scholarly journals Eigenvalues of Magnetohydrodynamic Mean-Field Dynamo Models: Bounds and Reliable Computation

2020 ◽  
Vol 80 (5) ◽  
pp. 2194-2225
Author(s):  
Sabine Boegli ◽  
Christiane Tretter
Keyword(s):  
Mean Field ◽  
Reliable Computation ◽  
Mean Field Dynamo

Magnetic helicity in non-axisymmetric mean-field dynamo

2016 ◽  
Vol 52 (1) ◽  
pp. 145-154
Author(s):  
V. V. Pipin ◽  
Keyword(s):  
Mean Field ◽  
Magnetic Helicity ◽  
Mean Field Dynamo

scholarly journals Global MHD phenomena and their importance for stellar surfaces

2010 ◽  
Vol 6 (S273) ◽  
pp. 141-147
Author(s):  
Rainer Arlt
Keyword(s):  
Magnetic Fields ◽  
Mean Field ◽  
Momentum Equation ◽  
Small Scale ◽  
Dynamo Action ◽  
Complex Activity ◽  
Mhd Instabilities ◽  
Stellar Magnetic Fields ◽  
Mean Field Dynamo

AbstractThis review is an attempt to elucidate MHD phenomena relevant for stellar magnetic fields. The full MHD treatment of a star is a problem which is numerically too demanding. Mean-field dynamo models use an approximation of the dynamo action from the small-scale motions and deliver global magnetic modes which can be cyclic, stationary, axisymmetric, and non-axisymmetric. Due to the lack of a momentum equation, MHD instabilities are not visible in this picture. However, magnetic instabilities must set in as a result of growing magnetic fields and/or buoyancy. Instabilities deliver new timescales, saturation limits and topologies to the system probably providing a key to the complex activity features observed on stars.

scholarly journals Magnetic Cycles and Rotation in Active Late–Type Stars

2004 ◽  
Vol 215 ◽  
pp. 289-291
Author(s):  
Ilkka Tuominen ◽  
Svetlana V. Berdyugina ◽  
Maarit J. Korpi
Keyword(s):  
Mean Field ◽  
Point Of View ◽  
Doppler Imaging ◽  
Late Type ◽  
Dynamo Theory ◽  
Flip Flop ◽  
Cyclic Behaviour ◽  
Magnetic Cycles ◽  
Mean Field Dynamo

Observational evidence, based both on spectroscopic Doppler imaging and long-term photometry, of strongly nonaxisymmetric spot distributions in magnetically very active late-type stars, with a special cyclic behaviour (the “flip-flop” effect), is presented. Theoretical implications of these results are discussed from the point of view of nonlinear mean-field dynamo theory.

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 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

scholarly journals Mean field dynamo action in shear flows. I: fixed kinetic helicity

2020 ◽  
Vol 495 (4) ◽  
pp. 4557-4569 ◽  
Author(s):  
Naveen Jingade ◽  
Nishant K Singh
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Magnetic Activity ◽  
Turnover Time ◽  
Cycle Period ◽  
Dynamo Action ◽  
Navier Stokes Equation ◽  
Axisymmetric Mode ◽  
Dynamo Wave ◽  
Mean Field Dynamo

ABSTRACT We study mean field dynamo action in a background linear shear flow by employing pulsed renewing flows with fixed kinetic helicity and non-zero correlation time (τ). We use plane shearing waves in terms of time-dependent exact solutions to the Navier–Stokes equation as derived by Singh & Sridhar (2017). This allows us to self-consistently include the anisotropic effects of shear on the stochastic flow. We determine the average response tensor governing the evolution of mean magnetic field, and study the properties of its eigenvalues that yield the growth rate (γ) and the cycle period (Pcyc) of the mean magnetic field. Both, γ and the wavenumber corresponding to the fastest growing axisymmetric mode vary non-monotonically with shear rate S when τ is comparable to the eddy turnover time T, in which case, we also find quenching of dynamo when shear becomes too strong. When $\tau /T\sim {\cal O}(1)$, the cycle period (Pcyc) of growing dynamo wave scales with shear as Pcyc ∝ |S|−1 at small shear, and it becomes nearly independent of shear as shear becomes too strong. This asymptotic behaviour at weak and strong shear has implications for magnetic activity cycles of stars in recent observations. Our study thus essentially generalizes the standard αΩ (or α2Ω) dynamo as also the α effect is affected by shear and the modelled random flow has a finite memory.

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