1st Edition

Mathematical Aspects of Natural Dynamos

Edited By Emmanuel Dormy, Andrew M. Soward Copyright 2007
    516 Pages 20 Color & 101 B/W Illustrations
    by Chapman & Hall

    516 Pages 20 Color & 101 B/W Illustrations
    by Chapman & Hall

    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.


    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


    Emmanuel Dormy, Andrew M. Soward

    "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