Large-scale dynamo action of magnetized Taylor-Couette flows

TL;DR

This paper investigates the conditions under which large-scale magnetic dynamos can operate in magnetized Taylor-Couette flows with quasi-Keplerian rotation, highlighting the roles of the Tayler instability, alpha effects, and turbulence assumptions.

Contribution

It demonstrates that a mean-field dynamo requires specific conditions on mode excitation, magnetic Reynolds number, and turbulence energy dependence, providing new insights into dynamo mechanisms in Taylor-Couette flows.

Findings

Finite alpha effects can be produced by the Tayler instability for single modes.

A minimum magnetic Reynolds number of about 2000 is needed for the alpha-omega dynamo.

Dynamo excitation depends critically on turbulence energy dependence and eddy diffusivity values.

Abstract

A conducting Taylor-Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler-Spruit-type. The flows are unstable against nonaxisymmetric perturbations which form electromotive forces defining $\alpha$ effect and eddy diffusivity. If both degenerated modes with $m=\pm 1$ are excited with the same power then the global $\alpha$ effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite $\alpha$ effects if only an isolated mode is considered but this intrinsic helicity of the single-mode is too low for an $\alpha^2$ dynamo. Moreover, an $\alpha\Om$ dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of ${\rm Rm}\simeq 2.000$ to work. Whether it really works depends on assumptions about the turbulence energy. For a steeper-than-quadratic dependence of the turbulence intensity on the magnetic field, however, dynamos are only excited if the resulting magnetic eddy diffusivity approximates its microscopic value, $\eta_{\rm T}\simeq \eta$. By basically lower or larger eddy diffusivities the dynamo instability is suppressed.