Energy distribution in nonaxisymmetric magnetic Taylor-Couette flow

Azimuthal magnetorotational instability is a mechanism that generates nonaxisymmetric field pattern. Nonlinear simulations in an infinite Taylor-Couette system with current-free external field show, that not only the linearly unstable mode m = 1 appears, but also an inverse cascade transporting energy into the axisymmetric field is possible. By varying the Reynolds number of the flow and the Hartmann number for the magnetic field, we find that the ratio between axisymmetric (m = 0) and dominating nonaxisymmetric mode (m = 1) can be nearly free chosen. On the surface of the outer cylinder this mode distribution appears similarly, but with weaker axisymmetric fields.We do not find significant differences in the case that a constant current within the flow is added. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On global solar dynamo simulations

Global dynamo simulations solving the equations of magnetohydrodynamics (MHD) have been a tool of astrophysicists who try to understand the magnetism of the Sun for several decades now. During recent years many fundamental issues in dynamo theory have been studied in detail by means of local numerical simulations that simplify the problem and allow the study of physical effects in isolation. Global simulations, however, continue to suffer from the age‐old problem of too low spatial resolution, leading to much lower Reynolds numbers and scale separation than in the Sun. Reproducing the internal rotation of the Sun, which plays a crucial role in the dynamo process, has also turned out to be a very difficult problem. In the present paper the current status of global dynamo simulations of the Sun is reviewed. Emphasis is put on efforts to understand how the large‐scale magnetic fields, i.e. whose length scale is greater than the scale of turbulence, are generated in the Sun. Some lessons from mean‐field theory and local simulations are reviewed and their possible implications to the global models are discussed. Possible remedies to some current issues of solar simulations are put forward (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling a Maunder minimum

We introduce on/off intermittency into a mean field dynamo model by imposing stochastic fluctuations in either the alpha effect or through the inclusion of a fluctuating electromotive force. Sufficiently strong small scale fluctuations with time scales of the order of 0.3–3 years can produce long term variations in the system on time scales of the order of hundreds of years. However, global suppression of magnetic activity in both hemispheres at once was not observed. The variation of the magnetic field does not resemble that of the sunspot number, but is more reminiscent of the ¹⁰Be record. The interpretation of our results focuses attention on the connection between the level of magnetic activity and the sunspot number, an issue that must be elucidated if long term solar effects are to be well understood. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Recent Progress of Hemispheric Coupling of Solar Activity Cycle

The hemispheric coupling phenomenon of solar activity cycle was discovered as early as the mid-20th century, and it is one of the most common topic in the long-term spatio-temporal evolution of the Sun, while the observational features and physical mechanism of hemispheric coupling have not been completely understood. The theoretical model of solar magnetohydrodynamics driven by this phenomenon is helpful in studying the basic information of the spatio-temporal evolution of solar activity cycle, and is also of great value to the short- and medium-term forecast of solar activity as well as the space weather. Here, we first give the discovery and observational history of the hemispheric coupling of solar activity. And then, the basic observational features of hemispheric coupling at different spatio-temporal scales and their possible mechanism are summarized. Finally, we give a discussion about the important unresolved issues and development trends in this important field.     

Equatorial magnetic helicity flux in simulations with different gauges

We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small‐scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo‐Lorenz gauge, where the speed of light is replaced by the sound speed, and the ‘resistive gauge’ in which the Laplacian of the magnetic vector potential acts as a resistive term. We find that, in the statistically steady state, the time‐averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear simulations of magnetic Taylor‐Couette flow with currentfree helical magnetic fields

Themagnetorotational instability (MRI) in cylindrical Taylor‐Couette flow with external helical magnetic field is simulated for infinite and finite aspect ratios. We solve the MHD equations in their small Prandtl number limit and confirm with timedependent nonlinear simulations that the additional toroidal component of the magnetic field reduces the critical Reynolds number from O (10⁶) (axial field only) to O (10³) for liquid metals with their small magnetic Prandtl number. Computing the saturated state we obtain velocity amplitudes which help designing proper experimental setups. Experiments with liquid gallium require axial field ∼50 Gauss and axial current ∼4 kA for the toroidal field. It is sufficient that the vertical velocity u_z of the flow can be measured with a precision of 0.1 mm/s.We also show that the endplates enclosing the cylinders do not destroy the traveling wave instability which can be observed as presented in earlier studies. For TC containers without and with endplates the angular momentum transport of the MRI instability is shown as to be outwards. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

3-D non-linear evolution of a magnetic flux tube in a spherical shell: The isentropic case

We present recent 3-D MHD numerical simulations of the non-linear dynamical evolution of magnetic flux tubes in an adiabatically stratified convection zone in spherical geometry, using the anelastic spherical harmonic (ASH) code.We seek to understand the mechanism of emergence of strong toroidal fields from the base of the solar convection zone to the solar surface as active regions. We confirm the results obtained in cartesian geometry that flux tubes that are not twisted split into two counter vortices before reaching the top of the convection zone. Moreover, we find that twisted tubes undergo the poleward-slip instability due to an unbalanced magnetic curvature force which gives the tube a poleward motion both in the non-rotating and in the rotating case. This poleward drift is found to be more pronounced on tubes originally located at high latitudes. Finally, rotation is found to decrease the rise velocity of the flux tubes through the convection zone, especially when the tube is introduced at low latitudes. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The dual role of shear in large‐scale dynamos

The role of shear in alleviating catastrophic quenching by shedding small‐scale magnetic helicity through fluxes along contours of constant shear is discussed. The level of quenching of the dynamo effect depends on the quenched value of the turbulent magnetic diffusivity. Earlier estimates that might have suffered from the force‐free degeneracy of Beltrami fields are now confirmed for shear flows where this degeneracy is lifted. For a dynamo that is saturated near equipartition field strength those estimates result in a 5‐fold decrease of the magnetic diffusivity as the magnetic Reynolds number based on the wavenumber of the energy‐carrying eddies is increased from 2 to 600. Finally, the role of shear in driving turbulence and large‐scale fields by the magneto‐rotational instability is emphasized. New simulations are presented and the 3π /4 phase shift between poloidal and toroidal fields is confirmed. It is suggested that this phase shift might be a useful diagnostic tool in identifying mean‐field dynamo action in simulations and to distinguish this from other scenarios invoking magnetic buoyancy as a means to explain migration away from the midplane. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)