Physics of the Earth's Core (eBook)

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