Nonlinear Physical Oceanography

A Dynamical Systems Approach to the Large Scale Ocean Circulation and El Niño,
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Henk A. Dijkstra
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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
Taken from a review of the first edition in SIAM:"This text is different from most others in that it combines several different disciplines and draws on many scientific studies in order to deduce mechanisms of ocean circulation. (...) Therefore (it) cannot be substituted, and (...) it meets its unique goals with clarity and thoroughness".
Henk A. Dijkstra is Full Professor for Physical Oceanography at Colorado State University, Fort Collins. After graduating in applied mathematics at the University of Groningen in 1984, he worked on his Ph.D. in Groningen on a Spacelab experiment and on Marangoni convection under microgravity conditions. He continued this research in chemical engineering at Cornell University. In 1990 he started working on physical oceanography and became Assistant Professor at Utrecht University, in 1996 an Associate Professor and in 2001 a Full Professor there. Henk Dijkstra has developed, consequently, the nonlinear dynamical systems approach to oceanography. Mainly to emphasize that he first computed explicit bifurcation diagram for a global ocean circulation model and explained the structure of equilibria for a hierarchy of models going from a single-hemispheric to the global configuration. He discovered the multidecadal mode in single-hemispheric thermohaline flows and explained its relevance in the Atlantic Multidecadal Oscillation. He demonstrated the existence of steady separation patterns in northern hemispheric western boundary currents and explained the subannual variability through barotropic destabilization of these states. He first analysed the stability of the double-gyre wind driven flows in quasi-geostrophic one- and two-layer models and demonstrated its relevance with respect to low-frequency variability of the ocean gyres.He became member of the Royal Dutch Academy of Sciences and Arts in 2002. He has published more than 100 papers and a book on Nonlinear Physical Oceanography in 2000. He has organized for several years a session at EGS/EGU meetings on this topic.

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