The alpha-effect in a turbulent liquid-metal plane Couette flow

TL;DR

This paper investigates the alpha-effect in turbulent liquid-metal plane Couette flow, highlighting how turbulence stratification and magnetic Reynolds number influence the electromotive force, with implications for experimental detection.

Contribution

It provides a detailed analysis of the alpha-effect in nonrotating turbulent liquid-metal flows, including theoretical and numerical insights into its dependence on magnetic Prandtl number and flow parameters.

Findings

Alpha effect exceeds spanwise component at high conductivity.

Alpha scales linearly with magnetic Reynolds number in high-conductivity limit.

Observable voltage of about 0.5 mV predicted for typical experimental conditions.

Abstract

We calculate the mean electromotive force in plane Couette flows of a nonrotating conducting fluid under the influence of a large-scale magnetic field for driven turbulence. A vertical stratification of the turbulence intensity results in an alpha effect owing to the presence of horizontal shear. Here we discuss the possibility of an experimental determination of the components of the alpha tensor using both quasilinear theory and nonlinear numerical simulations. For magnetic Prandtl numbers of the order of unity, we find that in the high-conductivity limit the alpha effect in the direction of the flow clearly exceeds the component in spanwise direction. In this limit, alpha runs linearly with the magnetic Reynolds number Rm while in the low-conductivity limit it runs with the product Rm*Re, where Re is the kinetic Reynolds number so that for given Rm the alpha effect grows with decreasing magnetic Prandtl number. For the small magnetic Prandtl numbers of liquid metals, a common value for the horizontal elements of the alpha tensor appears, which makes it unimportant whether the alpha effect is measured in the spanwise or streamwise directions. The resulting effect should lead to an observable voltage in both directions of about 0.5 mV for magnetic fields of 1 kgauss and velocity fluctuations of about 1 m/s in a channel of 50 cm height (independent of its width).