Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

1. Barotropic geophysical flows and two-dimensional fluid flows: an elementary introduction; 2. The Response to large scale forcing; 3. The selective decay principle for basic geophysical flows; 4. Nonlinear stability of steady geophysical flows; 5. Topographic mean-flow interaction, nonlinear instability, and chaotic dynamics; 6. Introduction to empirical statistical theory; 7. Equilibrium statistical mechanics for systems of ordinary differential equations; 8. Statistical mechanics for the truncated quasi-geostrophic equations; 9. Empirical statistical theories for most probable states; 10. Assessing the potential applicability of equilibrium statistical theories for geophysical flows: an overview; 11. Predictions and comparison of equilibrium statistical theories; 12. Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation; 13. Predicting the jets and spots on Jupiter by equilibrium statistical mechanics; 14. Statistically relevant and irrelevant conserved quantities for truncated quasi-geostrophic flow and the Burger–Hopf model; 15. A mathematical framework for quantifying predictability utilizing relative entropy; 16. Barotropic quasi-geostrophic equations on the sphere; Bibliography; Index.