TY - JOUR A1 - Rüdiger, Günther A1 - Schultz, Manfred T1 - On the toroidal-velocity antidynamo theorem under the presence of nonuniform electric conductivity JF - Astronomische Nachrichten = Astronomical notes N2 - Laminar electrically conducting Couette flows with the hydrodynamically stable quasi-Keplerian rotation profile and nonuniform conductivity are probed for dynamo instability. In spherical geometry, the equations for the poloidal and the toroidal field components completely decouple, resulting in free decay, regardless of the spatial distribution of the electric conductivity. In cylindrical geometry the poloidal and toroidal components do not decouple, but here also we do not find dynamo excitations for the cases that the electric conductivity only depends on the radius or - much more complex- that it only depends on the azimuthal or the axial coordinate. The transformation of the plane-flow dynamo model of Busse and Wicht (1992) to cylindrical or spherical geometry therefore fails. It is also shown that even the inclusion of axial flows of both directions does not support the dynamo mechanism. The Elsasser toroidal-velocity antidynamo theorem, according to which dynamos without any radial velocity component cannot work, is thus not softened by nonuniform conductivity distributions. KW - antidynamo theorem KW - MHD KW - Taylor-Couette flow Y1 - 2022 U6 - https://doi.org/10.1002/asna.20224011 SN - 0004-6337 SN - 1521-3994 VL - 343 IS - 5 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Rüdiger, Günther A1 - Küker, Manfred T1 - Angular momentum transport by magnetoconvection and the magnetic modulation of the solar differential rotation JF - Astronomy and astrophysics : an international weekly journal / European Southern Observatory (ESO) N2 - In order to explain the variance of the solar rotation law during the activity minima and maxima, the angular momentum transport by rotating magnetoconvection is simulated in a convective box penetrated by an inclined azimuthal magnetic field. Turbulence-induced kinetic and magnetic stresses and the Lorentz force of the large-scale magnetic background field are the basic transporters of angular momentum. Without rotation, the sign of the magnetic stresses naturally depends on the signs of the field components as positive (negative) B theta B phi transport the angular momentum poleward (equatorward). For fast enough rotation, however, the turbulence-originated Reynolds stresses start to dominate the transport of the angular momentum flux. The simulations show that positive ratios of the two meridional magnetic field components to the azimuthal field reduce the inward radial as well as the equatorward latitudinal transport, which result from hydrodynamic calculations. Only for B theta B phi>0 (generated by solar-type rotation laws with an accelerated equator) does the magnetic-influenced rotation at the solar surface prove to be flatter than the nonmagnetic profile together with the observed slight spin-down of the equator. The latter phenomenon does not appear for antisolar rotation with polar vortex as well as for rotation laws with prevailing radial shear. KW - magnetic fields KW - Sun KW - rotation KW - convection Y1 - 2021 U6 - https://doi.org/10.1051/0004-6361/202039912 SN - 1432-0746 VL - 649 PB - EDP Sciences CY - Les Ulis ER - TY - JOUR A1 - Rüdiger, Günther A1 - Schultz, Manfred A1 - Hollerbach, Rainer T1 - Destabilization of super-rotating Taylor-Couette flows by current-free helical magnetic fields JF - Journal of plasma physics N2 - In an earlier paper we showed that the combination of azimuthal magnetic fields and super-rotation in Taylor-Couette flows of conducting fluids can be unstable against non-axisymmetric perturbations if the magnetic Prandtl number of the fluid is Pm not equal 1. Here we demonstrate that the addition of a weak axial field component allows axisymmetric perturbation patterns for Pm of order unity depending on the boundary conditions. The axisymmetric modes only occur for magnetic Mach numbers (of the azimuthal field) of order unity, while higher values are necessary for the non-axisymmetric modes. The typical growth time of the instability and the characteristic time scale of the axial migration of the axisymmetric mode are long compared with the rotation period, but short compared with the magnetic diffusion time. The modes travel in the positive or negative z direction along the rotation axis depending on the sign of B phi Bz. We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if vertical bar B phi vertical bar >> vertical bar B-z vertical bar, independent of the form of the rotation law. Within a short-wave approximation for thin gaps it is also shown (in an appendix) that for ideal fluids the considered helical magnetorotational instability only exists for rotation laws with negative shear. KW - plasma instabilities KW - astrophysical plasmas Y1 - 2021 U6 - https://doi.org/10.1017/S0022377821000295 SN - 1469-7807 VL - 87 IS - 2 PB - Cambridge University Press CY - London ER - TY - JOUR A1 - Rüdiger, Günther A1 - Schultz, Manfred T1 - Large-scale dynamo action of magnetized Taylor-Couette flows JF - Monthly notices of the Royal Astronomical Society N2 - 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 non-axisymmetric perturbations which form electromotive forces defining a effect and eddy diffusivity. If both degenerated modes with m = +/- 1 are excited with the same power then the global a 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 Omega dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of Rm similar or equal to 2000 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(T) similar or equal to eta. By basically lower or larger eddy diffusivities the dynamo instability is suppressed. KW - dynamo KW - instabilities KW - MHD KW - magnetic fields Y1 - 2020 U6 - https://doi.org/10.1093/mnras/staa293 SN - 0035-8711 SN - 1365-2966 VL - 493 IS - 1 SP - 1249 EP - 1260 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Rüdiger, Günther A1 - Küker, Manfred A1 - Käpylä, Petri J. T1 - Electrodynamics of turbulent fluids with fluctuating electric conductivity JF - Journal of plasma physics N2 - Consequences of fluctuating microscopic conductivity in mean-field electrodynamics of turbulent fluids are formulated and discussed. If the conductivity fluctuations are assumed to be uncorrelated with the velocity fluctuations then only the turbulence-originated magnetic diffusivity of the fluid is reduced and the decay time of a large-scale magnetic field or the cycle times of oscillating turbulent dynamo models are increased. If, however, the fluctuations of conductivity and flow in a certain well-defined direction are correlated, an additional diamagnetic pumping effect results, transporting the magnetic field in the opposite direction to the diffusivity flux vector . In the presence of global rotation, even for homogeneous turbulence fields, an alpha effect appears. If the characteristic values of the outer core of the Earth or the solar convection zone are applied, the dynamo number of the new alpha effect does not reach supercritical values to operate as an alpha(2)-dynamo but oscillating alpha Omega-dynamos with differential rotation are not excluded. KW - astrophysical plasmas KW - plasma flows Y1 - 2020 U6 - https://doi.org/10.1017/S0022377820000665 SN - 0022-3778 SN - 1469-7807 VL - 86 IS - 3 PB - Cambridge Univ. Press CY - London ER - TY - JOUR A1 - Rüdiger, Günther A1 - Schultz, M. T1 - Non-diffusive angular momentum transport in rotating z-pinches JF - Journal of plasma physics N2 - The stability of conducting Taylor-Couette flows under the presence of toroidal magnetic background fields is considered. For strong enough magnetic amplitudes such magnetohydrodynamic flows are unstable against non-axisymmetric perturbations which may also transport angular momentum. In accordance with the often used diffusion approximation, one expects the angular momentum transport to be vanishing for rigid rotation. In the sense of a non-diffusive Lambda effect, however, even for rigidly rotating z-pinches, an axisymmetric angular momentum flux appears which is directed outward (inward) for large (small) magnetic Mach numbers. The internal rotation in a magnetized rotating tank can thus never be uniform. Those particular rotation laws are used to estimate the value of the instability-induced eddy viscosity for which the non-diffusive Lambda effect and the diffusive shear-induced transport compensate each other. The results provide the Shakura & Sunyaev viscosity ansatz leading to numerical values linearly growing with the applied magnetic field. KW - plasma instabilities KW - astrophysical plasmas Y1 - 2019 U6 - https://doi.org/10.1017/S0022377819000606 SN - 0022-3778 SN - 1469-7807 VL - 85 IS - 6 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Rüdiger, Günther A1 - Küker, Manfred A1 - Kapyla, P. J. A1 - Strassmeier, Klaus G. T1 - Antisolar differential rotation of slowly rotating cool stars JF - Astronomy and astrophysics : an international weekly journal N2 - Rotating stellar convection transports angular momentum towards the equator, generating the characteristic equatorial acceleration of the solar rotation while the radial flux of angular momentum is always inwards. New numerical box simulations for the meridional cross-correlation < u(theta)u(phi)>, however, reveal the angular momentum transport towards the poles for slow rotation and towards the equator for fast rotation. The explanation is that for slow rotation a negative radial gradient of the angular velocity always appears, which in combination with a so-far neglected rotation-induced off-diagonal eddy viscosity term nu(perpendicular to) provides "antisolar rotation" laws with a decelerated equator Similarly, the simulations provided positive values for the rotation-induced correlation < u(r)u(theta)>, which is relevant for the resulting latitudinal temperature profiles (cool or warm poles) for slow rotation and negative values for fast rotation. Observations of the differential rotation of slowly rotating stars will therefore lead to a better understanding of the actual stress-strain relation, the heat transport, and the underlying model of the rotating convection. KW - stars: solar-type KW - convection KW - stars: rotation KW - turbulence Y1 - 2019 U6 - https://doi.org/10.1051/0004-6361/201935280 SN - 1432-0746 VL - 630 PB - EDP Sciences CY - Les Ulis ER -