Turbulent magnetic Prandtl numbers obtained with MHD Taylor-Couette flow experiments

TL;DR

This study investigates the stability and turbulence characteristics of magnetohydrodynamic Taylor-Couette flows with toroidal magnetic fields, revealing how magnetic Prandtl numbers influence turbulence and potential laboratory measurement techniques.

Contribution

It provides numerical insights into turbulent magnetic Prandtl numbers and proposes experimental methods to measure eddy diffusivity and viscosity in MHD flows.

Findings

Turbulent magnetic Prandtl number is about 2.1 for Pm=0.01.

Eddy diffusivity in sodium experiments is approximately 4 times the molecular diffusivity.

Rotation stabilizes certain MHD instabilities, affecting magnetic field behavior.

Abstract

The stability problem of MHD Taylor-Couette flows with toroidal magnetic fields is considered in dependence on the magnetic Prandtl number. Only the most uniform (but not current-free) field with B\_in = B\_out has been considered. For high enough Hartmann numbers the toroidal field is always unstable. Rigid rotation, however, stabilizes the magnetic (kink-)instability. The axial current which drives the instability is reduced by the electromotive force induced by the instability itself. Numerical simulations are presented to probe this effect as a possibility to measure the turbulent conductivity in a laboratory. It is shown numerically that in a sodium experiment (without rotation) an eddy diffusivity 4 times the molecular diffusivity appears resulting in a potential difference of ~34 mV/m. If the cylinders are rotating then also the eddy viscosity can be measured. Nonlinear simulations of the instability lead to a turbulent magnetic Prandtl number of 2.1 for a molecular magnetic Prandtl number of 0.01. The trend goes to higher values for smaller Pm.