Mathematical Aspects of Natural Dynamos: 1st Edition (Hardback) book cover

Mathematical Aspects of Natural Dynamos

1st Edition

Edited by Emmanuel Dormy, Andrew M. Soward

Chapman and Hall/CRC

504 pages | 20 Color Illus. | 101 B/W Illus.

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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.


"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

Table of Contents



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


Convection in rotating spherical fluid shells


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


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


Survey of Experimental Results


Description of the experiments

What have we learned from the experimental approach?



Appendix A: Vectors and coordinates

Appendix B: Poloidal-Toroidal decomposition

Appendix C: Taylor's constraint

Appendix D: Units

Appendix E: Abbreviations


Reference Index

Subject Index

About the Series

The Fluid Mechanics of Astrophysics and Geophysics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Astrophysics & Space Science
SCIENCE / Geophysics
SCIENCE / Physics