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Mathematical Aspects of Natural Dynamos [Minkštas viršelis]

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Edited by (Newcastle University, UK), Edited by (CNRS-ENS-IPGP, Paris, France)
  • Formatas: Paperback / softback, 516 pages, aukštis x plotis: 254x178 mm, weight: 453 g, 6 Tables, black and white; 20 Illustrations, color; 101 Illustrations, black and white
  • Serija: The Fluid Mechanics of Astrophysics and Geophysics
  • Išleidimo metai: 19-Aug-2019
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 036737546X
  • ISBN-13: 9780367375461
Kitos knygos pagal šią temą:
Mathematical Aspects of Natural DynamosDidesnis paveikslėlis
  • Formatas: Paperback / softback, 516 pages, aukštis x plotis: 254x178 mm, weight: 453 g, 6 Tables, black and white; 20 Illustrations, color; 101 Illustrations, black and white
  • Serija: The Fluid Mechanics of Astrophysics and Geophysics
  • Išleidimo metai: 19-Aug-2019
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 036737546X
  • ISBN-13: 9780367375461
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780367375461.html
Raktažodžiai:
Although the origin of Earth's and other celestial bodies' magnetic fields remains unknown, we do know that the motion of electrically conducting fluids generates and maintains these fields, forming the basis of magnetohydrodynamics (MHD) and, to a larger extent, dynamo theory. Answering the need for a comprehensive, interdisciplinary introduction to this area, Mathematical Aspects of Natural Dynamos provides a foundation in dynamo theory before moving on to modeling aspects of natural dynamos.

Bringing together eminent international contributors, the book first introduces governing equations, outlines the kinematic dynamo theory, covers nonlinear effects, including amplitude saturation and polarity reversals, and discusses fluid dynamics. After establishing this base, the book describes the Earth's magnetic field and the current understanding of its characteristics. Subsequent chapters examine other planets in our solar system and the magnetic field of stars, including the sun. The book also addresses dynamo action on the large scale of galaxies, presents modeling experiments of natural dynamos, and speculates about future research directions.

After reading this well-illustrated, thorough, and unified exploration, you will be well prepared to embark on your own journey through this fascinating area of research.

Recenzijos

"Dormy and Soward are the editors of the book, they have done a magnificent job in taking what was evidently a series of paper written by scientists from around the world and combining them into a single book that has a consistent tone throughout out."

In Books-on-Line, August 2007

". . . the quality of the text is high, and the content is far from reiterating previous works . . . highly recommended; particularly those new to the field, but also as a reference and refresher for those already immersed in the topic."

Graeme Sarson, University of Newcastle, in GAFD, September 2008

Contributors xv
List of Tables
xvii
List of Notations
xix
Preface xxi
I Foundations of dynamo theory
1(198)
1 Introduction to self-excited dynamo action
3(56)
1.1 Governing equations
4(14)
1.1.1 Magnetic induction
4(4)
1.1.2 Thermodynamic equations
8(1)
1.1.3 Navier-Stokes equation
9(8)
1.1.4 Boundary conditions
17(1)
1.2 Homogeneous dynamos
18(6)
1.2.1 Disc dynamo
18(2)
1.2.2 Chirality and geometry
20(1)
1.2.3 Basic mechanisms of dynamo action
20(2)
1.2.4 Fast and slow dynamos
22(2)
1.3 Necessary conditions for dynamo action
24(7)
1.3.1 Definitions of dynamo action
24(1)
1.3.2 Non-normality of the induction equation
24(1)
1.3.3 Flow velocity bounds
25(1)
1.3.4 Geometrical constraints
26(5)
1.4 Steady and time-dependent velocities
31(3)
1.4.1 Two simple examples
31(1)
1.4.2 Pulsed flows
32(2)
1.5 Two-scale dynamos
34(7)
1.5.1 The two-scale concept and Parker's model
34(1)
1.5.2 Mean field electrodynamics
35(3)
1.5.3 Mean field models
38(3)
1.6 Large magnetic Reynolds numbers
41(18)
1.6.1 Slow dynamos in flows
42(5)
1.6.2 The stretch-twist-fold picture
47(2)
1.6.3 Fast dynamos in smooth flows
49(1)
1.6.4 Fast dynamos in mappings
50(4)
1.6.5 The stretch-fold-shear model
54(5)
2 Nonlinearities and saturation
59(60)
2.1 General considerations
59(3)
2.2 Saturation of a dynamo generated by a periodic flow
62(5)
2.2.1 Scale separation
63(1)
2.2.2 The G.O. Roberts dynamo
64(1)
2.2.3 Saturation of dynamos driven by the α-effect
65(2)
2.3 Saturation in the low Re limit in the vicinity of the dynamo threshold
67(3)
2.3.1 A Ponomarenko type dynamo as a tractable problem without scale separation
67(1)
2.3.2 Structure of the perturbation analysis
68(1)
2.3.3 The laminar scaling
69(1)
2.4 Saturation in the high Re limit in the vicinity of the dynamo threshold
70(2)
2.4.1 Dimensional arguments
70(1)
2.4.2 High Re dynamos close to the bifurcation threshold
71(1)
2.5 Effect of rotation
72(3)
2.5.1 Weak and strong field regimes of the geodynamo
72(1)
2.5.2 Further comments on weak and strong field regimes
73(1)
2.5.3 Scalings of magnetic energy using dimensional considerations
74(1)
2.6 Scaling laws in the limit of large Rm and Re
75(4)
2.6.1 Effect of turbulence on the dynamo threshold
76(1)
2.6.2 Batchelor's predictions for turbulent dynamo threshold and saturation
77(1)
2.6.3 A Kolmogorov type scaling in the limit Re << Rm << Rmc
78(1)
2.7 Nonlinear effects in mean field dynamo theory
79(18)
2.7.1 Nonlinear effects in the mean field formalism
81(7)
2.7.2 MHD turbulence theories
88(4)
2.7.3 Direct numerical simulations
92(5)
2.8 Physically-realistic Faraday-disc self-excited dynamos
97(22)
2.8.1 Historical survey
98(2)
2.8.2 Characteristics of self-excited dynamos
100(1)
2.8.3 Governing equations in dimensional form
101(2)
2.8.4 Energetics and equilibrium solutions
103(2)
2.8.5 Dimensionless equations
105(2)
2.8.6 Generic solutions
107(1)
2.8.7 Survey of behaviour
108(3)
2.8.8 Some numerical integrations
111(8)
3 Dynamics of rotating fluids
119(80)
3.1 Boundary and shear layers in rotating flows
120(16)
3.1.1 Ekman layers
121(3)
3.1.2 Sidewall E1/3--layers
124(3)
3.1.3 Sidewall E1/4--layers
127(4)
3.1.4 Differentially rotating spheres: The Proudman--Stewartson problem
131(5)
3.2 Boundary and shear layers in rotating MHD flows
136(15)
3.2.1 The Hartmann layer
137(2)
3.2.2 Differentially rotating spheres
139(3)
3.2.3 The Ekman--Hartmann layer
142(3)
3.2.4 Rotating MHD free shear layers; Λ M >> 1
145(6)
3.3 Waves
151(17)
3.3.1 Inertial waves
151(8)
3.3.2 Alfven waves
159(1)
3.3.3 MHD waves in rotating fluids
160(5)
3.3.4 Stratified rotating MHD waves
165(3)
3.4 Convection in rotating spherical fluid shells
168(31)
3.4.1 Physical motivations
168(1)
3.4.2 Convection in the rotating cylindrical annulus
169(8)
3.4.3 Mathematical formulation of the problem of convection in rotating spherical shells
177(2)
3.4.4 The onset of convection in rotating spherical shells
179(4)
3.4.5 Onset of inertial convection at low Prandtl numbers
183(1)
3.4.6 Evolution of convection columns at moderate Prandtl numbers
184(6)
3.4.7 Finite amplitude convection at higher Prandtl numbers
190(3)
3.4.8 Finite amplitude inertial convection
193(2)
3.4.9 Penetrative and compositional convection
195(2)
3.4.10 Concluding remarks on convection
197(2)
II Natural dynamos and models
199(214)
4 The geodynamo
201(56)
4.1 The Earth and its magnetic field
201(8)
4.1.1 A brief history
201(1)
4.1.2 Structure of the Earth
202(2)
4.1.3 The geomagnetic field
204(3)
4.1.4 Energy sources
207(2)
4.2 Governing equations and parameters
209(3)
4.3 Fundamental theoretical results
212(7)
4.3.1 Taylor's constraint
212(2)
4.3.2 The "arbitrary" geostrophic flow uG(S)
214(1)
4.3.3 Ekman states, Taylor states and model-Z: determination of the geostrophic flow uG
215(2)
4.3.4 The role of inertia
217(2)
4.4 Parameter constraints
219(4)
4.4.1 The Ekman number
220(1)
4.4.2 The magnetic Reynolds number
221(1)
4.4.3 The Roberts number
222(1)
4.4.4 The Rayleigh number
222(1)
4.4.5 The magnetic Ekman number
223(1)
4.5 Numerical models
223(6)
4.5.1 Nonlinear α2 and αω models
224(1)
4.5.2 2.5D models
224(1)
4.5.3 3D models
225(4)
4.6 Turbulence in the Earth's core: the ends justify the means?
229(2)
4.7 Preliminary considerations on turbulence
231(8)
4.7.1 The energy source
231(1)
4.7.2 Orders of magnitude
232(2)
4.7.3 Basic equations and their averages
234(1)
4.7.4 Qualitative descriptions of turbulence
235(4)
4.8 The traditional approach to turbulence
239(10)
4.8.1 A three-step program
239(1)
4.8.2 Linearised modes of a simple model
240(2)
4.8.3 The most easily excited mode
242(2)
4.8.4 More complicated and less complicated models
244(2)
4.8.5 Finite amplitudes
246(2)
4.8.6 An alternative application: DNS
248(1)
4.9 The engineering approach to turbulence
249(4)
4.9.1 Filtering
249(1)
4.9.2 Similarity and dynamical similarity
250(2)
4.9.3 Related methods
252(1)
4.10 Where are we now, and the future
253(4)
4.10.1 The geodynamo
253(1)
4.10.2 A critical summary of turbulence
254(3)
5 Planetary dynamos
257(24)
5.1 Observations of planetary magnetic fields
257(6)
5.2 Some outstanding problems in planetary dynamo theory
263(2)
5.3 Conditions needed for dynamo action in planets
265(2)
5.4 Energy sources for planetary dynamos
267(2)
5.5 Internal structure of the planets
269(4)
5.5.1 Giant planets
272(1)
5.5.2 Ice giants
273(1)
5.6 Dynamics of planetary interiors
273(5)
5.6.1 Typical velocity and field estimates
276(2)
5.7 Numerical dynamo models for the planets
278(3)
6 Stellar dynamos
281(32)
6.1 Stellar magnetic activity
281(3)
6.2 Linear αω--dynamos for the solar cycle
284(7)
6.2.1 Dynamo waves
285(2)
6.2.2 Spherical models
287(1)
6.2.3 The ω--effect
287(1)
6.2.4 The α--effect
288(2)
6.2.5 Magnetic pumping
290(1)
6.2.6 Meridional circulation
291(1)
6.3 Nonlinear quenching mechanisms
291(2)
6.4 Interface dynamos
293(4)
6.4.1 Spherical interface models
294(1)
6.4.2 Zonal shear flows
295(2)
6.5 Modulation of cyclic activity
297(11)
6.5.1 Deterministic modulation
299(5)
6.5.2 Low-order models
304(3)
6.5.3 On--off and in--out intermittency
307(1)
6.6 Rapidly rotating stars
308(3)
6.7 The future
311(2)
7 Galactic dynamos
313(48)
7.1 Introduction
313(3)
7.2 Interstellar medium in spiral galaxies
316(5)
7.2.1 Turbulence and multi-phase structure
316(3)
7.2.2 Galactic rotation
319(2)
7.3 Magnetic fields observed in galaxies
321(3)
7.4 The origin of galactic magnetic fields
324(18)
7.4.1 Mean-field models of the galactic dynamo
325(10)
7.4.2 The fluctuation dynamo and small-scale magnetic fields
335(3)
7.4.3 Magnetic helicity balance in the galactic disc
338(4)
7.5 Observational evidence for the origin of galactic magnetic fields
342(11)
7.5.1 Magnetic pitch angle
342(2)
7.5.2 The even (quadrupole) symmetry of magnetic field in the Milky Way
344(2)
7.5.3 The azimuthal structure
346(2)
7.5.4 A composite magnetic structure in M51 and magnetic reversals in the Milky Way
348(2)
7.5.5 The radial magnetic structure in M31
350(2)
7.5.6 Strength of the regular magnetic field
352(1)
7.6 Elliptical galaxies
353(2)
7.6.1 Turbulent interstellar gas in elliptical galaxies
354(1)
7.6.2 The fluctuation dynamo in elliptical galaxies
354(1)
7.7 Accretion discs
355(3)
7.8 Conclusions
358(3)
8 Survey of experimental results
361(48)
8.1 Introduction
361(3)
8.2 Description of the experiments
364(20)
8.2.1 A rapidly rotating disc in a cylinder of sodium
365(1)
8.2.2 A dynamo with two solid rotating cylinders
365(1)
8.2.3 The α--box experiment
366(2)
8.2.4 A precessing experiment in liquid sodium
368(1)
8.2.5 The first Ponomarenko type experiment
369(1)
8.2.6 The vortices of gallium
370(2)
8.2.7 The Riga dynamo
372(2)
8.2.8 The Karlsruhe dynamo
374(2)
8.2.9 The College Park experiments
376(1)
8.2.10 Von Karman Sodium experiments
377(1)
8.2.11 Derviche Tourneur Sodium project
378(1)
8.2.12 The Madison project
379(1)
8.2.13 The Perm project
379(1)
8.2.14 The Socorro project
380(1)
8.2.15 A new precessing project in sodium
380(1)
8.2.16 Technology and measurements in dynamo experiments
380(4)
8.3 What have we learnt from the experimental approach?
384(21)
8.3.1 The ω--effect
384(1)
8.3.2 Magnetic field expulsion
385(1)
8.3.3 The α--effect
386(3)
8.3.4 Quenching effects
389(1)
8.3.5 The experimental approach to a kinematic dynamo
390(4)
8.3.6 The onset of dynamo action
394(3)
8.3.7 The effect of turbulence
397(2)
8.3.8 Spectra
399(3)
8.3.9 The β-effect and turbulent viscosity
402(2)
8.3.10 Saturation of the dynamo
404(1)
8.4 Conclusions
405(4)
9 Prospects
409(4)
A Vectors and coordinates 413(4)
B Poloidal--Toroidal decomposition 417(2)
C Taylor's constraint 419(6)
D Units 425(2)
E Abbreviations 427(2)
References 429(42)
Reference Index 471(8)
Subject Index 479
Emmanuel Dormy, Andrew M. Soward