The macrodynamics of α-effect dynamos in rotating fluids

1975 ◽  
Vol 67 (3) ◽  
pp. 417-443 ◽  
Author(s):  
W. V. R. Maekus ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Fields ◽  
Large Scale ◽  
Magnetic Energy ◽  
Finite Amplitude ◽  
Small Scale ◽  
Past Study ◽  
Ohmic Loss ◽  
General Will ◽  
Rotating Systems ◽  
Stellar Magnetic Fields

Past study of the large-scale consequences of forced small-scale motions in electrically conducting fluids has led to the ‘α-effect’ dynamos. Various linear kinematic aspects of these dynamos have been explored, suggesting their value in the interpretation of observed planetary and stellar magnetic fields. However, large-scale magnetic fields with global boundary conditions can not be force free and in general will cause large-scale motions as they grow. I n this paper the finite amplitude behaviour of global magnetic fields and the large-scale flows induced by them in rotating systems is investigated. In general, viscous and ohmic dissipative mechanisms both play a role in determining the amplitude and structure of the flows and magnetic fields which evolve. In circumstances where ohmic loss is the principal dissipation, it is found that determination of a geo- strophic flow is an essential part of the solution of the basic stability problem. Nonlinear aspects of the theory include flow amplitudes which are independent of the rotation and a total magnetic energy which is directly proportional to the rotation. Constant a is the simplest example exhibiting the various dynamic balances of this stabilizing mechanism for planetary dynamos. A detailed analysis is made for this case to determine the initial equilibrium of fields and flows in a rotating sphere.

Renormalization group analysis of the magnetohydrodynamic turbulence and dynamo

2021 ◽  
Vol 926 ◽  
Author(s):  
Krzysztof A. Mizerski
Keyword(s):  
Renormalization Group ◽  
Magnetic Fields ◽  
Large Scale ◽  
Magnetic Energy ◽  
Group Analysis ◽  
Small Scale ◽  
Mhd Turbulence ◽  
Dynamical Equations ◽  
Renormalization Group Analysis ◽  
Magnetic Diffusivity

The magnetohydrodynamic (MHD) turbulence appears in engineering laboratory flows and is a common phenomenon in natural systems, e.g. stellar and planetary interiors and atmospheres and the interstellar medium. The applications in engineering are particularly interesting due to the recent advancement of tokamak devices, reaching very high plasma temperatures, thus giving hope for the production of thermonuclear fusion power. In the case of astrophysical applications, perhaps the main feature of the MHD turbulence is its ability to generate and sustain large-scale and small-scale magnetic fields. However, a crucial effect of the MHD turbulence is also the enhancement of large-scale diffusion via interactions of small-scale pulsations, i.e. the generation of the so-called turbulent viscosity and turbulent magnetic diffusivity, which typically exceed by orders of magnitude their molecular counterparts. The enhanced resistivity plays an important role in the turbulent dynamo process. Estimates of the turbulent electromotive force (EMF), including the so-called $\alpha$ -effect responsible for amplification of the magnetic energy and the turbulent magnetic diffusion are desired. Here, we apply the renormalization group technique to extract the final expression for the turbulent EMF from the fully nonlinear dynamical equations (Navier–Stokes, induction equation). The simplified renormalized set of dynamical equations, including the equations for the means and fluctuations, is derived and the effective turbulent coefficients such as the viscosity, resistivity, the $\alpha$ -coefficient and the Lorentz-force coefficients are explicitly calculated. The results are also used to demonstrate the influence of magnetic fields on energy and helicity spectra of strongly turbulent flows, in particular the magnetic energy spectrum.

scholarly journals Direct and inverse cascades in the geodynamo

2008 ◽  
Vol 15 (6) ◽  
pp. 873-880 ◽  
Author(s):  
M. Reshetnyak ◽  
P. Hejda
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Magnetic Energy ◽  
Vector Spaces ◽  
Wave Number ◽  
Small Scale ◽  
Rapid Rotation ◽  
Thermal Turbulence ◽  
Geostrophic Flows

Abstract. The rapid rotation of planets causes cyclonic thermal turbulence in their cores which may generate the large-scale magnetic fields observed outside the planets. We investigate numerically a model based on the geodynamo equations in simplified geometry, which enables us to reproduce the main features of small-scale geostrophic flows in physical and wave vector spaces. We find fluxes of kinetic and magnetic energy as a function of the wave number and demonstrate the co-existence of forward and inverse cascades. We also explain the mechanism of magnetic field saturation at the end of the kinematic dynamo regime.

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 Magnetosheath-cusp interface

2004 ◽  
Vol 22 (1) ◽  
pp. 183-212 ◽  
Author(s):  
S. Savin ◽  
L. Zelenyi ◽  
S. Romanov ◽  
I. Sandahl ◽  
J. Pickett ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Solar Wind ◽  
Magnetic Fields ◽  
Large Scale ◽  
Traditional Approach ◽  
Qualitative Difference ◽  
Small Scale ◽  
Nonlinear Phenomena ◽  
Solar Wind Interaction ◽  
Linear Superposition

Abstract. We advance the achievements of Interball-1 and other contemporary missions in exploration of the magnetosheath-cusp interface. Extensive discussion of published results is accompanied by presentation of new data from a case study and a comparison of those data within the broader context of three-year magnetopause (MP) crossings by Interball-1. Multi-spacecraft boundary layer studies reveal that in ∼80% of the cases the interaction of the magnetosheath (MSH) flow with the high latitude MP produces a layer containing strong nonlinear turbulence, called the turbulent boundary layer (TBL). The TBL contains wave trains with flows at approximately the Alfvén speed along field lines and "diamagnetic bubbles" with small magnetic fields inside. A comparison of the multi-point measurements obtained on 29 May 1996 with a global MHD model indicates that three types of populating processes should be operative: large-scale (∼few RE) anti-parallel merging at sites remote from the cusp; medium-scale (few thousandkm) local TBL-merging of fields that are anti-parallel on average; small-scale (few hundredkm) bursty reconnection of fluctuating magnetic fields, representing a continuous mechanism for MSH plasma inflow into the magnetosphere, which could dominate in quasi-steady cases. The lowest frequency (∼1–2mHz) TBL fluctuations are traced throughout the magnetosheath from the post-bow shock region up to the inner magnetopause border. The resonance of these fluctuations with dayside flux tubes might provide an effective correlative link for the entire dayside region of the solar wind interaction with the magnetopause and cusp ionosphere. The TBL disturbances are characterized by kinked, double-sloped wave power spectra and, most probably, three-wave cascading. Both elliptical polarization and nearly Alfvénic phase velocities with characteristic dispersion indicate the kinetic Alfvénic nature of the TBL waves. The three-wave phase coupling could effectively support the self-organization of the TBL plasma by means of coherent resonant-like structures. The estimated characteristic scale of the "resonator" is of the order of the TBL dimension over the cusps. Inverse cascades of kinetic Alfvén waves are proposed for forming the larger scale "organizing" structures, which in turn synchronize all nonlinear cascades within the TBL in a self-consistent manner. This infers a qualitative difference from the traditional approach, wherein the MSH/cusp interaction is regarded as a linear superposition of magnetospheric responses on the solar wind or MSH disturbances. Key words. Magnetospheric physics (magnetopause, cusp, and boundary layers) – Space plasma physics (turbulence; nonlinear phenomena)

scholarly journals Excitation of zonal flow by the modulational instability in electron temperature gradient driven turbulence

2008 ◽  
Vol 74 (3) ◽  
pp. 381-389 ◽  
Author(s):  
Yu. A. ZALIZNYAK ◽  
A. I. YAKIMENKO ◽  
V. M. LASHKIN
Keyword(s):  
Temperature Gradient ◽  
Electron Temperature ◽  
Large Scale ◽  
Modulational Instability ◽  
Zonal Flow ◽  
Finite Amplitude ◽  
Small Scale ◽  
Drift Waves ◽  
Zonal Flows ◽  
Electron Temperature Gradient

AbstractThe generation of large-scale zonal flows by small-scale electrostatic drift waves in electron temperature gradient driven turbulence model is considered. The generation mechanism is based on the modulational instability of a finite amplitude monochromatic drift wave. The threshold and growth rate of the instability as well as the optimal spatial scale of zonal flow are obtained.

scholarly journals Viscosity and Large-Scale Magnetic Fields from Accretion Disc Dynamos

1997 ◽  
Vol 163 ◽  
pp. 190-200
Author(s):  
Christopher A. Tout
Keyword(s):  
Magnetic Fields ◽  
Large Scale ◽  
Small Scale ◽  
Cascade Process ◽  
Jet Formation ◽  
Magnetohydrodynamic Turbulence ◽  
Discs Large ◽  
Scale Field ◽  
Large Scale Field ◽  
Nova Outbursts

AbstractWe review those processes associated with accretion discs that are probably influenced by magnetic fields, specifically, accretiondisc viscosity, energy dissipation and jet formation. We consider how magnetic instabilities in the disc can lead to a self-sustaining dynamical dynamo and how this is manifested as magnetohydrodynamic turbulence in numerical simulations. We show that currently these models do not fit with observational constraints imposed by dwarf-nova outbursts. We also show that the drop in ionisation fraction does not lead to the apparently necessary drop in viscosity in quiescent cataclysmic variable discs. Large-scale magnetic fields are required to launch and collimate jets form discs. We describe an inverse cascade process that can construct sufficient large-scale field from small-scale field generated by a dynamo.

scholarly journals Characterising the surface magnetic fields of T Tauri stars with high-resolution near-infrared spectroscopy

2019 ◽  
Vol 630 ◽  
pp. A99 ◽  
Author(s):  
A. Lavail ◽  
O. Kochukhov ◽  
G. A. J. Hussain
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Magnetic Fields ◽  
Large Scale ◽  
Near Infrared ◽  
Field Measurements ◽  
T Tauri Stars ◽  
Small Scale ◽  
Surface Magnetic Field ◽  
T Tauri

Aims. In this paper, we aim to characterise the surface magnetic fields of a sample of eight T Tauri stars from high-resolution near-infrared spectroscopy. Some stars in our sample are known to be magnetic from previous spectroscopic or spectropolarimetric studies. Our goals are firstly to apply Zeeman broadening modelling to T Tauri stars with high-resolution data, secondly to expand the sample of stars with measured surface magnetic field strengths, thirdly to investigate possible rotational or long-term magnetic variability by comparing spectral time series of given targets, and fourthly to compare the magnetic field modulus ⟨B⟩ tracing small-scale magnetic fields to those of large-scale magnetic fields derived by Stokes V Zeeman Doppler Imaging (ZDI) studies. Methods. We modelled the Zeeman broadening of magnetically sensitive spectral lines in the near-infrared K-band from high-resolution spectra by using magnetic spectrum synthesis based on realistic model atmospheres and by using different descriptions of the surface magnetic field. We developped a Bayesian framework that selects the complexity of the magnetic field prescription based on the information contained in the data. Results. We obtain individual magnetic field measurements for each star in our sample using four different models. We find that the Bayesian Model 4 performs best in the range of magnetic fields measured on the sample (from 1.5 kG to 4.4 kG). We do not detect a strong rotational variation of ⟨B⟩ with a mean peak-to-peak variation of 0.3 kG. Our confidence intervals are of the same order of magnitude, which suggests that the Zeeman broadening is produced by a small-scale magnetic field homogeneously distributed over stellar surfaces. A comparison of our results with mean large-scale magnetic field measurements from Stokes V ZDI show different fractions of mean field strength being recovered, from 25–42% for relatively simple poloidal axisymmetric field topologies to 2–11% for more complex fields.

scholarly journals Disruption of circumstellar discs by large-scale stellar magnetic fields

2018 ◽  
Vol 478 (3) ◽  
pp. 3049-3055 ◽  
Author(s):  
Asif ud-Doula ◽  
Stanley P Owocki ◽  
Nathaniel Dylan Kee
Keyword(s):  
Magnetic Fields ◽  
Large Scale ◽  
Stellar Magnetic Fields

scholarly journals Our dynamic sun: 2017 Hannes Alfvén Medal lecture at the EGU

2017 ◽  
Vol 35 (4) ◽  
pp. 805-816 ◽  
Author(s):  
Eric Priest
Keyword(s):  
Magnetic Fields ◽  
Magnetic Energy ◽  
Active Regions ◽  
Particle Energy ◽  
Space Environment ◽  
Small Scale ◽  
The Sun ◽  
Strong Shear ◽  
Outer Atmosphere ◽  
Mass Ejection

Abstract. This lecture summarises how our understanding of many aspects of the Sun has been revolutionised over the past few years by new observations and models. Much of the dynamic behaviour of the Sun is driven by the magnetic field since, in the outer atmosphere, it represents the largest source of energy by far. The interior of the Sun possesses a strong shear layer at the base of the convection zone, where sunspot magnetic fields are generated. A small-scale dynamo may also be operating near the surface of the Sun, generating magnetic fields that thread the lowest layer of the solar atmosphere, the turbulent photosphere. Above the photosphere lies the highly dynamic fine-scale chromosphere, and beyond that is the rare corona at high temperatures exceeding 1 million degrees K. Possible magnetic mechanisms for heating the corona and driving the solar wind (two intriguing and unsolved puzzles) are described. Other puzzles include the structure of giant flux ropes, known as prominences, which have complex fine structure. Occasionally, they erupt and produce huge ejections of mass and magnetic fields (coronal mass ejections), which can disrupt the space environment of the Earth. When such eruptions originate in active regions around sunspots, they are also associated with solar flares, in which magnetic energy is converted to kinetic energy, heat and fast-particle energy. A new theory will be presented for the origin of the twist that is observed in erupting prominences and for the nature of reconnection in the rise phase of an eruptive flare or coronal mass ejection.

scholarly journals On the peculiarities of manifestation of kG magnetic elements in observations of the Sun with low spatial resolution

2014 ◽  
Vol 10 (S305) ◽  
pp. 86-91 ◽  
Author(s):  
Mikhail L. Demidov ◽  
Renat M. Veretsky ◽  
Alexander V. Kiselev
Keyword(s):  
Magnetic Fields ◽  
Magnetic Flux ◽  
Spatial Resolution ◽  
Large Scale ◽  
Disk Center ◽  
Stellar Disk ◽  
The Sun ◽  
Surface Mapping ◽  
Cross Calibration ◽  
Stellar Magnetic Fields

AbstractOn the agenda of modern astrophysics is the exploration of not only disk-integrated stellar magnetic fields but surface mapping of them. However, it is hardly possible to expect that spatial resolution better than some dozens or hundreds pixels over stellar disk will be achieved for this goal in the foreseeable future. Among other reasons this fact makes very important observations of the average and large-scale magnetic fields of the Sun, which can be naturally used for testing polarimetric measurements on other stars, especially on solar-type stars. In this study we explore different aspects of observations of solar magnetic fields (SMF) with low spatial resolution, including Sun-as-a-star observations, which are characterized by extremely low magnetic flux densities. Comparison of disk-integrated and spatially resolved Stokes observations of the Sun allow us to demonstrate how Stokes V profiles depend on the distribution of large-scale magnetic fields in the disk center. It is shown that center-to-limb variations of magnetic strength ratios (MSR) and area asymetries, most likely could be interpreted as the manifestation of kG magnetic flux tubes. We have made cross-calibration of the full-disk magnetograms obtained by space-borned SDO/HMI and by the ground-based STOP telescope, and pretty good agreement is found. Finally, the absence of significant systematic time variations of MSRs with solar cycle is demonstrated.

Sign in / Sign up

Export Citation Format

Share Document