Melchior The Physics of the Earth's Core

An Introduction
1. Auflage 2013
ISBN: 978-1-4832-8646-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 265 Seiten, Web PDF

An expanded version of a course on the physics of the Earth's interior by an internationally recognised expert in the field. It is a reference text providing condensed information on those essential physical topics needed by both the non-specialist scientist and student to follow the most recent developments in internal geophysics. It is a key to understanding papers covering theoretical geophysics where the basic formulae, definitions and theorems cannot be explained in detail due to the limited space and thus enables the reader to remain aware of the continuous progress being made in studying the Earth's interior.

Autoren/Hrsg.

Melchior, P.

Inhaltsverzeichnis

1;Front Cover;1
2;The Physics of the Earth's Core: An Introduction;6
3;Copyright Page;7
4;Table of Contents;8
5;Introduction;10
5.1;Bibliography;13
5.2;Additional references;14
6;CHAPTER 1. THE MODEL OF THE EARTH;15
6.1;1.1 Shape and dimensions of the model;15
6.2;1.2 The rotation of the model of the Earth;18
6.3;1.3 Gravity and pressure inside the Earth;28
6.4;1.4 Seismological model for the internal structure of the Earth;30
6.5;1.5 Stratification of the liquid core;42
6.6;1.6 Topography of the core-mantle interface;47
6.7;Bibliography;50
7;CHAPTER 2. THERMODYNAMICS;53
7.1;2.1 Fundamental thermodynamic relations;53
7.2;2.2 Definitions of fundamental thermodynamic parameters;55
7.3;2.3 Adiabatic gradient of temperature;56
7.4;2.4 The Wiedemann-Franz law;57
7.5;2.5 Measurements of electrical conductivity;58
7.6;2.6 The Grüneisen parameter .;61
7.7;2.7 Introduction of the Grüneisen parameter in fundamental relations;65
7.8;2.8 The Clausius Clapeyron Equation;66
7.9;2.9 Lindemann's law of fusion;68
7.10;2.10 Chemical constitution of the liquid core;69
7.11;2.11 The temperature profile inside the Earth;72
7.12;2.12 Two "core paradoxes";76
7.13;2.13 Transport properties - diffusivity and conductivity;77
7.14;2.14 Heat flow from the core;79
7.15;2.15 Viscosity;83
7.16;2.16 Diffusion in a medium composed by two substances: "Onsager relations";87
7.17;Bibliography;90
8;CHAPTER 3. HYDRODYNAMICS;93
8.1;3.1 Lagrangian and Eulerian descriptions;93
8.2;3.2 Equations of conservation;95
8.3;3.3 Dimensionless characteristic numbers in hydrodynamics;101
8.4;3.4 Heimholtz equation;104
8.5;3.5 Geostrophic flow, Taylor columns;104
8.6;3.6 Classical approximations;108
8.7;3.7 Differential equations of the perturbed pressure in a rotating spheroid;111
8.8;3.8 Boundary condition for the reduced pressure;118
8.9;3.9 Solution of the Poincaré equation by separation of variables;118
8.10;3.10 Greenspan equation in cylindrical coordinates;120
8.11;3.11 A Poincaré equation for the velocity field;121
8.12;3.12 Stratified fluids, internal gravity waves;122
8.13;3.13 Turbulence in hydrodynamics;130
8.14;3.14 The boundary layers in hydrodynamics;135
8.15;3.15 Rotating fluid - elementary properties of the viscous Ekman boundary layer;141
8.16;3.16 The rotating vertical cylinder: Stewartson sidewall boundary layers;145
8.17;3.17 Spin-up, Ekman suction;148
8.18;3.18 Thermal instability—the Rayleigh number;149
8.19;3.19 An application of Navier equation and boundary layer theory to the problem of differential rotation speed of the core and mantle of the Earth;151
8.20;Bibliography;158
9;CHAPTER 4. GEOMAGNETISM;162
9.1;4.1 Fundamental laws of electromagnetism;162
9.2;4.2 Main features of the geomagnetic field;166
9.3;4.3 Penetration of the magnetic field and currents into the lower mantle: skin depth;174
9.4;4.4 Analogy between the magnetic induction equation and the vorticity equation;175
9.5;4.5 Magnetic dimensionless characteristic numbers;176
9.6;4.6 Lorentz force and Maxwell stresses;177
9.7;4.7 Magnetohydrodynamic waves: the Alfvén waves;179
9.8;4.8 Magnetostrophic waves;182
9.9;4.9 The Hartmann number;185
9.10;4.10 Hydromagnetic boundary layers;186
9.11;4.11 Energy budget;194
9.12;4.12 The geodynamo;199
9.13;4.13 Fluid movements in the core;205
9.14;4.14 Electric radius of the core;209
9.15;Bibliography;212
10;CHAPTER 5. GEOPHYSICAL IMPLICATIONS IN THE EARTH'S CORE;218
10.1;5.1 Review summary of the different kinds of waves in the core: classification and terminology;218
10.2;5.2 Possible sources of mechanical energy to entertain convection in the Earth's core;221
10.3;5.3 Gravitational potential energy liberated during the formation of the inner core;223
10.4;5.4 Some remarks about the boundary layers;224
10.5;5.5 Core-mantle coupling;227
10.6;Bibliography;238
11;Appendix;241
11.1;Correspondence of units currently used in internal geophysics;241
11.2;The Earth;242
11.3;The Earth's core;243
11.4;Thermodynamic properties of the Earth's core;243
11.5;Electromagnetic properties of the Earth's core;244
11.6;Dimensionless numbers in the Earth's core;244
11.7;The Earth's inner core;244
11.8;Differential operators and fundamental formulas;246
11.9;Differential equations of the second order;249
11.10;Toroidal and poloidal vectorial fields;252
12;Glossary;254
13;Author Index;258
14;Subject Index;262