α effect in a turbulent liquid-metal plane Couette flow.

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 α effect owing to the presence of horizontal shear. Here we discuss the possibility of an experimental determination of the components of the α 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 α effect in the direction of the flow clearly exceeds the component in spanwise direction. In this limit, α 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 a given Rm the α 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 α tensor appears, which makes it unimportant whether the α effect is measured in the spanwise or the streamwise directions. The resulting effect should lead to an observable voltage of about 0.5 mV in both directions for magnetic fields of 1 kG and velocity fluctuations of about 1m/s in a channel of 50-cm height (independent of its width).