What is included with this book?
Preface | p. v |
Planets and Inspiration | p. 1 |
Venus | p. 1 |
Titan | p. 4 |
The Great Red Spot | p. 5 |
Polar Vortices and Other Curiosities | p. 7 |
Outline | p. 9 |
Barotropic and Shallow-Water Models | p. 13 |
The Physical Model | p. 13 |
Voronoi Cells and the Spin-Lattice Approximation | p. 16 |
The Solid Sphere Model | p. 20 |
The Shallow-Water Equations on the Rotating Sphere | p. 25 |
The Spin-Lattice Shallow-Water Model | p. 32 |
Circulation Constraints | p. 36 |
Enstrophy Constraints | p. 37 |
Gibbs Ensemble | p. 37 |
Dynamic Equilibria of the Barotropic Model - Variational Approach | p. 41 |
Energy-Relative Enstrophy Variational Theory | p. 41 |
The Augmented Energy Functional | p. 46 |
Extremals: Existence and Properties | p. 52 |
Statistical Mechanics | p. 61 |
Introduction | p. 61 |
Microstates and Macrostates | p. 63 |
Entropy | p. 63 |
Partition Functions | p. 64 |
Free Energies | p. 65 |
Planck's Theorem in Negative Temperatures | p. 66 |
Latent Heat and Orders of Phase Transitions | p. 68 |
The Monte Carlo Approach | p. 71 |
Introduction | p. 71 |
Markov Chains | p. 72 |
Detailed Balance | p. 74 |
The Metropolis Rule | p. 75 |
Multiple Canonical Constraints | p. 77 |
Ensemble Averages | p. 78 |
Metropolis-Hastings Monte Carlo Algorithm | p. 82 |
Phase Transitions in Energy-Relative Enstrophy Models | p. 85 |
Introduction | p. 85 |
Classical and Recent Energy-Enstrophy Theories | p. 86 |
Gaussian Model | p. 87 |
Spherical Model for Coupled Barotropic Flows | p. 88 |
Monte Carlo Simulations of the Energy-Relative Enstrophy Model | p. 89 |
Free Energy | p. 99 |
Extremal Free Energy in the Mean-Field Theory | p. 107 |
Introduction | p. 107 |
Equilibrium Statistical Mechanics | p. 108 |
Mean-Field Theory | p. 109 |
Setting Up Coupled Barotropic Flows | p. 111 |
Proofs for a Non-Rotating Planet | p. 113 |
Mean-Field Theory on a Rotating Sphere | p. 116 |
Positive Temperatures | p. 120 |
Negative Temperatures | p. 122 |
Phase Transitions of Barotropic Flow | p. 129 |
Introduction | p. 129 |
Statistical Mechanics of Macroscopic Flows | p. 131 |
Bragg-Williams Approximation | p. 133 |
Internal Energy | p. 136 |
Entropy | p. 140 |
Helmholtz Free Energy | p. 141 |
Polar State Criteria | p. 142 |
The Non-Rotating Case | p. 143 |
The Rotating Case | p. 146 |
Summary of Main Results | p. 154 |
The Infinite-Dimensional Non-Extensive Limit | p. 155 |
Phase Transitions to Super-Rotation - Exact Closed-Form Solutions | p. 159 |
Introduction | p. 159 |
The Rotating Sphere Model | p. 160 |
Solution of the Spherical Model | p. 162 |
The Shallow-Water Models - High Energy, Cyclonic Solutions | p. 169 |
Introduction | p. 169 |
First Order Transitions | p. 171 |
Antipodal Symmetry | p. 172 |
Monte Carlo Results | p. 174 |
Phase Transitions in Latent Heat | p. 177 |
Conclusion | p. 178 |
The Shallow-Water Model - Low-Energy Solutions | p. 183 |
Introduction | p. 183 |
Theoretical Predictions of the Shallow-Water Model | p. 185 |
The Energy Gap from Large Planetary Spin and Anticyclonic Spots | p. 186 |
North-South Asymmetry and the Energy Terms | p. 186 |
Large Relative Enstrophies and High Rim Velocities | p. 187 |
Angular Momentum, Moment of Inertia, Entropy, and the Location of the High Spot | p. 188 |
Monte Carlo Simulations and Results | p. 189 |
Key Features of the Great Red Spot-like Structure | p. 190 |
First-Order Phase Transition with Latent Heat | p. 191 |
Multiple High Spots in the Same Macrostate | p. 193 |
Belts and Zones | p. 193 |
Conclusion | p. 194 |
Bibliography | p. 201 |
Index | p. 207 |
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