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Preface Author biography 1 Introduction 1.1 The fluid approximation 1.2 The hydrodynamic equations Exercise 2 Some basic concepts 2.1 Visualisation 2.2 Sound waves 2.3 Compressibility 2.3.1 The incompressible equations of motion 2.4 Rotation of fluid elements 2.4.1 Cireulation 2.4.2 Vorticity 2.4.3 Potential flo w 2.5 Gravitationally stratified fluid 2.5.1 Hydrostatic equilibrium 2.5.2 The Boussinesq and anelastic approximations 2.5.3 The hydrostatic approximation Exercises References 3 Steady flow of an ideal fluid 3.I Bernoulli's equation 3.1.1 Applications of Bernoulli's equation 3.2 Subsonic and supersonic flow 3.3 Flow through a nozzle 3.4 Stellar winds and accretion Exercises References 4 Viscosity 4.1 The viscous stress tensor 4.2 Viscous heating 4.3 Examples of viscous flow 4.4 Similarity and dimensionless parameters 4.5 Regimes of viscous flow: example of flow past a solid body 4.6 Boundary layers 4.7 Heat diffusion Exercises Reference 5 Waves and instabilities 5.1 Surface gravity waves 5.1.1 The shallow-water equations 5.2 One fluid on top of another fluid 5.3 Shear instability between two fluids 5.4 Internal gravity waves 5.5 Convection 5.6 Baroclinic instability 5.7 Turbulence 5.8 The Jeans instability Exercises References 6 Shocks 6.1 Viscous versus pressure gradient force 6.2 The jump conditions 6.3 Contexts 6.4 Hydraulic jumps Exercises 7 Vorticity and rotating fluids 7.1 Vortices 7.2 The vorticity equation 7.3 The momentum equation in a rotating frame of reference 7.4 The centrifugal force and the von Zeipel paradox 7.5 The vorticity equation in a rotating frame 7.6 Inertial waves 7.7 The Taylor-Proudman theorem 7.8 The geostrophic approximation 7.9 Rossby waves Exercises References 8 Magnetohydrodynamics: equations and basic concepts 8.1 The MHD equations 8.2 The MHD approximation 8.3 The magnetic and other fields 8.4 A brief note concerning units 8.5 Field lines, flux conservation and flux freezing 8.6 Magnetic diffusivity 8.7 Magnetic pressure, tension and energy density 8.8 Waves 8.9 Different regimes in MHD 8.10 Magnetic helicity 8.11 MHD equilibria Exercises References 9 MHD: astrophysical contexts 9.1 The solar corona 9.1.1 Force-free and potential fields 9.1.2 Energy minima 9.1.3 Reconnection 9.2 Jets: launching, collimation and instabilities 9.2.1 Launching 9.2.2 Collimation 9.2.3 Instability 9.3 Angular momentum transport in discs 9.3.1 MRI: physical mechanism and stability condition 9.3.2 The dispersion relation 9.3.3 MRI:remarks Exercises References Appendix A: Useful information ±à¼­ÊÖ¼Ç