angular momentum transport to chemical mixing.

Findings

Magnetic instability transports angular momentum outward in subrotation and inward in superrotation.

Eddy viscosities due to magnetic instability exceed microscopic values by factors of 10-100.

The Schmidt number is approximately 30, indicating dominant angular momentum transport over chemical mixing.

Abstract

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 subAlfvenic to allow instability while for differential rotation with negative shear also an unstable domain with superAlfvenic rotation exists. The rotational quenching of the magnetic instability is strongest for magnetic Prandtl number Pm=1 and becomes much weaker for Pm unequal 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 superAlfvenic 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.