Valery Pipin

Helicity and the solar dynamo

The central mechanism in traditional mean-field dynamo theory is the α-effect, and it has been found that the presence of kinetic or magnetic helicities is favourable for the effect, which corresponds to the simultaneous generation of magnetic helicities in the mean field and in the fluctuations, the generation rates being equal in magnitude and opposite in sign. Generally, the two helicities generated by the α-effect, that in the mean field and that in the fluctuations, have either to be dissipated in the generation region or to be transported out of this region. The latter presumably leads to the observed appearance of magnetic helicity in the solar atmosphere, which thus provides valuable information on dynamo processes inaccessible to in situ measurements. We have included details of two numerical dynamo studies in the present review, one for a “laminar” dynamo, where no averaging is applied, the other for a mean-field dynamo. In the first case the full nonlinear system of the incompressible MHD equations is studied in idealized rectangular geometry, with an external forcing of the Roberts type driving a flow in the form of an array of convection-like rolls. Defining mean fields by appropriate averages, it is found that there is a segregation of magnetic helicity between the mean field and the fluctuations similar to that predicted by the mean-field theory of the α-effect. The mean-field calculations are done in a quasi-linear approximation for the turbulence, for realistic spherical geometry, with compressibihy included and using a profile of the solar internal rotation rate obtained from helioseismic inversions. The results are compared with observations, concentrating on the observational finding that the moduli of the averaged values of the force-free twist parameter αff and and the current helicity HC increase from zero at the equator towards higher latitudes and attain a certain saturation level at middle latitudes (at about 20°–30°). On the assumption that the α-effect is operating in a thin spherical shell, the best coincidence between calculated and observed quantities is found for α-effect operation close to the bottom of the convection zone.

TURBULENT CROSS-HELICITY IN THE MEAN-FIELD SOLAR DYNAMO PROBLEM

We study the dynamical and statistical properties of turbulent cross-helicity (correlation of the aligned fluctuating velocity and magnetic field components). We derive an equation governing generation and evolution of the turbulent cross-helicity and discuss its meaning for the dynamo. Using the symmetry properties of the problem we suggest a general expression for the turbulent cross-helicity. Effects of the density stratification, large-scale magnetic fields, differential rotation, and turbulent convection are taken into account. We investigate the relative contribution of these effects to the cross-helicity evolution for two kinds of dynamo models of the solar cycle: a distributed mean-field model and a flux-transport dynamo model. We show that the contribution from the density stratification follows the evolution of the radial magnetic field, while large-scale electric currents produce a more complicated pattern of the cross-helicity of comparable magnitude. The pattern of the cross-helicity evolution strongly depends on details of the dynamo mechanism. Thus, we anticipate that direct observations of the cross-helicity on the Sun may serve for the diagnostic purpose of the solar dynamo process.

A new simple dynamo model for stellar activity cycle

A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous mean flow effect on turbulence, it is shown that turbulent cross helicity (velocity--magnetic-field correlation) should enter the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. The inclusion of the cross-helicity effect makes the present model different from the current

Generation of a Large-scale Magnetic Field in a Convective Full-sphere Cross-helicity Dynamo

alpha

Angular momentum fluxes caused by Λ-effect and meridional circulation structure of the Sun

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Advances in mean-field dynamo theories

Omega

On the Origin of the Double-cell Meridional Circulation in the Solar Convection Zone

-type models mainly in two points. First, in addition to the usual

DEPENDENCE OF STELLAR MAGNETIC ACTIVITY CYCLES ON ROTATIONAL PERIOD IN A NONLINEAR SOLAR-TYPE DYNAMO

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Probing current and cross-helicity in the solar atmosphere: A challenge for theory

(helicity effect) and

Helioseismic Constraints and Paradigm Shift in Solar Dynamo

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