Preface ....................................................... ix
1 Introduction ................................................ 1
1.1 Background and motivation .............................. 1
1.2 Outline of the book .................................... 6
1.3 General references ..................................... 7
2 Basic MHD ................................................... 9
2.1 The induction equation ................................. 9
2.2 Kinematic MHD ......................................... 17
2.3 The Lorentz force ..................................... 26
2.4 Kinematic dynamos ..................................... 31
3 Linearized Boussinesq magnet о convection .................. 38
3.1 Onset of convection in a vertical magnetic field ...... 39
3.2 Inclined magnetic fields .............................. 50
3.3 Other boundary conditions ............................. 60
4 The nonlinear regime ....................................... 64
4.1 Weakly nonlinear behaviour ............................ 66
4.2 Bifurcations from nonlinear solutions ................. 78
4.3 Period-doubling and chaos at a heteroclinic
bifurcation ........................................... 92
4.4 Travelling waves ..................................... 105
4.5 Transverse rolls in a horizontal field ............... 109
5 2D Boussinesq magnetoconvection ........................... 113
5.1 Numerical results: Cartesian geometry ................ 113
5.2 Axisymmetric magnetoconvection ....................... 134
5.3 Transitions to chaos ................................. 144
5.4 Shearing instabilities ............................... 152
5.5 Localized patterns, snaking and convectons ........... 158
5.6 The strong field limit ............................... 172
5.7 Inclined magnetic fields ............................. 176
6 3D Boussinesq magnetoconvection ........................... 180
6.1 Pattern selection .................................... 181
6.2 Convection and small-scale dynamos ................... 198
6.3 Fully nonlinear magnetoconvection .................... 206
6.4 The strong field regime .............................. 211
7 Magnetoconvection, rotation and the dynamo ................ 215
7.1 Linear theory of rotating convection and
magnetoconvection .................................... 216
7.2 Dynamos due to nonlinear rotating convection
in a layer ........................................... 229
7.3 Dynamos in spherical shells .......................... 240
7.4 Laboratory dynamos ................................... 246
8 Compressible magnetoconvection ............................ 251
8.1 The fully compressible regime ........................ 252
8.2 Two-dimensional behaviour ............................ 258
8.3 Three-dimensional behaviour .......................... 278
8.4 Inclined magnetic fields ............................. 307
9 Solar and stellar magnetic fields ......................... 320
9.1 Global magnetic activity ............................. 321
9.2 Photospheric magnetoconvection ....................... 330
9.3 Magnetoconvection in sunspots ........................ 338
9.4 From simple idealized models to massive nonlinear
computations ......................................... 347
Appendix A The Boussinesq and anelastic approximations ...... 349
A.l The Boussinesq approximation ......................... 350
A.2 The anelastic approximation .......................... 352
A.3 The strong anelastic approximation ................... 353
Appendix В Chaotic systems .................................. 355
B.l The logistic map ..................................... 355
B.2 The Lorenz equations ................................. 356
B.3 The Shilnikov bifurcation ............................ 358
Appendix С Double-diffusive convection ...................... 360
C.l Chaos in 2D thermosolutal convection ................. 360
C.2 Low-order model systems .............................. 365
Appendix D Magnetic buoyancy and the magneto-Boussinesq
approximation ............................................. 367
References ................................................ 370
Index ........................................................ 395
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