MHD Turbulence in spin-down flows of liquid metals

TL;DR

This study investigates the small-scale dynamo effects in liquid metal spin-down flows, revealing that sodium flows exhibit strong magnetic induction at high rotation speeds, with dynamo efficiency influenced by magnetic Prandtl number.

Contribution

The paper extends simulations of liquid metal spin-down flows beyond laboratory limits, analyzing dynamo effects at high rotation speeds and varying magnetic Prandtl numbers, providing new insights into magnetic energy generation.

Findings

Sodium flows show strong magnetic induction at high rotation velocities.

Dynamo effects become significant at rotation speeds around 100 rps.

Small-scale dynamo efficiency depends on magnetic Prandtl number, activating at Pm>10^{-4}.

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.