Magnetohydrodynamics and the Earth's Core
Selected Works by Paul Roberts
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Paul Roberts' research contributions are remarkable in their diversity, depth and international appeal. Papers from the Paul Roberts' Anniversary meeting at the University of Exeter are presented in this volume. Topics include geomagnetism and dynamos, fluid mechanics and MHD, superfluidity, mixed phase regions, mean field electrodynamics and the Earth's inner core. An incisive commentary of the papers puts the work of Paul Roberts into historical context. Magnetohydrodynamics and the Earth's Core provides a valuable source of reference for graduates and researchers working in this area of geoscience.
Table of Contents
Section A: Geomagnetism and Dynamos. Propagation of induced fields through the Core. On analysis of the secular variation, 1 hydromagnetic constraint: Theory. Some comments on the theory of homogeneous dynamos. Nearly symmetric hydromagnetic dynamos. Magnetic core-mantle coupling by inertial waves. A three-dimensional Kinematic dynamo. Are planetary dynamos driven by gravitational setting? A study of conditions at the inner core boundary of the Earth. Structure of the Earth's inner core. Time-dependent electromagnetic core-mantle coupling. On topographic core-mantle coupling. A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle. A three-dimensional self-consistent computer simulation of the geomagnetic field. An anelastic evolutionary geodynamo simulation driven by compositional and thermal convection. Rotation and magnetism of Earth's inner core. Section B: Fluid Mechanics and MHD. Characteristic value problems posed by differential equations arising in hydrodynamics and hydromagnetics. On the motion of liquid in a spheroidal cavity of a precessing rigis body. The ellipticity of a slowly rotating configuration. Singularities of Hartmann layers. The critical layer in stratified shear flow. On the hydromagnetics of rotating fluids. A transformation of the stellar wind equations. A Hamiltonian theory for weakly interacting vortices. A unified approach to mean field electrodynamics. MAC waves. On the motion of a fluid that is incompressible in a generalized sense, and its relationship to the Bousinesq approximation. Nonlinear theory of localized standing waves. Ideal instabilities in rapidly rotating MPD systems that have critical layers. Structure and stability of a spherical implosion. Thermal inertial waves in a rotating fluid layer: Exact and asymptotic solutions. The decay of bubble oscillations. Section C: Superfluidity. Roton-phonon relaxation times in helium II. Nucleation of quantized vortex rings by ions in helium II. Theory of the onset of superflow. Motion of ions at finite velocities in helium II. Dynamics of rotons. A simple theory of temperature dependent energy levels : application to He II. The electron bubble in liquid helium. Calculation of the static healing length in helium II. Superflow in restricted geometries. Non-linear hydrodynamics and one fluid theory of Superfluid He4. What happens to vortex rings that shrink? Section D: Mixed Phase Regions. On the life cycle of a mush. Relaxation effects and the evolution of a mush. Superfluidity D. Mixed Phase Regions.