| Organizers |
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ix | |
| Lecturers |
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xi | |
| Participants |
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xiii | |
| Preface |
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xv | |
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1 | (44) |
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5 | (5) |
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6 | (1) |
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The electromagnetism chain |
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6 | (1) |
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A short history of magnetohydrodynamics |
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7 | (3) |
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10 | (2) |
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12 | (1) |
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12 | (4) |
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12 | (1) |
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13 | (1) |
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13 | (1) |
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Balance of internal energy |
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14 | (1) |
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14 | (1) |
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Gross Heat budget for the Earth's core |
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15 | (1) |
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Joule versus viscous dissipation |
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15 | (1) |
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16 | (1) |
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16 | (6) |
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16 | (1) |
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17 | (1) |
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Zero dimensionless parameter |
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18 | (1) |
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One dimensionless parameter |
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18 | (1) |
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Two dimensionless parameters |
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19 | (2) |
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Three dimensionless parameters |
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21 | (1) |
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22 | (1) |
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22 | (2) |
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Quasi-linear approximation |
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22 | (1) |
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Quasi-static approximation |
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23 | (1) |
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A quick look at turbulence in the Earth core |
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24 | (1) |
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24 | (1) |
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24 | (1) |
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24 | (6) |
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25 | (1) |
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Two dimensional core flow |
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25 | (1) |
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26 | (1) |
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26 | (1) |
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27 | (1) |
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Skin effect/field expulsion |
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27 | (1) |
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28 | (2) |
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30 | (1) |
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30 | (7) |
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30 | (1) |
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Small magnetic Reynolds number |
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30 | (3) |
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Kinematic dynamo threshold |
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33 | (1) |
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33 | (1) |
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Dissipative energy stability |
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33 | (2) |
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Stability of non-dissipative MHD |
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35 | (2) |
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37 | (1) |
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38 | (5) |
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38 | (1) |
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Initial evolution of MHD turbulence |
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38 | (2) |
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40 | (1) |
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41 | (1) |
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Turbulence in Hartmann layers |
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41 | (1) |
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42 | (1) |
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43 | (2) |
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45 | (92) |
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51 | (15) |
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Maxwell and pre-Maxwell equations |
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51 | (2) |
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Integral form of the MHD equations |
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53 | (1) |
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53 | (1) |
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53 | (1) |
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54 | (1) |
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Electromagnetic theory in a moving frame |
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54 | (2) |
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Ohm's law, induction equation and boundary conditions |
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56 | (1) |
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56 | (1) |
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57 | (1) |
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57 | (1) |
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Nature of the induction equation: Magnetic Reynolds number |
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58 | (2) |
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The kinematic dynamo problem |
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60 | (1) |
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Vector potential, toroidal and poloidal decomposition |
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61 | (1) |
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61 | (1) |
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Toroidal-poloidal decomposition |
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61 | (1) |
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Axisymmetric field decomposition |
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62 | (1) |
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63 | (1) |
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63 | (1) |
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64 | (2) |
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Working kinematic dynamos |
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66 | (16) |
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Minimum Rm for dynamo action |
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66 | (1) |
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66 | (1) |
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67 | (1) |
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67 | (1) |
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Original Faraday disc dynamo (Fig. 2a) |
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67 | (1) |
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Homopolar self-excited dynamo (Fig. 2b) |
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68 | (1) |
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Moffatt's segmented homopolar dynamo (Fig. 3) |
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69 | (1) |
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69 | (1) |
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70 | (3) |
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Ponomarenko dynamo results |
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73 | (1) |
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Smooth Ponomarenko dynamo |
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73 | (1) |
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74 | (2) |
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Large Rm G.O. Roberts dynamo |
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76 | (1) |
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76 | (1) |
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77 | (1) |
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77 | (3) |
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80 | (1) |
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More specimens from the dynamo zoo! |
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80 | (1) |
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80 | (1) |
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81 | (1) |
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Lowes-Wilkinson dynamo experiment |
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81 | (1) |
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82 | (11) |
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Averaging the dynamo equations |
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82 | (1) |
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Mean field induction equation |
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83 | (1) |
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83 | (1) |
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84 | (1) |
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84 | (1) |
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Evaluation of (u' x B'), a closer look |
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85 | (1) |
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Tensor representation of ε |
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86 | (1) |
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87 | (1) |
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88 | (1) |
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Connection with G.O. Roberts dynamo |
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88 | (1) |
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89 | (1) |
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90 | (1) |
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Axisymmetric mean field dynamos |
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90 | (1) |
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90 | (1) |
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91 | (1) |
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91 | (1) |
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92 | (1) |
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93 | (10) |
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94 | (1) |
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The stretch-twist-fold dynamo |
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95 | (1) |
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Stretching and folding in 2D |
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96 | (1) |
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Baker's maps and stretch, fold, shear |
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96 | (1) |
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97 | (1) |
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Stretch-fold-shear in G.O. Roberts dynamo |
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98 | (1) |
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99 | (1) |
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100 | (1) |
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100 | (1) |
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100 | (1) |
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Time dependent flow fields |
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101 | (2) |
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103 | (10) |
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Basic ideas in nonlinear dynamos |
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103 | (1) |
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104 | (1) |
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Stellar dynamo saturation mechanisms |
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104 | (1) |
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Modelling saturation mechanisms |
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105 | (1) |
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105 | (1) |
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106 | (1) |
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α-quenching: small or large scale? |
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106 | (1) |
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α-quenching: magnetic helicity |
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107 | (1) |
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107 | (1) |
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Saturation in rapidly rotating systems |
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108 | (1) |
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108 | (1) |
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109 | (1) |
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110 | (1) |
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Dynamo models and Taylor's constraint |
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111 | (1) |
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Equipartition in rapid rotation? |
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111 | (1) |
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111 | (1) |
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Dynamo saturation in experiments |
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112 | (1) |
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Numerical methods for dynamos |
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113 | (9) |
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The pseudo-spectral method for a convection-driven plane layer dynamo |
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113 | (1) |
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Dimensionless plane layer equations |
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114 | (1) |
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Toroidal-poloidal expansion |
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114 | (1) |
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Toroidal-poloidal equations |
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115 | (1) |
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115 | (1) |
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115 | (1) |
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116 | (1) |
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117 | (1) |
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Methods for kinematic dynamos |
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118 | (1) |
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118 | (1) |
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119 | (1) |
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119 | (1) |
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Dynamical similarity model |
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120 | (1) |
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120 | (1) |
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Spherical geometry: spectral methods |
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121 | (1) |
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Spherical geometry: finite volume/element methods |
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121 | (1) |
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Convection driven plane layer dynamos |
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122 | (10) |
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122 | (2) |
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Weak field---strong field branches |
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124 | (1) |
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124 | (1) |
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Meneguzzi and Pouquet results |
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124 | (1) |
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124 | (1) |
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Jones and Roberts results |
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125 | (2) |
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127 | (1) |
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Stellmach and Hansen model |
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128 | (2) |
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Cattaneo and Hughes 2006 model |
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130 | (2) |
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132 | (5) |
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137 | (114) |
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Planetary dynamos introduction |
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143 | (12) |
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Planetary magnetic fields |
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143 | (1) |
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Definition of a planetary magnetic field |
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143 | (2) |
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What can be learned from planetary magnetic fields? |
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145 | (1) |
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Internal sources for planetary magnetic fields |
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145 | (1) |
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Rationale for the self-sustaining fluid dynamo mechanism for planetary magnetism |
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146 | (1) |
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Planet interior classification |
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146 | (1) |
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How to make a self-sustaining planetary dynamo |
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147 | (3) |
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150 | (2) |
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152 | (2) |
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Implications for planetary dynamos |
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154 | (1) |
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155 | (1) |
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Planetary dynamos, a short tour |
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156 | (23) |
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Planetary magnetic fields: comparison parameters |
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156 | (3) |
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Internal magnetic field intensity |
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159 | (1) |
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Sketches of individual planetary dynamos |
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159 | (1) |
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159 | (4) |
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163 | (1) |
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163 | (4) |
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167 | (2) |
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Why did the Martian dynamo die? |
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169 | (1) |
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170 | (1) |
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170 | (2) |
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172 | (1) |
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172 | (1) |
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173 | (1) |
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174 | (1) |
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174 | (1) |
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175 | (1) |
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Comparison of the magnetic state of the Galilean satellites |
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176 | (1) |
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177 | (1) |
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Outstanding questions in planetary dynamo theory |
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178 | (1) |
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179 | (1) |
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180 | (14) |
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The structure of the Earth's core |
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180 | (2) |
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182 | (1) |
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182 | (1) |
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183 | (4) |
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The adiabatic temperature gradient in the core |
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187 | (1) |
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Heat conduction and the core adiabat |
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188 | (1) |
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Adiabatic cooling of the core |
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188 | (1) |
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Heterogeneity in the lower mantle |
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189 | (1) |
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Dynamical interpretations of D'' |
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189 | (1) |
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The surprising inner core |
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190 | (2) |
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Summary of deep Earth structure |
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192 | (1) |
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193 | (1) |
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194 | (1) |
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Composition and physical properties of the core |
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194 | (12) |
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194 | (2) |
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The phase diagram of iron |
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196 | (1) |
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Light elements in the core |
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197 | (1) |
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Thermal significance of light elements in the core |
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198 | (1) |
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Constraints on the deep Earth geotherm |
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199 | (1) |
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Thermal boundary conditions at the cmb |
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200 | (1) |
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Thermal and chemical conditions near the inner core boundary |
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201 | (2) |
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Causes inner core anisotropy |
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203 | (1) |
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Radioactivity in the core |
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203 | (1) |
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Transport properties in the core |
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204 | (1) |
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204 | (1) |
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Thermal and electrical conductivity |
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204 | (1) |
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205 | (1) |
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206 | (1) |
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Energetics of the core and the geodynamo |
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207 | (22) |
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Growth of the solid inner core |
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207 | (1) |
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Chemical evolution of the core |
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208 | (1) |
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Gravitational dynamo mechanism |
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208 | (2) |
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Light element transport in the outer core |
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210 | (1) |
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211 | (1) |
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212 | (5) |
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217 | (1) |
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217 | (1) |
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218 | (1) |
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218 | (4) |
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Dynamo efficiency vs inner core radius |
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222 | (1) |
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Estimating the Ohmic dissipation in the core |
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222 | (1) |
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Ohmic dissipation estimated from the core field structure |
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223 | (1) |
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Ohmic dissipation estimated from numerical dynamos |
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223 | (2) |
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A simple evolution model of the core |
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225 | (1) |
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Detailed thermal evolution modeling |
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225 | (2) |
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227 | (2) |
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229 | (1) |
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Planetary dynamo scaling laws |
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230 | (9) |
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233 | (1) |
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233 | (1) |
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Scaling the dynamo equations |
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234 | (1) |
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Scaling with numerical dynamo models |
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235 | (1) |
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236 | (3) |
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239 | (1) |
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Gravitational and tomographic dynamo examples |
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240 | (9) |
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240 | (1) |
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Goals for numerical models of the geodynamo |
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240 | (1) |
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Gravitational dynamo model equations |
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241 | (3) |
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Behavior of chaotic gravitational dynamos |
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244 | (1) |
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Tomographic dynamo models |
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244 | (5) |
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249 | (2) |
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251 | (50) |
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255 | (1) |
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Observations of astrophysical magnetic fields |
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256 | (9) |
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256 | (2) |
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Synchrotron emission and Faraday rotation |
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258 | (2) |
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260 | (1) |
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260 | (1) |
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261 | (1) |
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262 | (3) |
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265 | (5) |
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266 | (1) |
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267 | (1) |
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Turbulence and multi-phase structure |
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267 | (2) |
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269 | (1) |
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270 | (1) |
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The necessity of dynamo action |
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270 | (2) |
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272 | (1) |
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Perturbation solutions for mean-field dynamos |
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273 | (11) |
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273 | (1) |
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274 | (1) |
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The perturbation expansion |
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275 | (4) |
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279 | (3) |
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Diffusion in mean-field dynamos |
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282 | (2) |
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Turbulent magnetic fields in galaxies and galaxy clusters |
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284 | (11) |
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284 | (2) |
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286 | (4) |
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Turbulence in galaxy clusters: three evolutionary stages |
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290 | (1) |
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The epoch of major mergers |
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290 | (1) |
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291 | (1) |
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Turbulent wakes of subclusters and galaxies |
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292 | (2) |
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Magnetic fields in the intracluster gas |
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294 | (1) |
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Interstellar turbulent magnetic fields |
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294 | (1) |
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295 | (1) |
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296 | (5) |
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301 | (58) |
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Introduction: turbulence AND dynamo? |
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305 | (1) |
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305 | (25) |
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305 | (2) |
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Spectra and number of degrees of freedom |
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307 | (1) |
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307 | (3) |
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310 | (1) |
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311 | (3) |
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314 | (2) |
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316 | (1) |
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317 | (2) |
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Stochastic description of turbulence |
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319 | (5) |
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324 | (1) |
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324 | (1) |
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325 | (1) |
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326 | (1) |
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Fluctuations modifications |
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327 | (1) |
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328 | (2) |
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330 | (27) |
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330 | (1) |
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330 | (1) |
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330 | (1) |
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Linear theory: instability |
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331 | (1) |
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331 | (1) |
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331 | (2) |
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333 | (8) |
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341 | (1) |
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342 | (1) |
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Non-linear dynamo: saturation and transport |
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343 | (1) |
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Weakly non-linear: saturation |
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344 | (3) |
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347 | (7) |
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354 | (3) |
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357 | (2) |
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Numerical modeling of liquid metal dynamo experiments |
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359 | (24) |
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363 | (1) |
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363 | (1) |
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364 | (3) |
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The periodic box numerical experiment |
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364 | (1) |
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364 | (1) |
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365 | (1) |
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366 | (1) |
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Turbulence and subgrid modeling |
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366 | (1) |
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367 | (2) |
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369 | (4) |
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Static or turbulent kinematic dynamo |
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369 | (1) |
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370 | (3) |
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373 | (4) |
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373 | (2) |
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On-Off intermittency dynamo |
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375 | (2) |
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377 | (1) |
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378 | (1) |
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378 | (5) |
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Taylor's constraint and torsional oscillations |
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383 | (20) |
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387 | (1) |
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387 | (5) |
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392 | (3) |
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Taylor's constraint and numerical models of the geodynamo |
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395 | (2) |
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Observations of rigid flow and torsional oscillations |
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397 | (2) |
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Conclusions and future direction |
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399 | (1) |
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400 | (3) |
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Waves in the presence of magnetic fields, rotation and convection |
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403 | (48) |
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407 | (4) |
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Some motivating thoughts concerning the study of waves |
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407 | (2) |
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Historical sketch and literature survey |
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409 | (2) |
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Inertial waves and intrinsic stability due to rotation |
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411 | (2) |
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The Coriolis force, vortex lines and Inertial oscillations in rotating fluids |
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411 | (1) |
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The Inertial wave equation |
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411 | (1) |
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Inertial wave dispersion relation and properties |
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412 | (1) |
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Alfven waves and magnetic tension |
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413 | (3) |
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The Lorentz force, magnetic field lines and Magneto-Inertial oscillations |
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413 | (1) |
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|
414 | (2) |
|
Alfven wave dispersion relation and properties |
|
|
416 | (1) |
|
Magnetic Coriolis (MC) waves |
|
|
416 | (4) |
|
Force balances in rapidly-rotating, hydromagnetic fluids |
|
|
416 | (1) |
|
|
|
417 | (1) |
|
MC wave dispersion relation and properties |
|
|
418 | (2) |
|
Magnetic Archimedes Coriolis (MAC) waves |
|
|
420 | (5) |
|
Influence of density stratification and convective instability |
|
|
420 | (4) |
|
|
|
424 | (1) |
|
MAC waves in spherical geometry |
|
|
425 | (6) |
|
Quasi-geostrophic (QG) models of MAC waves |
|
|
425 | (5) |
|
MAC waves in full sphere geometry |
|
|
430 | (1) |
|
Limitations of linear models and towards nonlinear models |
|
|
431 | (4) |
|
|
|
435 | (2) |
|
Waves in numerical dynamo simulations |
|
|
437 | (1) |
|
Concluding remarks on waves in geophysical and astrophysical systems |
|
|
438 | (1) |
|
Appendix A. Hide's β-plane model of MC Rossby waves |
|
|
439 | (2) |
|
Appendix B. Malkus' model of MC waves in a full sphere |
|
|
441 | (4) |
|
Appendix C. Busse and Soward's QG model of MAC waves |
|
|
445 | (2) |
|
|
|
447 | (4) |
|
Dynamos of the ice giants |
|
|
451 | |
|
|
|
|
|
455 | |
|
|
|
459 | |
|
Insights from numerical dynamo models |
|
|
460 | |
|
Conclusions and future prospects |
|
|
462 | |
|
|
|
463 | |
