Core-mantle coupling mechanisms

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Table of contents

1 Introduction 
1.1 Overview
1.2 Earth’s core
1.2.1 Earth’s interior structure
1.2.2 Properties of the liquid outer core
1.2.3 Geodynamo and convection in the outer core
1.2.4 Core-mantle boundary topography
1.3 The equations governing flows in planetary cores
1.3.1 Fluid description in the rotating frame
1.3.2 Magnetohydrodynamic equations
1.3.3 Dimensional analysis
1.3.4 Reduced models in planetary fluid dynamics
1.4 Length-of-day variations and core-mantle interactions
1.4.1 Observed length-of-day variations
1.4.2 Torque balance
1.4.3 Core-mantle coupling mechanisms
1.5 Geomagnetic field changes and core flow inversions
2 Quasi-geostrophic models 
2.1 Small slope approximation
2.2 Quasi-geostrophic approximation
2.3 Vorticity equation
2.4 Galerkin approach
2.5 Lagrangian formalism
2.6 Columnar magnetic field
2.7 Non-axisymmetric core volume
2.7.1 Cartesian basis in the ellipsoid
2.7.2 Non-orthogonal coordinate systems
3 Modes in a planetary core 
3.1 Inertial modes
3.2 Quasi-geostrophic inertial modes
3.3 Magneto-Coriolis modes
3.4 Taylor’s constraint and torsional Alfvén modes
3.5 Excitation and presence of hydromagnetic modes in Earth’s core
3.6 Numerical calculation of modes
3.6.1 Solving the generalized eigen problem
3.6.2 Code examples
4 Torsional Alfvén modes in a non-axisymmetric domain 
4.1 Pressure torque of torsional Alfvén modes acting on an ellipsoidal mantle
4.2 Pressure in a quasi-geostrophic model
4.3 Towards more complex geometries using non-orthogonal coordinates
5 On quasi-geostrophic Magneto-Coriolis modes 
5.1 Fast quasi-geostrophic Magneto-Coriolis modes in the Earth’s core
5.2 Diffusive Magneto-Coriolis modes
5.3 Towards an insulating magnetic field basis in the ellipsoid
6 Conclusions & Perspectives