Nonlinear Physical Oceanography

Preface Acknowledgments 1. Introduction 1.1 Past Climate Variability 1.2 The Present Ocean Circulation 1.3 Present Climate Variability 1.4 Physics of Climate Variability 1.5 Exercises on Chapter 1 2. Background Material 2.1 Basic Equations 2.2 Vorticity Transport 2.3 Potential Vorticity 2.4 Stability 2.5 Exercises on Chapter 2 3. A Dynamical Systems Point of View 3.1 An Elementary Problem 3.2 Dynamical Systems: Fixed Points 3.3 Periodic Solutions and their Stability 3.4 Bifurcations of Periodic Orbits 3.5 Global Bifurcations 3.6 Synchronization Phenomena 3.7 Physics of Bifurcation Behavior 3.8 Exercises on Chapter 3 4. Numerical Techniques 4.1 A Prototype Problem 4.2 Computation of Steady Solutions 4.3 Detection and Switching 4.4 Linear Stability Problem 4.5 Implicit Time Integration 4.6 Linear System Solvers: Direct Methods 4.7 Linear System Solvers: Iterative Methods 4.8 Application to the Prototype Problem 4.9 Exercises on Chapter 4 5. The Wind-driven Ocean Circulation 5.1 Phenomena 5.2 Models of the Midlatitude Ocean Circulation 5.3 Shallow-water and Quasi-geostrophic Models 5.4 Classical Results 5.5 Bifurcations of flows in Quasi-geostrophic Models 5.6 Bifurcations of flows in Shallow-water Models 5.7 Effects of Continental Geometry 5.8 High-resolution OGCMs 5.9 Observations 5.10 Synthesis 5.11 Exercises on Chapter 5 6. The Thermohaline Ocean Circulation 6.1 Low-frequency North Atlantic Climate Variability 6.2 Potential Mechanisms 6.3 Two-dimensional Boussinesq Models 6.4 Diffusive Thermohaline Flows 6.5 Convective Thermohaline Flows 6.6 Zonally Averaged Ocean Models 6.7 Three-dimensional Ocean Models 6.8 Coupled Ocean-atmosphere Models 6.9 Synthesis 6.10 Exercises on Chapter 6 7. The Dynamics and Physics of ENSO 7.1 Basic Phenomena 7.2 Models of the Equatorial Ocean 7.3 Physics of Ocean-Atmosphere Coupling 7.4 The Zebiak-Cane Model 7.5 Towards the Delayed Oscillator 7.6 Coupled Processes and the Annual Mean State 7.7 Unifying Mean State and Variability 7.8 Presence of the Seasonal Cycle 7.9 ENSO in Coupled General Circulation Models 7.10 Synthesis| 7.11 Exercises on Chapter 7