scholarly journals Advances in mean-field dynamo theories

2012 ◽  
Vol 8 (S294) ◽  
pp. 375-386 ◽  
Author(s):  
V. V. Pipin
Keyword(s):  
Turbulent Flows ◽  
Electromotive Force ◽  
Mean Field ◽  
Nonlinear Effects ◽  
Solar Dynamo ◽  
Dynamo Model ◽  
Dynamo Theory ◽  
Numerical Work ◽  
The Mean ◽  
Mean Field Dynamo

AbstractWe 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.

scholarly journals The Alpha-Effect in Galaxies is Highly Anisotropic

1990 ◽  
Vol 140 ◽  
pp. 113-114
Author(s):  
G. Rüdiger
Keyword(s):  
Large Scale ◽  
Rotation Axis ◽  
Mean Field ◽  
Dynamo Model ◽  
Mean Flow ◽  
Dynamo Theory ◽  
Input Quantity ◽  
Alpha Effect ◽  
The Mean ◽  
Mean Field Dynamo

Besides the mean flow the alpha is the other input quantity for any mean-field dynamo model. It describes the generation of turbulent electromotive force <u × B> from a large-scale field <B> for a given turbulence. The necessary helicity of the turbulence results from the joint action of Coriolis force and density stratification. The standard estimate of 1 km/s for alpha in galaxies is a surely well-established approximation. One of the essentials, however, remains open. Due to the extremely anisotropic structure of disks the tensorial character of alpha can no longer be ignored. In stellar applications anisotropy in the α-tensor leads to a preferred excitation of non-axisymmetric magnetic fields. That is true for α2 -dynamos if the alpha parallel to the rotation axis, α||, is much smaller than that in the equatorial plane, α⊥. The idea is that also for disk-like configurations a similar behaviour makes the existence of the observed large-scale non-axisymmetric magnetic BSS modes understandable within the frame of the mean-field dynamo theory.

scholarly journals Does the mean-field α effect have any impact on the memory of the solar cycle?

2020 ◽  
Vol 642 ◽  
pp. A51
Author(s):  
Soumitra Hazra ◽  
Allan Sacha Brun ◽  
Dibyendu Nandy
Keyword(s):  
Solar Cycle ◽  
Mean Field ◽  
Solar Dynamo ◽  
Dynamo Model ◽  
Solar Cycles ◽  
Poloidal Field ◽  
Flux Transport ◽  
Solar Convection ◽  
The Mean ◽  
And Diffusion

Context. Predictions of solar cycle 24 obtained from advection-dominated and diffusion-dominated kinematic dynamo models are different if the Babcock–Leighton mechanism is the only source of the poloidal field. Some previous studies argue that the discrepancy arises due to different memories of the solar dynamo for advection- and diffusion-dominated solar convection zones. Aims. We aim to investigate the differences in solar cycle memory obtained from advection-dominated and diffusion-dominated kinematic solar dynamo models. Specifically, we explore whether inclusion of Parker’s mean-field α effect, in addition to the Babcock–Leighton mechanism, has any impact on the memory of the solar cycle. Methods. We used a kinematic flux transport solar dynamo model where poloidal field generation takes place due to both the Babcock–Leighton mechanism and the mean-field α effect. We additionally considered stochastic fluctuations in this model and explored cycle-to-cycle correlations between the polar field at minima and toroidal field at cycle maxima. Results. Solar dynamo memory is always limited to only one cycle in diffusion-dominated dynamo regimes while in advection-dominated regimes the memory is distributed over a few solar cycles. However, the addition of a mean-field α effect reduces the memory of the solar dynamo to within one cycle in the advection-dominated dynamo regime when there are no fluctuations in the mean-field α effect. When fluctuations are introduced in the mean-field poloidal source a more complex scenario is evident, with very weak but significant correlations emerging across a few cycles. Conclusions. Our results imply that inclusion of a mean-field α effect in the framework of a flux transport Babcock–Leighton dynamo model leads to additional complexities that may impact memory and predictability of predictive dynamo models of the solar cycle.

Existence and Energy Balance of the Solar Dynamo

1993 ◽  
Vol 157 ◽  
pp. 19-23
Author(s):  
J.H.G.M. van Geffen
Keyword(s):  
Magnetic Field ◽  
Energy Balance ◽  
Energy Method ◽  
Magnetic Energy ◽  
Mean Field ◽  
Solar Dynamo ◽  
Ensemble Averaging ◽  
Dynamo Theory ◽  
The Magnetic Field ◽  
Mean Field Dynamo

The idea behind the use of ensemble averaging and the finite magnetic energy method of van Geffen and Hoyng (1992) is briefly discussed. Applying this method to the solar dynamo shows that the turbulence — an essential ingredient of traditional mean field dynamo theory — poses grave problems: the turbulence makes the magnetic field so unstable that it becomes impossible to recognize any period.

scholarly journals On the mean-field theory of the Karlsruhe Dynamo Experiment

2002 ◽  
Vol 9 (3/4) ◽  
pp. 171-187 ◽  
Author(s):  
K.-H. Rädler ◽  
M. Rheinhardt ◽  
E. Apstein ◽  
H. Fuchs
Keyword(s):  
Field Theory ◽  
Key Words ◽  
Mean Field Theory ◽  
Mean Field ◽  
Experimental Results ◽  
Dynamo Theory ◽  
The Mean ◽  
Earth’S Interior ◽  
Earth's Interior ◽  
Mean Field Dynamo

Abstract. In the Forschungszentrum Karlsruhe an experiment has been constructed which demonstrates a homogeneous dynamo as is expected to exist in the Earth's interior. This experiment is discussed within the framework of mean-field dynamo theory. The main predictions of this theory are explained and compared with the experimental results. Key words. Dynamo, geodynamo, dynamo experiment, mean-field dynamo theory, a-effect

scholarly journals Current helicity constraints in solar dynamo models

2012 ◽  
Vol 8 (S294) ◽  
pp. 313-318
Author(s):  
D. Sokoloff ◽  
H. Zhang ◽  
D. Moss ◽  
N. Kleeorin ◽  
K. Kuzanyan ◽  
...  
Keyword(s):  
Large Scale ◽  
Numerical Models ◽  
Mean Field ◽  
Active Regions ◽  
Solar Dynamo ◽  
Magnetic Helicity ◽  
Dynamo Model ◽  
Small Scale ◽  
Mean Field Dynamo ◽  
Current Helicity

AbstractWe investigate to what extent the current helicity distribution observed in solar active regions is compatible with solar dynamo models. We use an advanced 2D mean-field dynamo model with dynamo action largely concentrated near the bottom of the convective zone, and dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtain butterfly diagrams for both the small-scale current helicity and the large-scale magnetic helicity, and compare them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by −A·B evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here B and A are respectively the dynamo generated mean magnetic field and its vector potential.

The mean-field dynamo model in geodynamo

2014 ◽  
Vol 14 (2) ◽  
pp. 1-7 ◽  
Author(s):  
M. Yu. Reshetnyak
Keyword(s):  
Mean Field ◽  
Dynamo Model ◽  
The Mean ◽  
Mean Field Dynamo

scholarly journals The Solar Dynamo

1990 ◽  
Vol 121 ◽  
pp. 385-402 ◽  
Author(s):  
K.-H. Rädler
Keyword(s):  
Magnetic Field ◽  
Differential Rotation ◽  
Mean Field ◽  
Solar Dynamo ◽  
Back Reaction ◽  
Dynamo Theory ◽  
Open Questions ◽  
Convective Motions ◽  
The Mean ◽  
Basic Ideas

AbstractThe phenomena of solar activity are connected with a general magnetic field of-the Sun which is due to a dynamo process essentially determined by the α-effect and the differential rotation in the convection zone. A few observational facts are summarized which are important for modelling this process. The basic ideas of the solar dynamo theory, with emphasis on the mean-field approach, are explained, and a critical review of the dynamo models investigated so far is given. Although several models reflect a number of essential features of the solar magnetic cycle there are many open questions. Part of them result from lack of knowledge of the structure of the convective motions and the differential rotation. Other questions concern, for example, details of the connection of the α-effect and related effects with the convective motions, or the way in which the behaviour of the dynamo is influenced by the back-reaction of the magnetic field on the motions.

scholarly journals Turbulent transport coefficients in galactic dynamo simulations using singular value decomposition

2019 ◽  
Vol 491 (3) ◽  
pp. 3870-3883 ◽  
Author(s):  
Abhijit B Bendre ◽  
Kandaswamy Subramanian ◽  
Detlef Elstner ◽  
Oliver Gressel
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Turbulent Transport ◽  
Transport Coefficients ◽  
Mean Field ◽  
Dynamo Model ◽  
The Mean ◽  
Value Decomposition ◽  
Svd Method ◽  
Mean Field Dynamo

ABSTRACT Coherent magnetic fields in disc galaxies are thought to be generated by a large-scale (or mean-field) dynamo operating in their interstellar medium. A key driver of mean magnetic field growth is the turbulent electromotive force (EMF), which represents the influence of correlated small-scale (or fluctuating) velocity and magnetic fields on the mean field. The EMF is usually expressed as a linear expansion in the mean magnetic field and its derivatives, with the dynamo tensors as expansion coefficients. Here, we adopt the singular value decomposition (SVD) method to directly measure these turbulent transport coefficients in a simulation of the turbulent interstellar medium that realizes a large-scale dynamo. Specifically, the SVD is used to least-square fit the time series data of the EMF with that of the mean field and its derivatives, to determine these coefficients. We demonstrate that the spatial profiles of the EMF reconstructed from the SVD coefficients match well with that taken directly from the simulation. Also, as a direct test, we use the coefficients to simulate a 1D mean-field dynamo model and find an overall similarity in the evolution of the mean magnetic field between the dynamo model and the direct simulation. We also compare the results with those which arise using simple regression and the ones obtained previously using the test-field method, to find reasonable qualitative agreement. Overall, the SVD method provides an effective post-processing tool to determine turbulent transport coefficients from simulations.

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