Magnetohydrodynamics with Hydrodynamics (eBook)

Front Cover 1
Magnetohydrodynamics with Hydrodynamics 4
Copyright Page 5
Table of Contents 6
Preface to Volume 1 10
Chapter I. TECHNIQUES 12
1:1 The development of the subject 12
1:2 Dimensional analysis 14
1:3 Vector analysis 16
1:4 Normal modes of oscillation and instability 23
1:5 Variational methods and instability 31
1:6 Linearizing an expression 35
1:7 Tensors 37
Exercises I 43
Chapter II. FUNDAMENTAL IDEAS IN HYDROSTATICS AND HYDRODYNAMICS 50
2:1 Introduction 50
2:2 The equations of inviscidì hydrodynamics 51
2:3 Hydrostatics and the equilibrium of gases 58
2:4 Steady motion of incompressible inviscid liquids 61
2:5 Viscous motion 74
2:6 Compressible fluids 78
2:7 Surface waves 90
Special references for Chapter II 94
Exercises 2 95
Chapter III. ELECTROMAGNETIC EFFECTS 100
3:1 Maxwell's equations 100
3:2 The Lorentz force and its transformations 102
3:3 Ohm's Law 106
3:4 The induction equation 108
3:5 The mechanical equations 109
3:6 The Poynting yector(50) 109
3:7 The boundary conditions 114
3:8 Simplification of the magnetohydrodynamic equations by dimensional analysis (53) 121
3:9 The motion of tubes of force in a perfectly conducting medium(55) 123
3:10 Dynamical principles 126
Exercises III 126
Chapter IV. MOTION OF A FLUID IN A UNIFORM MAGNETIC FIELD 132
4:1 Alfvén waves 132
4:2 Reflection and transmission of Alfvén waves at a discontinuity in the density(58) 136
4:3 The acoustic and hydromagnetic modes of wave propagation in a uniform infinitely conducting plasma (59) 138
4:4 Hydromagnetic oscillations(60) 141
4:5 Fitting an external magnetic field 144
4:6 Dispersion of surface currents when there is a normal magnetic field(62) 147
4:7 Effects of finite conductivity on hydromagnetic waves (63) 149
4:8 Hydromagnetic waves in a uniformly rotating liquid (64) 152
Chapter V. STEADY STATES AND EQUILIBRIUM CONFIGURATIONS 159
5:1 Magnetohydrostatic equilibrium 159
5:2 Simple equilibrium states 160
5:3 A variational property of the magnetic field 164
5:4 Similarities between magnetohydrostatic equilibria and hydrodynamic steady states 166
5:5 Magnetohydrodynamic steady states of an inviscid infinitely conducting fluid 169
5:6 Corpuscular flux (C-F) problems 170
5:7 Laminar flow of a conducting viscous liquid between parallel walls with a transverse magnetic field 177
REFERENCES 185
INDEX 190