We explore a response of a non-linear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservat
ion, and the depth of perturbation. It is found that a perturbation which is anchored at r=0.9R has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric with respect to the equator perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on the turbulent magnetic Reynolds number R_m. In the range of R_m=10^{4-6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a non-linear alpha-effect and magnetic buoyancy. In the stationary state the large-scale magnetic field demonstrates a phenomenon of active longitudes with cyclic 180 degree flip-flop changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However this effect disappears in the model which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period, and carries important information about the dynamo process.
Parameters of magnetic activity on the solar type stars depend on the properties of the dynamo processes operating in stellar convection zones. We apply nonlinear mean-field axisymmetric $alpha^2Omega$ dynamo models to calculate of the magnetic cycle
parameters, such as the dynamo cycle period, the total magnetic flux and the Poynting magnetic energy flux on the surface of solar analogs with the rotation periods from 15 to 30 days. The models take into account the principal nonlinear mechanisms of the large-scale dynamo, such as the magnetic helicity conservation, magnetic buoyancy, and effects of magnetic forces on the angular momentum balance inside the convection zones. Also, we consider two types of the dynamo models. The distributed (D-type) models employ the standard alpha-effect distributed on the whole convection zone. The boundary (B-type) models employ the non-local alpha- effect, which is confined to the boundaries of the convection zone. Both the D- and B-type models show that the dynamo-generated magnetic flux increases with the increase of the stellar rotation rate. {It is found that for the considered range of the rotational periods} the magnetic helicity conservation is the most significant effect for the nonlinear quenching of the dynamo. This quenching is more efficient in the B-type than in the D-type dynamo models. The D-type dynamo reproduces the observed dependence of the cycle period on the rotation rate for the Sun analogs. For the solar analog rotating with a period of 15 days we find nonlinear dynamo regimes with multiply cycles.
We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of
the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.
We study the effect of turbulent drift of a large-scale magnetic field that results from the interaction of helical convective motions and differential rotation in the solar convection zone. The principal direction of the drift corresponds to the dir
ection of the large-scale vorticity vector. Thus, the effect produces a latitudinal transport of the large-scale magnetic field in the convective zone wherever the angular velocity has a strong radial gradient. The direction of the drift depends on the sign of helicity and it is defined by the Parker-Yoshimura rule. The analytic calculations are done within the framework of mean-field magnetohydrodynamics using the minimal tau-approximation. We estimate the magnitude of the drift velocity and find that it can be several m/s near the base of the solar convection zone. The implications of this effect for the solar dynamo are illustrated on the basis of an axisymmetric mean-field dynamo model with a subsurface shear layer. We find that the helicity--vorticity pumping effect can have an influence on the features of the sunspot time--latitude diagram, producing a fast drift of the sunspot activity maximum at the rise phase of the cycle and a slow drift at the decay phase of the cycle.
We study the possibility to reproduce the statistical relations of the sunspot activity cycle, like the so-called Waldmeier relations, the cycle period - amplitude and the cycle rise rate - amplitude relations, by means of the mean field dynamo model
s with the fluctuating alpha-effect. The dynamo model includes the long-term fluctuations of the alpha-effect and two types of the nonlinear feedback of the mean-field on the alpha-effect including the algebraic quenching and the dynamic quenching due to the magnetic helicity generation. We found that the models are able to reproduce qualitatively and quantitatively the inclination and dispersion across the Waldmeier relations with the 20% fluctuations of the alpha-effect. The models with the dynamic quenching are in a better agreement with observations than the models with the algebraic alpha-quenching. We compare the statistical distributions of the modeled parameters, like the amplitude, period, the rise and decay rates of the sunspot cycles, with observations.
We study axisymmetric mean-field dynamo models containing differential rotation, the $alpha$ effect and the additional turbulent induction effects. The additional effects result from the combined action of rotation and an inhomogeneity of the large-s
cale magnetic field. The best known of them is the $vec{Omega}timesvec{J}$ effect. We also include anisotropic diffusion and a new dynamo term which is of third order in the rotation vector $vec{Omega}$ The model calculations are carried out using the rotation profile of the Sun as obtained from helioseismic measurements and radial profiles of other quantities according to a standard model of the solar interior. In addition, we consider a dynamo model for a full sphere which is solely based on the joint induction effects of rotation and an inhomogeneity of the large-scale magnetic field, without differential rotation and the $alpha$ effect (a $delta^{2}$ dynamo model). This kind of dynamo model may be relevant for fully convective stars.
Recently, Jouve et al(A&A, 2008) published the paper that presents the numerical benchmark for the solar dynamo models. Here, I would like to show a way how to get it with help of computer algebra system Maxima. This way was used in our paper (Pipin
& Seehafer, A&A 2008, in print) to test some new ideas in the large-scale stellar dynamos. In the present paper I complement the dynamo benchmark with the standard test that address the problem of the free-decay modes in the sphere which is submerged in vacuum.
