The Magnetic Universe: Geophysical and Astrophysical Dynamo TheoryISBN: 9783527404094
343 pages
August 2004

1 Introduction.
2 Earth and Planets.
2.1 Observational Overview.
2.1.1 Reversals.
2.1.2 Other TimeVariability.
2.2 Basic Equations and Parameters.
2.2.1 Anelastic and Boussinesq Equations.
2.2.2 Nondimensionalization.
2.3 Magnetoconvection.
2.3.1 Rotationor Magnetism Alone.
2.3.2 Rotation and Magnetism Together.
2.3.3 Weakversus Strong Fields.
2.3.4 Oscillatory Convection Modes.
2.4 Taylor’s Constraint.
2.4.1 Taylor’s Original Analysis.
2.4.2 Relaxation of Ro=E=0.
2.4.3 Taylor States versus Ekman States.
2.4.4 From Ekman States to Taylor States.
2.4.5 Torsional Oscillations.
2.4.6 αΩDynamos.
2.4.7 Taylor’s Constraint in the Anelastic Approximation.
2.5 Hydromagnetic Waves.
2.6 The Inner Core.
2.6.1 Stewartson Layers on C.
2.6.2 Nonaxisymmetric Shear Layers on C.
2.6.3 Finite Conductivity of the Inner Core.
2.6.4 Rotation of the Inner Core.
2.7 Numerical Simulations.
2.8 Magnetic Instabilities.
2.9 Other Planets.
2.9.1 Mercury, Venus and Mars.
2.9.2 Jupiter’s Moons.
2.9.3 Jupiter and Saturn.
2.9.4 Uranus and Neptune.
3 Differential Rotation Theory.
3.1 The Solar Rotation.
3.1.1 Torsional Oscillations.
3.1.2 Meridional Flow.
3.1.3 Ward’s Correlation.
3.1.4 Stellar Observations.
3.2 Angular Momentum Transport in Convection Zones.
3.2.1 The Taylor Number Puzzle.
3.2.2 The ΛEffect.
3.2.3 The Eddy Viscosity Tensor.
3.2.4 MeanField Thermodynamics.
3.3 Differential Rotation and Meridional Circulation for SolarType Stars.
3.4 Kinetic Helicity and the DIVCURLCorrelation.
3.5 Overshoot Region and the Tachocline.
3.5.1 The NIRVANA Code.
3.5.2 Penetration into the Stable Layer.
3.5.3 A Magnetic Theory of the Solar Tachocline.
4 The Stellar Dynamo.
4.1 The SolarStellar Connection.
4.1.1 The Phase Relation.
4.1.2 The Nonlinear Cycle.
4.1.3 Parity.
4.1.4 Dynamorelated Stellar Observations.
4.1.5 The FlipFlop Phenomenon.
4.1.6 More Cyclicities.
4.2 The αTensor.
4.2.1 The MagneticField Advection.
4.2.2 The Highly Anisotropic αEffect.
4.2.3 The Magnetic Quenching of the αEffect.
4.2.4 WeakCompressible Turbulence.
4.3 MagneticDiffusivity Tensor and ηQuenching.
4.3.1 The Eddy Diffusivity Tensor.
4.3.2 Sunspot Decay.
4.4 MeanField Stellar Dynamo Models.
4.4.1 The α2Dynamo.
4.4.2 The αΩDynamo for Slow Rotation.
4.4.3 Meridional Flow Influence.
4.5 The Solar Dynamo.
4.5.1 The Overshoot Dynamo.
4.5.2 The AdvectionDominated Dynamo.
4.6 Dynamos with Random α.
4.6.1 Aturbulence Model.
4.6.2 Dynamo Models with Fluctuating αEffect.
4.7 Nonlinear Dynamo Models.
4.7.1 MalkusProctor Mechanism.
4.7.2 αQuenching.
4.7.3 Magnetic Saturation by Turbulent Pumping.
4.7.4 ηQuenching.
4.8 ΛQuenching and Maunder Minimum.
5 The Magnetorotational Instability (MRI).
5.1 Star Formation.
5.1.1 Molecular Clouds.
5.1.2 The Angular Momentum Problem.
5.1.3 Turbulence and Planet Formation.
5.2 Stability of Differential Rotation in Hydrodynamics.
5.2.1 Combined Stability Conditions.
5.2.2 Sufficient Condition for Stability.
5.2.3 Numerical Simulations.
5.2.4 Vertical Shear.
5.3 Stability of Differential Rotation in Hydromagnetics.
5.3.1 Ideal MHD.
5.3.2 Baroclinic Instability.
5.4 Stability of Differential Rotation with Strong Hall Effect.
5.4.1 Criteria of Instability of Protostellar Disks.
5.4.2 Growth Rates.
5.5 Global Models.
5.5.1 A Spherical Model with Shear.
5.5.2 A Global Disk Model.
5.6 MRI of Differential Stellar Rotation.
5.6.1 T Tauri Stars (TTS).
5.6.2 The ApStar Magnetism.
5.6.3 Decay of Differential Rotation.
5.7 CirculationDriven Stellar Dynamos.
5.7.1 The Gailitis Dynamo.
5.7.2 Meridional Circulation plus Shear.
5.8 MRI in Kepler Disks.
5.8.1 The Shearing Box Model.
5.8.2 A Global Disk Dynamo?
5.9 AccretionDisk Dynamo and JetLaunching Theory.
5.9.1 AccretionDisk Dynamo Models.
5.9.2 JetLaunching.
5.9.3 AccretionDisk Outflows.
5.9.4 DiskDynamo Interaction.
6 The Galactic Dynamo.
6.1 Magnetic Fields of Galaxies.
6.1.1 Field Strength.
6.1.2 Pitch Angles.
6.1.3 Axisymmetry.
6.1.4 Two Exceptions: Magnetic Torus and Vertical Halo Fields.
6.1.5 The Disk Geometry.
6.2 Nonlinear Winding and the Seed Field Problem.
6.2.1 Uniform Initial Field.
6.2.2 Seed Field Amplitude and Geometry.
6.3 Interstellar Turbulence.
6.3.1 The Advection Problem.
6.3.2 Hydrostatic Equilibrium and Interstellar Turbulence.
6.4 From Spheres to Disks.
6.4.1 1DdynamoWaves.
6.4.2 Oscillatory vs. Steady Solutions.
6.5 Linear 3DModels.
6.6 The Nonlinear Galactic Dynamo with Uniform Density.
6.6.1 The Model.
6.6.2 The Influences of Geometry and Turbulence Field.
6.7 Density Wave Theory and Swing Excitation.
6.7.1 Density Wav Theory.
6.7.2 The ShortWave Approximation.
6.7.3 Swing Excitation in Magnetic Spirals.
6.7.4 Nonlocal Density Wave Theory in Kepler Disks.
6.8 MeanField Dynamos with Strong Halo Turbulence.
6.8.1 Nonlinear 2D Dynamo Model with Magnetic Supported Vertical Stratification.
6.8.2 Nonlinear 3D Dynamo Models for Spiral Galaxies.
6.9 New Simulations: Macroscale and Microscale.
6.9.1 ParticleHydrodynamics for the Macroscale.
6.9.2 MHD for the Microscale.
6.10 MRI in Galaxies.
7 Neutron Star Magnetism.
7.1 Introduction.
7.2 Equations.
7.3 Without Stratification.
7.4 With Stratification.
7.5 MagneticDominated Heat Transport.
7.6 White Dwarfs.
8 The Magnetic Taylor–Couette Flow.
8.1 History.
8.2 The Equations.
8.3 Results without Hall Effect.
8.3.1 Subcritical Excitation for Large Pm.
8.3.2 The Rayleigh Line (a = 0) and Beyond.
8.3.3 Excitation of Nonaxisymmetric or Oscillatory Modes.
8.3.4 Wave Number and Drift Frequencies.
8.4 Results with Hall Effect.
8.4.1 Hall Effect with Positive Shear.
8.4.2 Hall Effect with Negative Shear.
8.4.3 A HallDriven DiskDynamo?
8.5 Endplate effects.
8.6 Water Experiments.
8.7 Taylor–Couette Flow as Kinematic Dynamo.
9 Bibliography.
Index.
Rainer Hollerbach is Reader in Applied Mathematics at the University of Glasgow, Scotland. He has a PhD in Geophysics from the University of California, San Diego. He recently spent a year in Germany as a Research Fellow of the Alexander von Humboldt Foundation.
“…does contain many deep insights and there is valuable material…that is not easily accessible elsewhere…” (Geophysical and Astrophysical Fluid Dynamics, August 2005, Vol 99 (4))
"...the authors do a good job of conveying the excitement of the subject and of bringing together much of the research of important topics...a welcome addition to the bookshelves..." (The Observatory, Vol.25, No.1186, June 2005)
"Ruder and Hollerbach have brought together the significant research on this topic…will be of interest to both the geophysicist and the astrophysicist, and perhaps the physicist or engineer…" (ESTREAMS, April 2005)
"Researchers and advanced students will greatly profit from this
book."
—Rainer Beck, MaxPlanckInstitut für fadioastronomie,
Bonn
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