MHD Turbulence in spin-down flows of liquid metals

Abstract: Intense spin-down flows allow one to reach high Rm in relatively small laboratory setups using moderate mass of liquid metals. The spin-down flow in toroidal channels was the first flow configuration used for studying dynamo effects in non-stationary flows. In this paper, we estimate the effect of small-scale dynamo in liquid metal spin-down flows realized in laboratory experiments. Our simulations have confirmed the conclusion that the dynamo effects observed in the experiments done on gallium are weak -- a slight burst of small-scale magnetic energy arises only at the highest available rotation velocity of the channel. In sodium flows, the induction effects are quite strong -- an essential part of kinetic energy of sodium spin-down flows is converted into magnetic energy and dissipates because of 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 Omega>> 50 rps. It has been found that $\Omega\approx 100$rps is enough to reach the equipartition of magnetic and kinetic spectral power density at the lowest wave numbers (largest scales), whereas at Omega >= 200rps the intensity of the magnetic field becomes comparable to the intensity of velocity field fluctuations. We have also studied the influence of the Pm on the efficiency of small-scale dynamo in spin-down flows. In the experimental spin-down flows, the small-scale dynamo remains in a quasi-kinematic regime, and magnetic energy is mainly dissipated at the same scale, wherein it is converted from kinetic energy. The real small-scale dynamo starts to operate at Pm>10^{-4}, and the inertial range of the magnetic energy spectrum appears. Thereupon the energy dissipation is postponed to a later time and smaller scales, and the peak of turbulent energy (both kinetic and magnetic) slightly increases with Pm.