Alpha-effect in three-dimensional coherent vortex of conducting rotating liquid

TL;DR

This paper analytically investigates the alpha-effect in three-dimensional rotating conducting liquids with vortex turbulence, revealing how the effect depends on Rossby and magnetic Prandtl numbers and identifying conditions for magnetic field instability.

Contribution

It provides an analytical calculation of the alpha-effect in rotating conducting fluids, linking it to key dimensionless parameters and establishing criteria for magnetic field instability.

Findings

Alpha-effect elements depend on Rossby and magnetic Prandtl numbers.

Criteria for alpha-effect-induced magnetic field instability are established.

Analytical expressions for velocity-vorticity mean and anisotropy are derived.

Abstract

We study one-point statistics of spiral turbulent pulsations on the background of three-dimensional large-scale vortex in a rotating fluid. Assuming that the helical flow is created by a statistically axially symmetric random force with broken mirror symmetry, we analytically calculate velocity-vorticity mean including its magnitude and the anisotropy. For electrically conducting liquid, we examine the $\alpha$-effect in the system. The found elements of $\alpha$-matrix strongly depend on relation between Rossby $\mathrm{Ro}$ and magnetic Prandtl $\mathrm{Pr}_{\mathrm{m}}$ numbers in considered region $\mathrm{Ro}\lesssim 1$, $\mathrm{Pr}_{\mathrm{m}} \lesssim 1$. We establish criterion for the numbers when the $\alpha$-effect leads to instability of large-scale magnetic field