Contributors |
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xv | |
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xvii | |
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xix | |
Preface |
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xxi | |
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I. Foundations of dynamo theory |
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1 | (198) |
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Introduction to self-excited dynamo action |
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3 | (56) |
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4 | (14) |
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4 | (4) |
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8 | (1) |
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9 | (8) |
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17 | (1) |
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18 | (6) |
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18 | (2) |
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20 | (1) |
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Basic mechanisms of dynamo action |
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20 | (2) |
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22 | (2) |
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Necessary conditions for dynamo action |
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24 | (7) |
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Definitions of dynamo action |
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24 | (1) |
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Non-normality of the induction equation |
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24 | (1) |
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25 | (1) |
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26 | (5) |
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Steady and time-dependent velocities |
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31 | (3) |
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31 | (1) |
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32 | (2) |
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34 | (7) |
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The two--scale concept and Parker's model |
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34 | (1) |
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Mean field electrodynamics |
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35 | (3) |
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38 | (3) |
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Large magnetic Reynolds numbers |
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41 | (18) |
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42 | (5) |
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The stretch--twist--fold picture |
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47 | (2) |
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Fast dynamos in smooth flows |
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49 | (1) |
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50 | (4) |
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The stretch--fold--shear model |
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54 | (5) |
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Nonlinearities and saturation |
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59 | (60) |
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59 | (3) |
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Saturation of a dynamo generated by a periodic flow |
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62 | (5) |
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63 | (1) |
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64 | (1) |
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Saturation of dynamos driven by the α--effect |
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65 | (2) |
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Saturation in the low Re limit in the vicinity of the dynamo threshold |
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67 | (3) |
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A Ponomarenko type dynamo as a tractable problem without scale separation |
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67 | (1) |
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Structure of the perturbation analysis |
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68 | (1) |
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69 | (1) |
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Saturation in the high Re limit in the vicinity of the dynamo threshold |
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70 | (2) |
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70 | (1) |
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High Re dynamos close to the bifurcation threshold |
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71 | (1) |
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72 | (3) |
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Weak and strong field regimes of the geodynamo |
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72 | (1) |
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Further comments on weak and strong field regimes |
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73 | (1) |
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Scalings of magnetic energy using dimensional considerations |
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74 | (1) |
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Scaling laws in the limit of large Rm and Re |
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75 | (4) |
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Effect of turbulence on the dynamo threshold |
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76 | (1) |
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Batchelor's predictions for turbulent dynamo threshold and saturation |
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77 | (1) |
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A Kolmogorov type scaling in the limit Re >> Rm << Rmc |
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78 | (1) |
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Nonlinear effects in mean field dynamo theory |
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79 | (18) |
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Nonlinear effects in the mean field formalism |
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81 | (7) |
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88 | (4) |
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Direct numerical simulations |
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92 | (5) |
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Physically-realistic Faraday-disc self-excited dynamos |
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97 | (22) |
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98 | (2) |
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Characteristics of self-excited dynamos |
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100 | (1) |
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Governing equations in dimensional form |
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101 | (2) |
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Energetics and equilibrium solutions |
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103 | (2) |
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105 | (2) |
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107 | (1) |
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108 | (3) |
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Some numerical integrations |
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111 | (8) |
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Dynamics of rotating fluids |
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119 | (80) |
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Boundary and shear layers in rotating flows |
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120 | (16) |
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121 | (3) |
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124 | (3) |
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127 | (4) |
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Differentially rotating spheres: The Proudman--Stewartson problem |
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131 | (5) |
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Boundary and shear layers in rotating MHD flows |
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136 | (15) |
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137 | (2) |
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Differentially rotating spheres |
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139 | (3) |
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The Ekman--Hartmann layer |
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142 | (3) |
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Rotating MHD free shear layers; A < 1 |
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145 | (6) |
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151 | (17) |
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151 | (8) |
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159 | (1) |
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MHD waves in rotating fluids |
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160 | (5) |
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Stratified rotating MHD waves |
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165 | (3) |
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Convection in rotating spherical fluid shells |
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168 | (31) |
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168 | (1) |
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Convection in the rotating cylindrical annulus |
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169 | (8) |
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Mathematical formulation of the problem of convection in rotating spherical shells |
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177 | (2) |
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The onset of convection in rotating spherical shells |
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179 | (4) |
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Onset of inertial convection at low Prandtl numbers |
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183 | (1) |
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Evolution of convection columns at moderate Prandtl numbers |
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184 | (6) |
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Finite amplitude convection at higher Prandtl numbers |
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190 | (3) |
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Finite amplitude inertial convection |
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193 | (2) |
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Penetrative and compositional convection |
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195 | (2) |
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Concluding remarks on convection |
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197 | (2) |
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II. Natural dynamos and models |
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199 | (214) |
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201 | (56) |
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The Earth and its magnetic field |
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201 | (8) |
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201 | (1) |
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202 | (2) |
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204 | (3) |
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207 | (2) |
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Governing equations and parameters |
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209 | (3) |
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Fundamental theoretical results |
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212 | (7) |
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212 | (2) |
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The ``arbitrary'' geostrophic flow uG(S) |
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214 | (1) |
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Ekman states, Taylor states and model-Z: determination of the geostrophic flow uG |
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215 | (2) |
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217 | (2) |
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219 | (4) |
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220 | (1) |
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The magnetic Reynolds number |
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221 | (1) |
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222 | (1) |
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222 | (1) |
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The magnetic Ekman number |
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223 | (1) |
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223 | (6) |
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Nonlinear α2 and αω models |
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224 | (1) |
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224 | (1) |
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225 | (4) |
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Turbulence in the Earth's core: the ends justify the means? |
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229 | (2) |
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Preliminary considerations on turbulence |
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231 | (8) |
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231 | (1) |
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232 | (2) |
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Basic equations and their averages |
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234 | (1) |
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Qualitative descriptions of turbulence |
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235 | (4) |
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The traditional approach to turbulence |
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239 | (10) |
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239 | (1) |
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Linearised modes of a simple model |
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240 | (2) |
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The most easily excited mode |
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242 | (2) |
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More complicated and less complicated models |
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244 | (2) |
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246 | (2) |
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An alternative application: DNS |
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248 | (1) |
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The engineering approach to turbulence |
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249 | (4) |
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249 | (1) |
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Similarity and dynamical similarity |
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250 | (2) |
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252 | (1) |
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Where are we now, and the future |
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253 | (4) |
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253 | (1) |
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A critical summary of turbulence |
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254 | (3) |
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257 | (24) |
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Observations of planetary magnetic fields |
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257 | (6) |
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Some outstanding problems in planetary dynamo theory |
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263 | (2) |
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Conditions needed for dynamo action in planets |
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265 | (2) |
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Energy sources for planetary dynamos |
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267 | (2) |
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Internal structure of the planets |
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269 | (4) |
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272 | (1) |
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273 | (1) |
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Dynamics of planetary interiors |
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273 | (5) |
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Typical velocity and field estimates |
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276 | (2) |
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Numerical dynamo models for the planets |
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278 | (3) |
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281 | (32) |
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Stellar magnetic activity |
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281 | (3) |
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Linear αω--dynamos for the solar cycle |
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284 | (7) |
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285 | (2) |
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287 | (1) |
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287 | (1) |
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288 | (2) |
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290 | (1) |
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291 | (1) |
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Nonlinear quenching mechanisms |
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291 | (2) |
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293 | (4) |
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Spherical interface models |
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294 | (1) |
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295 | (2) |
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Modulation of cyclic activity |
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297 | (11) |
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299 | (5) |
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304 | (3) |
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On--off and in--out intermittency |
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307 | (1) |
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308 | (3) |
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311 | (2) |
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313 | (48) |
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313 | (3) |
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Interstellar medium in spiral galaxies |
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316 | (5) |
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Turbulence and multi-phase structure |
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316 | (3) |
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319 | (2) |
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Magnetic fields observed in galaxies |
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321 | (3) |
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The origin of galactic magnetic fields |
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324 | (18) |
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Mean-field models of the galactic dynamo |
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325 | (10) |
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The fluctuation dynamo and small-scale magnetic fields |
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335 | (3) |
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Magnetic helicity balance in the galactic disc |
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338 | (4) |
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Observational evidence for the origin of galactic magnetic fields |
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342 | (11) |
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342 | (2) |
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The even (quadrupole) symmetry of magnetic field in the Milky Way |
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344 | (2) |
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346 | (2) |
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A composite magnetic structure in M51 and magnetic reversals in the Milky Way |
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348 | (2) |
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The radial magnetic structure in M31 |
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350 | (2) |
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Strength of the regular magnetic field |
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352 | (1) |
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353 | (2) |
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Turbulent interstellar gas in elliptical galaxies |
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354 | (1) |
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The fluctuation dynamo in elliptical galaxies |
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354 | (1) |
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355 | (3) |
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358 | (3) |
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Survey of experimental results |
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361 | (48) |
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361 | (3) |
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Description of the experiments |
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364 | (20) |
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A rapidly rotating disc in a cylinder of sodium |
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365 | (1) |
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A dynamo with two solid rotating cylinders |
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365 | (1) |
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366 | (2) |
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A precessing experiment in liquid sodium |
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368 | (1) |
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The first Ponomarenko type experiment |
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369 | (1) |
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370 | (2) |
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372 | (2) |
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374 | (2) |
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The College Park experiments |
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376 | (1) |
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Von Karman Sodium experiments |
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377 | (1) |
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Derviche Tourneur Sodium project |
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378 | (1) |
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379 | (1) |
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379 | (1) |
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380 | (1) |
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A new precessing project in sodium |
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380 | (1) |
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Technology and measurements in dynamo experiments |
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380 | (4) |
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What have we learnt from the experimental approach? |
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384 | (21) |
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384 | (1) |
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385 | (1) |
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386 | (3) |
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389 | (1) |
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The experimental approach to a kinematic dynamo |
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390 | (4) |
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The onset of dynamo action |
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394 | (3) |
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397 | (2) |
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399 | (3) |
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The β--effect and turbulent viscosity |
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402 | (2) |
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404 | (1) |
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405 | (4) |
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409 | (4) |
Vectors and coordinates |
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413 | (4) |
Poloidal--Toroidal decomposition |
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417 | (2) |
Taylor's constraint |
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419 | (6) |
Units |
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425 | (2) |
Abbreviations |
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427 | (2) |
References |
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429 | (42) |
Reference Index |
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471 | (8) |
Subject Index |
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479 | |