Title: 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.