Large-scale dynamo action of magnetized Taylor-Couette flows

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 $α\Om$ dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of $\mathrm{Rm}\simeq 2.000$ 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, ${\eta }_{\mathrm{T}}\simeq \eta$. By basically lower or larger eddy diffusivities the dynamo instability is suppressed.

12 pages, 12 figures

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Cited by in corpus (2)

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• Transition to chaos and modal structure of magnetized Taylor-Couette flow