Mathematical Aspects of Natural Dynamos

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.

PREFACEFOUNDATIONS OF DYNAMO THEORYIntroduction to Self-Excited Dynamo ActionGoverning equations Homogeneous dynamos Necessary conditions for dynamo actionSteady and time-dependent velocities Two-scale dynamos Large magnetic Reynolds numbersNonlinearities 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 rotationScaling laws in the limit of large Rm and ReNonlinear effects in mean field dynamo theoryPhysically realistic Faraday-disc self-excited dynamosDynamics of Rotating Fluids Boundary and shear layers in rotating flows Boundary and shear layers in rotating MHD flows Waves Convection in rotating spherical fluid shellsNATURAL DYNAMOS AND MODELS The Geodynamo The Earth and its magnetic fieldGoverning equations and parameters Fundamental theoretical results Parameter constraints Numerical modelsTurbulence in the Earth's core: the ends justify the means? Preliminary considerations on turbulenceThe traditional approach to turbulence The engineering approach to turbulence Where are we now, and the futurePlanetary Dynamos Observations of planetary magnetic fields Some outstanding problems in planetary dynamo theoryConditions needed for dynamo action in planets Energy sources for planetary dynamosInternal structure of the planetsDynamics of planetary interiorsNumerical dynamo models for the planetsStellar DynamosStellar magnetic activityLinear a?-dynamos for the solar cycleNonlinear quenching mechanisms Interface dynamos Modulation of cyclic activity Rapidly rotating starsThe futureGalactic Dynamos Introduction Interstellar medium in spiral galaxies Magnetic fields observed in galaxiesThe origin of galactic magnetic fields Observational evidence for the origin of galactic magnetic fieldsElliptical galaxies Accretion discs Conclusions Survey of Experimental ResultsIntroductionDescription of the experimentsWhat have we learned from the experimental approach?ConclusionsProspectsAppendix 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