## Chaotic processes in the geological sciencesThe subject matter of chaos and nonlinear dynamics has begun to spread to the geological sciences in the last several years. The articles in this book are from a workshop held at the University of Minnesota in June 1990 in which well-renowned geophysicists, geologists and applied mathematicians were in attendance. There were three areas of focus in the workshop: thermal convection as applied to the earth's mantle, magmatic dynamics and processes in geodynamo. The nonlinear nature of convection was discussed especially in light of recent advances made in the physics community of the phenomenon of hard-turbulent convection. This book is useful for graduate students and researchers in geophysics, applied mechanics, and applied mathematics. It should also be of interest to workers in other areas of thermal convection. |

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### Contents

Foreword ix | 1 |

Convection and chaos | 43 |

Strongly chaotic Newtonian and nonNewtonian | 71 |

Copyright | |

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amplitude analysis anomaly aspect-ratio axisymmetric bifurcation boundary conditions boundary layer buoyancy cells chaotic coefficient component composition conductivity constant core country rock density diffusion dimensionless dispersion model dynamics Earth earth's mantle effects eigenvalue energy equations equilibrium eruptions eutectic evolution Figure fixed-point subspaces flow Fluid Mech fraction solid geodynamo geoid geomagnetic Geophys geophysical hard turbulent heat horizontal infinite Prandtl number initial instabilities interface isotropy kinetic lava lakes linear liquid lower mantle Lyapunov exponent magma chambers mantle convection mantle viscosity mass flux melt motions mush region mushy layer non-Newtonian nonlinear nucleation Nusselt observed parameter pattern Peltier phase transitions Phys plate plumes predicted pressure problem radial rheology scale seismic seismic tomography shows simulations spherical harmonic spherical shell stable stream function structure subspace surface symmetry temperature theory thermal boundary layer thermal convection thickness time-dependent upwelling variables variations velocity viscosity volcanic volume vorticity Yuen