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

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