Toroidal field instability and eddy viscosity in Taylor-Couette flows

TL;DR

This paper investigates how toroidal magnetic fields affected by the Tayler instability influence angular momentum transport in Taylor-Couette flows, revealing linear dependencies on shear and magnetic Reynolds number, and defining an eddy viscosity.

Contribution

It introduces a linear relation between shear and angular momentum transport in Tayler instability-affected flows and quantifies the eddy viscosity dependence on magnetic Reynolds number.

Findings

Angular momentum transport scales linearly with shear.

Eddy viscosity depends linearly on magnetic Reynolds number.

Maximum eddy viscosity reaches about 30 times microscopic value at Rm=1000.

Abstract

Toroidal magnetic fields subject to the Tayler instability can transport angular momentum. We show that the Maxwell and Reynolds stress of the nonaxisymmetric field pattern depend linearly on the shear in the cylindrical gap geometry. Resulting angular momentum transport also scales linear with shear. It is directed outwards for astrophysical relevant flows and directed inwards for superrotating flows with dOmega/dR>0. We define an eddy viscosity based on the linear relation between shear and angular momentum transport and show that its maximum for given Prandtl and Hartmann number depends linear on the magnetic Reynolds number Rm. For Rm=1000 the eddy viscosity is of the size of 30 in units of the microscopic value.