scholarly journals Dynamo Theory and the Solar Cycle

1976 ◽  
Vol 71 ◽  
pp. 367-388 ◽  
Author(s):  
M. Stix
Keyword(s):  
Solar Cycle ◽  
Differential Rotation ◽  
Large Scale ◽  
Mean Field ◽  
Spherical Geometry ◽  
Dynamo Theory ◽  
Field Induction ◽  
Induction Equation ◽  
The Mean ◽  
Dynamo Waves

In this paper solutions of the mean field induction equation in a spherical geometry are discussed. In particular, the 22-year solar magnetic cycle is considered to be governed by an axisymmetric, periodic solution which is antisymmetric with respect to the equatorial plane. This solution essentially describes flux tubes travelling as waves from mid-latitudes towards the equator. In a layer of infinite extent the period of such dynamo waves solely depends on the strength of the two induction effects, differential rotation and α-effect (cyclonic turbulence). In a spherical shell, however, mean flux must be destroyed by turbulent diffusion, so the latter process might actually control the time scale of the solar cycle.A special discussion is devoted to the question of whether the angular velocityincreaseswith increasing depth, as the dynamo waves seem to require, or whether itdecreases, as many theoretical models concerned with the Sun's differential rotation predict. Finally, theories for the sector structure of the large scale photospheric field are reviewed. These describe magnetic sectors as a consequence of the sectoral pattern in the underlying large scale convection, as non-axisymmetric solutions of the mean field induction equation, or as hydromagnetic waves, modified by rotational effects.

scholarly journals Dynamo Theory of the Sun's General Magnetic Field on the Basis of a Mean-Field Magnetohydrodynamics

1971 ◽  
Vol 43 ◽  
pp. 770-779 ◽  
Author(s):  
F. Krause ◽  
K.-H. Rädler
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Differential Rotation ◽  
Mean Field ◽  
Dynamo Model ◽  
Dynamo Theory ◽  
General Magnetic Field ◽  
The Mean

An outline of the mean-field magnetohydrodynamics suggested and developed by M. Steenbeck and the authors and its application to the dynamo theory of the solar cycle is presented. Four basic requirements are formulated which have to be satisfied by any dynamo model which claims to explain the solar cycle. The models investigated allow conclusions about the differential rotation. In this connection Leighton's work is criticized.

scholarly journals The mean tilt of sunspot bipolar regions: theory, simulations and comparison with observations

2020 ◽  
Vol 495 (1) ◽  
pp. 238-248
Author(s):  
N Kleeorin ◽  
N Safiullin ◽  
K Kuzanyan ◽  
I Rogachevskii ◽  
A Tlatov ◽  
...  
Keyword(s):  
Coriolis Force ◽  
Large Scale ◽  
Mean Field ◽  
Wolf Number ◽  
Additional Contribution ◽  
Solar Cycles ◽  
Dynamo Theory ◽  
Large Scale Magnetic Field ◽  
Budget Equation ◽  
The Mean

ABSTRACT A theory of the mean tilt of sunspot bipolar regions (the angle between a line connecting the leading and following sunspots and the solar equator) is developed. A mechanism of formation of the mean tilt is related to the effect of the Coriolis force on meso-scale motions of super-granular convection and large-scale meridional circulation. The balance between the Coriolis force and the Lorentz force (the magnetic tension) determines an additional contribution caused by the large-scale magnetic field to the mean tilt of the sunspot bipolar regions at low latitudes. The latitudinal dependence of the solar differential rotation affects the mean tilt, which can explain deviations from Joy’s law for the sunspot bipolar regions at high latitudes. The theoretical results obtained and the results from numerical simulations based on the non-linear mean-field dynamo theory, which takes into account conservation of the total magnetic helicity and the budget equation for the evolution of the Wolf number density, are in agreement with observational data of the mean tilt of sunspot bipolar regions over individual solar cycles 15–24.

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 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 Filaments and the Solar Dynamo

1998 ◽  
Vol 167 ◽  
pp. 406-414
Author(s):  
N. Seehafer
Keyword(s):  
Mean Field ◽  
Decisive Role ◽  
Dynamo Theory ◽  
Simultaneous Generation ◽  
Alpha Effect ◽  
Generation Region ◽  
The Mean ◽  
Numerical Bifurcation ◽  
Dynamo Effect

AbstractFilaments are a global phenomenon and their formation, structure and dynamics are determined by magnetic fields. So they are an important signature of the solar magnetism. The central mechanism in traditional mean-field dynamo theory is the alpha effect and it is a major result of this theory that the presence of kinetic or magnetic helicities is at least favourable for the effect. Recent studies of the magnetohydrodynamic equations by means of numerical bifurcation-analysis techniques have confirmed the decisive role of helicity for a dynamo effect. The alpha effect 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. In the case of statistically stationary and homogeneous fluctuations, in particular, the alpha effect can increase the energy in the mean magnetic field only under the condition that also magnetic helicity is accumulated there. Generally, the two helicities generated by the alpha 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 may lead to the appearance of helicity in the atmosphere, in particular in filaments, and thus provide valuable information on dynamo processes inaccessible to in situ measurements.

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.

scholarly journals Mean-Field Magnetohydrodynamics as a Basis of Solar Dynamo Theory

1976 ◽  
Vol 71 ◽  
pp. 323-344 ◽  
Author(s):  
K.-H. Rädler
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Strong Relationship ◽  
Solar Radius ◽  
Small Scale ◽  
Dynamo Theory ◽  
The Magnetic Field ◽  
Complicated Situation ◽  
Insight Into

One of the most striking features of both the magnetic field and the motions observed at the Sun is their highly irregular or random character which indicates the presence of rather complicated magnetohydrodynamic processes. Of great importance in this context is a comprehension of the behaviour of the large scale components of the magnetic field; large scales are understood here as length scales in the order of the solar radius and time scales of a few years. Since there is a strong relationship between these components and the solar 22-years cycle, an insight into the mechanism controlling these components also provides for an insight into the mechanism of the cycle. The large scale components of the magnetic field are determined not only by their interaction with the large scale components of motion. On the contrary, a very important part is played also by an interaction between the large and the small scale components of magnetic field and motion so that a very complicated situation has to be considered.

scholarly journals Grand Minima in a spherical non-kinematic α2Ω mean-field dynamo model

2020 ◽  
Vol 10 ◽  
pp. 9 ◽  
Author(s):  
Corinne Simard ◽  
Paul Charbonneau
Keyword(s):  
Differential Rotation ◽  
Large Scale ◽  
Mean Field ◽  
Cyclic Behavior ◽  
Dynamo Model ◽  
Cycle Period ◽  
Cycle Amplitude ◽  
Primary Cycle ◽  
Mean Field Dynamo ◽  
Grand Minima

We present a non-kinematic axisymetric α2Ω mean-field dynamo model in which the complete α-tensor and mean differential rotation profile are both extracted from a global magnetohydrodynamical simulation of solar convection producing cycling large-scale magnetic fields. The nonlinear backreaction of the Lorentz force on differential rotation is the only amplitude-limiting mechanism introduced in the mean-field model. We compare and contrast the amplitude modulation patterns characterizing this mean-field dynamo, to those already well-studied in the context of non-kinematic αΩ models using a scalar α-effect. As in the latter, we find that large quasi-periodic modulation of the primary cycle are produced at low magnetic Prandtl number (Pm), with the ratio of modulation period to the primary cycle period scaling inversely with Pm. The variations of differential rotation remain well within the bounds set by observed solar torsional oscillations. In this low-Pm regime, moderately supercritical solutions can also exhibit aperiodic Maunder Minimum-like periods of strongly reduced cycle amplitude. The inter-event waiting time distribution is approximately exponential, in agreement with solar activity reconstructions based on cosmogenic radioisotopes. Secular variations in low-latitude surface differential rotation during Grand Minima, as compared to epochs of normal cyclic behavior, are commensurate in amplitude with historical inferences based on sunspot drawings. Our modeling results suggest that the low levels of observed variations in the solar differential rotation in the course of the activity cycle may nonetheless contribute to, or perhaps even dominate, the regulation of the magnetic cycle amplitude.

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

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