Suppression of the large-scale Lorentz force by turbulence

The components of the total stress tensor (Reynolds stress plus Maxwell stress) are computed within the quasilinear approximation for a driven turbulence influenced by a large-scale magnetic background field. The conducting fluid has an arbitrary magnetic Prandtl number and the turbulence without the background field is assumed as homogeneous and isotropic with a free Strouhal number St. The total large-scale magnetic tension is always reduced by the turbulence with the possibility of a `catastrophic quenching' for large magnetic Reynolds number Rm so that even its sign is reversed. The total magnetic pressure is enhanced by turbulence with short correlation time (`white noise') but it is reduced by turbulence with long correlation time. Also in this case the sign of the total pressure may reverse but only for special turbulences with sufficiently large St> 1. The turbulence-induced terms of the stress tensor are suppressed by strong magnetic fields. For the tension term this quenching grows with the square of the Hartmann number of the magnetic field. For microscopic (i.e. small) diffusivity values the magnetic tension term becomes thus highly quenched even for field amplitudes much smaller than their equipartition value. In the opposite case of large-eddy simulations the magnetic quenching is only mild but then also the turbulence-induced Maxwell tensor components for weak fields remain rather small.Comment: 7 pages, 5 figures, submitted to Astron. Nach

The negative magnetic pressure effect in stratified turbulence

While the rising flux tube paradigm is an elegant theory, its basic assumptions, thin flux tubes at the bottom of the convection zone with field strengths two orders of magnitude above equipartition, remain numerically unverified at best. As such, in recent years the idea of a formation of sunspots near the top of the convection zone has generated some interest. The presence of turbulence can strongly enhance diffusive transport mechanisms, leading to an effective transport coefficient formalism in the mean-field formulation. The question is what happens to these coefficients when the turbulence becomes anisotropic due to a strong large-scale mean magnetic field. It has been noted in the past that this anisotropy can also lead to highly non-diffusive behaviour. In the present work we investigate the formation of large-scale magnetic structures as a result of a negative contribution of turbulence to the large-scale effective magnetic pressure in the presence of stratification. In direct numerical simulations of forced turbulence in a stratified box, we verify the existence of this effect. This phenomenon can cause formation of large-scale magnetic structures even from initially uniform large-scale magnetic field.Comment: 5 pages, 2 figures, submitted conference proceedings IAU symposium 273 "Physics of Sun and Star Spots

Magnetic Helicity Evolution During the Solar Activity Cycle: Observations and Dynamo Theory

We study a simple model for the solar dynamo in the framework of the Parker migratory dynamo, with a nonlinear dynamo saturation mechanism based on magnetic helicity conservation arguments. We find a parameter range in which the model demonstrates a cyclic behaviour with properties similar to that of Parker dynamo with the simplest form of algebraic alpha-quenching. We compare the nonlinear current helicity evolution in this model with data for the current helicity evolution obtained during 10 years of observations at the Huairou Solar Station of China. On one hand, our simulated data demonstrate behaviour comparable with the observed phenomenology, provided that a suitable set of governing dynamo parameters is chosen. On the other hand, the observational data are shown to be rich enough to reject some other sets of governing parameters. We conclude that, in spite of the very preliminary state of the observations and the crude nature of the model, the idea of using observational data to constrain our ideas concerning magnetic field generation in the framework of the solar dynamo appears promising.Comment: 10 pages, 3 Postscript figures, uses aa.cl

The dynamics of Wolf numbers based on nonlinear dynamo with magnetic helicity: comparisons with observations

We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution of Wolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behavior of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 years ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 % correlation over all intervals of observation (about 270 years). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependencies are in good agreement with observations.Comment: 9 pages, 13 figures, final revised paper for MNRA