arXiv subjects

V. V. Pipin

Publications and source records attributed to V. V. Pipin.

52 records · Page 3Linked to original sources

arXiv2012

Helicity conservation in nonlinear mean-field solar dynamo

We explore the impact of magnetic helicity conservation on the mean-field solar dynamo using the axisymmetric dynamo model which includes the subsurface shear. Our results support the recent findings by Hubbard & Brandenburg (2012), who suggested that the catastrophic quenching in the mean-field dynamo is alleviated if conservation of the total magnetic helicity is taken into account. We show that the solar dynamo can operate in the wide rage of the magnetic Reynolds number up to $10^{6}$. We also found that the boundary conditions for the magnetic helicity influence the distribution of the $α$-effect near the solar surface.

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arXiv2012

Helicity-vorticity turbulent pumping of magnetic fields in solar convection zone

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 direction 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 τ-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.

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arXiv2012

Variations of the solar cycle profile in a solar dynamo with fluctuating dynamo governing parameters

Solar cycles vary in their amplitude and shape. There are several empirical relations between various parameters linking cycle's shape and amplitude, in particular the Waldmeier relations. As solar cycle is believed to be a result of the solar dynamo action, these relations require explanation in the framework of this theory.Here we aim to present a possible explanation of such kind. We relate the cycle-to-cycle variability of solar activity to fluctuations of solar dynamo drivers and primarily to fluctuations in the parameter responsible for recovery of the poloidal magnetic field from the toroidal one. To be specific, we develop such a model in the framework of the mean-field dynamo based on the differential rotation and $α$-effect. We demonstrate that the mean-field dynamo based on a realistic rotation curve and nonlinearity associated with the magnetic helicity balance reproduces both qualitatively and quantitatively the Waldmeier relations observed in sunspot data since 1750 (SIDC data). The model also reproduces more or less successfully other relations between the parameters under discussion, in particular, the link between odd and even cycles (Gnevyshev-Ohl rule). We conclude that the contemporary solar dynamo theory provides a way to explain the cycle-to-cycle variability of solar activity as recorded in sunspots. We discuss the importance of the model for stellar activity cycles which, as known from the data of HK project, demonstrate the cycle-to-cycle variability similar to solar cycles.

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arXiv2011

The fluctuating α-effect and Waldmeier relations in the nonlinear dynamo models

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 models with the fluctuating α-effect. The dynamo model includes the long-term fluctuations of the α-effect and two types of the nonlinear feedback of the mean-field on the α-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 α-effect. The models with the dynamic quenching are in a better agreement with observations than the models with the algebraic α-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.

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arXiv2011

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 symmetry properties of the problem we suggest a general expression for the turbulent cross-helicity pseudo-scalar and compute the turbulent coefficients in this expression. 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 including 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 the comparable magnitude. We suggest that the results of observational analysis of the cross-helicity will depend on the averaging scales. Our results show that 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.

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arXiv2011

The asymmetry of sunspot cycles and Waldmeier relations as due to nonlinear surface-shear shaped dynamo

The paper presents a study of a solar dynamo model operating in the bulk of the convection zone with the toroidal magnetic field flux concentrated in the subsurface rotational shear layer. We explore how this type of dynamo may depend on spatial variations of turbulent parameters and on the differential rotation near the surface. The mean-field dynamo model takes into account the evolution of magnetic helicity and describes its nonlinear feedback on the generation of large-scale magnetic field by the $α$-effect. We compare the magnetic cycle characteristics predicted by the model, including the cycle asymmetry (associated with the growth and decay times) and the duration - amplitude relation (Waldmeier's effects), with the observed sunspot cycle properties. We show that the model qualitatively reproduces the basic properties of the solar cycles.

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arXiv2011

Mean-field solar dynamo models with strong meridional flow at the bottom of the convection zone

The paper presents a study of kinematic axisymmetric mean-field dynamo models for a case of the meridional circulation with a deep-seated stagnation point and a strong return flow at the bottom of the convection zone. This kind of circulation follows from mean-field models of the angular momentum balance in the solar convection zone. We show that it is possible for this types of meridional circulation to construct kinematic dynamo models that resemble in some aspects the sunspot magnetic activity cycle. The dynamo model includes turbulent sources of the large-scale poloidal magnetic field production, due to kinetic helicity and a combined effect due to Coriolis force and the large-scale current. In these models the toroidal magnetic field, which is responsible for the sunspot production, is concentrated at the bottom of the convection zone, and is transported to low-latitude regions by the meridional flow. The meridional component of the poloidal field is also concentrated at the bottom of the convection zone while the radial component is concentrated in near polar regions. There are some issues which, perhaps, are resulted from the given meridional circulation pattern and the distribution of the magnetic diffusivity inside convection zone. In particular, in the near-equatorial regions the phase relations between the toroidal and poloidal components disagree with observations. Also, we show that the period of the magnetic cycle may not always monotonically decrease with the increase of the meridional flow speed. Thus, for the further progress it is important to determine the structure of the meridional circulation, which is one of the critical properties, from helioseismology observations.

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arXiv2010

The subsurface-shear shaped solar $αΩ$ dynamo

We propose a solar dynamo model distributed in the bulk of the convection zone with the toroidal magnetic field the flux concentrated in the near-surface layer. We show that if the boundary conditions at the top of the dynamo region allow the large-scale toroidal magnetic fields to penetrate closer to the surface, then the pattern of the modeled butterfly diagram for the toroidal magnetic fields in the upper part of the convection zone is formed by the surface rotational shear layer. The model is in agreement with observed properties of the magnetic solar cycle.

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arXiv2009

An advective solar-type dynamo without the alpha effect

Context: Most solar and stellar dynamo models use the alpha-Omega scenario where the magnetic field is generated by the interplay between differential rotation (the Omega effect) and a mean electromotive force due to helical turbulent convection flows (the alpha effect). There are, however, turbulent dynamo mechnisms that may complement the alpha effect or may be an alternative to it. Aims: We investigate models of solar-type dynamos where the alpha effect is completely replaced by two other turbulent dynamo mechanisms, namely the Omega x J effect and the shear-current effect, which both result from an inhomogeneity of the mean magnetic field. Methods: We studied axisymmetric mean-field dynamo models containing differential rotation, the Omega x J and shear-current effects, and a meridional circulation. The model calculations were 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. Results: Without meridional flow, no satisfactory agreement of the models with the solar observations can be obtained. With a sufficiently strong meridional circulation included, however, the main properties of the large-scale solar magnetic field, namely, its oscillatory behavior, its latitudinal drift towards the equator within each half cycle, and its dipolar parity with respect to the equatorial plane, are correctly reproduced. Conclusions: We have thereby constructed the first mean-field models of solar-type dynamos that do not use the alpha effect.

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arXiv2008

On the turbulent sources of the solar dynamo

We revisit the possible turbulent sources of the solar dynamo. Studying axisymmetric mean-field dynamo models, we find that the large-scale poloidal magnetic field could be generated not only by the famous alpha effect, but also by the Omega x J and shear-current effects. The inclusion of these additional turbulent sources alleviates several of the known problems of solar mean-field dynamo models.

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arXiv2008

Stellar dynamos with $\vecΩ\times \vec{J}$ effect

We study axisymmetric mean-field dynamo models containing differential rotation, the $α$ effect and the additional turbulent induction effects. The additional effects result from the combined action of rotation and an inhomogeneity of the large-scale magnetic field. The best known of them is the $\vecΩ\times\vec{J}$ effect. We also include anisotropic diffusion and a new dynamo term which is of third order in the rotation vector $\vecΩ$ 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 $α$ effect (a $δ^{2}$ dynamo model). This kind of dynamo model may be relevant for fully convective stars.

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arXiv2007

Closure tests for mean field magnetohydrodynamics using a self consistent reduced model

The mean electromotive force and alpha effect are computed for a forced turbulent flow using a simple nonlinear dynamical model. The results are used to check the applicability of two basic analytic ansatze of mean-field magnetohydrodynamics - the second order correlation approximation (SOCA) and the tau approximation. In the numerical simulations the effective Reynolds number Re is 2-20, while the magnetic Prandtl number varies from 0.1 to $10^{7}$. We present evidence that the $τ$ approximation may be appropriate in dynamical regimes where there is a small-scale dynamo. Catastrophic quenching of the $α$ effect is found for high $P_{m}$. Our results indicate that for high $P_{m}$ SOCA gives a very large value of the $α$ coefficient compared with the ``exact'' solution. The discrepancy depends on the properties of the random force that drives the flow, with a larger difference occuring for $δ$-correlated force compared with that for a steady random force.

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arXiv2007

The shear-induced alpha-effect and long-term variations in solar dynamo

The consequences of the shear-induced alpha effect to the long-term modulation of magnetic activity are examined with the help of the axisymmetric numerical dynamo model that includes the self-consistent description of the angular momentum balance, heat transport and magnetic field generation in the spherical shell. We find that the shear contributions to alpha effect can complicate the long-term behaviour of the large-scale magnetic activity and differential rotation in nonlinear dynamo. Additionally we consider the impact secular magnetic activity variations to the secular modulations of the solar luminosity and radius.

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arXiv2007

The mean electro-motive force, current- and cross-helicity under the influence of rotation, magnetic field and shear

The mean electromotive force (MEMF) in a rotating stratified magnetohydrodynamical turbulence is studied.Our study rests on the mean-field magnetohydrodynamics framework and $τ$ approximation. We compute the effects of the large-scale magnetic fields (LSMF), global rotation and large-scale shear flow on the different parts of the MEMF (such as $α$ - effect, turbulent diffusion, turbulent transport, etc.) in an explicit form. The influence of the helical magnetic fluctuations which stem from the small-scale dynamo is taken into account, as well. In the paper, we derive the equation governing the current helicity evolution. It is shown that the joint effect of the differential rotation and magnetic fluctuations in the stratified media can be responsible for the generation, maintenance and redistribution of the current helicity. The implication of the obtained results to astrophysical dynamos is considered as well.

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arXiv2005

The alpha-effect and current helicity for fast sheared rotators

We explore the alpha-effect and the small-scale current helicity, for the case of weakly compressible magnetically driven turbulence that is subjected to the differential rotation. No restriction is applied to the amplitude of angular velocity, i.e., the derivations presented are valid for an arbitrary Coriolis number, though the differential rotation itself is assumed to be weak. The expressions obtained are used to explore the possible distributions of alpha-effect and current helicity in convection zones (CZ) of the solar-type stars. The implications of the obtained results to the mean-field dynamo models are discussed.

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arXiv2001

Lithium as a passive tracer probing the rotating solar tachocline turbulence

The rotational influence on the eddy-diffusivity tensor D_ij for anisotropic turbulence fields is considered in order to explain the lithium decay law during the spin-down process of solar-type stars. Rotation proves to be highly effective in the transfer of chemicals through the solar tachocline (beneath the convection zone) which is assumed to contain only turbulence with horizontal motions. The effect is so strong that the tachocline turbulence must not exceed a limit of ~10^-(3...4) of the rms velocity in the convection zone in order to let the lithium survive after Gigayears. Such long depletion times can also be explained by a very small rotational influence upon the eddy-diffusion tensor if it is realized with correlation times shorter than 15 min. It is argued that such slow and/or short-living turbulence beneath the convection zone could hardly drive the solar dynamo. In our theory the diffusion remains small for rapid rotation due to the rotational quenching of the turbulence. In young stellar clusters like Pleiades, there should be a (positive) correlation between rotation rate and lithium abundance, where the fastest stars should have maximal lithium. First inspections of the data seem to confirm this finding.

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