MHD turbulence in non-stationary flows of liquid metals

P. Frick^{1, 2} - I. Mizeva¹

¹ Institute of Continuous Media Mechanics, 1 Korolyov str., Perm 614013, Russia
² Perm State University, 15 Bukireva str., Perm, Russia

Abstract
Intense pulse flows allow one to reach high magnetic Reynolds numbers in relatively small laboratory setups using moderate masses of liquid metals. A spin-down flow in toroidal channels was the first flow configuration used for laboratory study of MHD effects in non-stationary flows. In this paper, we estimate the effect of small-scale dynamo in liquid metal non-stationary flows using a shell model of MHD turbulence. Our simulations showed that the induction effects in experiments with gallium should be weak - a slight burst of small-scale magnetic energy could arise only at the highest available rotation velocity of the channel. In existing laboratory sodium flows, the available induction effects can be strong - an essential part of kinetic energy of sodium spin-down flows can be converted into magnetic energy and dissipate due Joule heat losses. We have extended our simulations beyond the capabilities of existing laboratory facilities and examined the spin-down flows at the channel rotation velocity Ω >> 50 rps. It has been found that at Ω ≈ 100 rps the equipartition of the magnetic and kinetic spectral power density at the lowest wave numbers (largest scales) can be reached, whereas at Ω >~200 rps the intensity of the magnetic field becomes comparable to the intensity of velocity field fluctuations. We have also studied the influence of the magnetic Prandtl number on the efficiency of small-scale dynamo in non-stationary flows. In the experimental flows, the small-scale dynamo remains in a quasi-kinematic regime, and the magnetic energy is mainly dissipated at the same scale, wherein it is converted from kinetic energy. An efficient small-scale dynamo starts to operate at Pm >~10⁻⁴, and an inertial range appears in the magnetic energy spectrum. Thereupon the energy dissipation is postponed to a later time and smaller scales, and the peak of turbulent energy (kinetic and magnetic) slightly increases with \Pm. Tables 1, Figs 4, Refs 28.