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Mathematical Aspects of Natural Dynamos





ISBN 9780367375461
Published August 19, 2019 by Chapman and Hall/CRC
20 Color & 101 B/W Illustrations

 
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Book Description

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.

Table of Contents

PREFACE

FOUNDATIONS OF DYNAMO THEORY
Introduction to Self-Excited Dynamo Action
Governing equations
Homogeneous dynamos
Necessary conditions for dynamo action
Steady and time-dependent velocities
Two-scale dynamos
Large magnetic Reynolds numbers

Nonlinearities and Saturation
General considerations
Saturation of a dynamo generated by a periodic flow
Saturation in the low Re limit in the vicinity of the dynamo threshold
Saturation in the high Re limit in the vicinity of the dynamo threshold
Effect of rotation
Scaling laws in the limit of large Rm and Re
Nonlinear effects in mean field dynamo theory
Physically realistic Faraday-disc self-excited dynamos

Dynamics of Rotating Fluids
Boundary and shear layers in rotating flows
Boundary and shear layers in rotating MHD flows
Waves
Convection in rotating spherical fluid shells

NATURAL DYNAMOS AND MODELS
The Geodynamo
The Earth and its magnetic field
Governing equations and parameters
Fundamental theoretical results
Parameter constraints
Numerical models
Turbulence in the Earth's core: the ends justify the means?
Preliminary considerations on turbulence
The traditional approach to turbulence
The engineering approach to turbulence
Where are we now, and the future

Planetary Dynamos
Observations of planetary magnetic fields
Some outstanding problems in planetary dynamo theory
Conditions needed for dynamo action in planets
Energy sources for planetary dynamos
Internal structure of the planets
Dynamics of planetary interiors
Numerical dynamo models for the planets

Stellar Dynamos
Stellar magnetic activity
Linear a?-dynamos for the solar cycle
Nonlinear quenching mechanisms
Interface dynamos
Modulation of cyclic activity
Rapidly rotating stars
The future

Galactic Dynamos
Introduction
Interstellar medium in spiral galaxies
Magnetic fields observed in galaxies
The origin of galactic magnetic fields
Observational evidence for the origin of galactic magnetic fields
Elliptical galaxies
Accretion discs
Conclusions

Survey of Experimental Results
Introduction
Description of the experiments
What have we learned from the experimental approach?
Conclusions

Prospects

Appendix A: Vectors and coordinates
Appendix B: Poloidal-Toroidal decomposition
Appendix C: Taylor's constraint
Appendix D: Units
Appendix E: Abbreviations

References

Reference Index
Subject Index

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Reviews

"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