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E-raamat: Nonlinear Physical Oceanography: A Dynamical Systems Approach to the Large Scale Ocean Circulation and El Nino

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In this book, the methodology of dynamical systems theory is applied to investigate the physics of the global ocean circulation. Topics include the dynamics of the Gulf Stream in the Atlantic Ocean, the stability of the thermohaline circulation and the El Niño/Southern Oscillation phenomenon in the Tropical Pacific. On the other hand, the book also deals with the numerical methods for applying bifurcation analysis on large dimensional dynamical systems, with thousands or more degrees of freedom, which arise through discretization of ocean models. The novel approach in understanding the phenomena of climate variability is through a systematic analysis within a hierarchy of models using these techniques. In this way, a nice overview is obtained of the relations between the results of the different models within the hierarchy. Mechanistic description of the physics of the results is provided and, where possible, links with results of state-of-the-art models and observations are sought. The reader is expected to have a background in basic incompressible fluid dynamics and applied mathematics, although the level of the text is mixed and sometimes quite introductory. Each chapter is rather self-contained and many details of derivations are provided. The book is aimed at graduate students and researchers in meteorology, oceanography, and related fields who are interested in tackling fundamental problems in dynamical oceanography and climate dynamics.
Preface xiii
Acknowledgments xvii
Introduction
1(32)
Past Climate Variability
2(11)
The last 2.5 million years
3(2)
The Younger Dryas
5(3)
The Little Ice Age
8(1)
Causes of past climate variability
9(4)
The Present Ocean Circulation
13(8)
Surface forcing
13(2)
Ocean circulation patterns
15(3)
Heat and freshwater transport
18(1)
Ocean circulation and past climate variability
19(2)
Present Climate Variability
21(6)
ENSO
22(3)
North Atlantic interdecadal variability
25(2)
Physics of Climate Variability
27(6)
Separation of scales?
27(2)
Central questions
29(1)
Approach
30(3)
Background Material
33(22)
Basic Equations
34(9)
Coordinate free
34(2)
Spherical coordinates
36(2)
Dissipative processes
38(2)
Boundary conditions
40(1)
Integral constraints
41(2)
Vorticity
43(4)
Potential Vorticity
47(3)
Stability
50(5)
A Dynamical Systems Point of View
55(50)
An Elementary Problem
56(11)
The Stommel two-box model
57(3)
Equilibrium solutions
60(2)
Stability of equilibrium solutions
62(1)
The presence of symmetry
63(3)
Imperfections
66(1)
Dynamical Systems: Fixed Points
67(13)
Elementary concepts
67(3)
Codimension-1 bifurcations
70(1)
A single zero eigenvalue
71(3)
A single complex pair of eigenvalues
74(1)
Imperfection theory
75(3)
Codimension-2 bifurcations
78(2)
Periodic Solutions and their Stability
80(8)
Poincare section and Poincare map
80(5)
Floquet theory
85(3)
Bifurcations of Periodic Orbits
88(8)
Destabilization of periodic orbits
89(2)
Homoclinic orbits
91(2)
Frequency locking
93(3)
Physics of Bifurcation Behavior
96(9)
Physical constraints and bifurcation diagrams
96(1)
Qualitative versus quantitative sensitivity
97(3)
Instability mechanisms
100(1)
Saddle node
100(1)
Transcritical and pitchfork bifurcation
101(1)
Hopf bifurcation
102(3)
Numerical Techniques
105(46)
A Prototype Problem
108(5)
Introduction
108(1)
Model
109(2)
Motionless solution
111(1)
Non-dimensional equations
112(1)
Computation of Steady Solutions
113(7)
Discretization
113(3)
Pseudo-arclength continuation
116(2)
The Euler-Newton method
118(2)
Detection and Branch Switching
120(4)
Detection of bifurcations
120(2)
Branch switching
122(2)
Linear Stability Problem
124(8)
The simultaneous iteration method
126(3)
The Jacobi-Davidson QZ-method
129(3)
Implicit Time Integration
132(1)
Linear System Solvers: Direct Methods
133(3)
Basic principle
133(2)
Pivoting
135(1)
Linear System Solvers: Iterative Methods
136(8)
Relaxation methods
136(2)
Projection techniques
138(1)
The GMRES technique
139(1)
The BICGSTAB technique
140(2)
Preconditioning
142(2)
Application to the Prototype Problem
144(7)
The Wind-Driven Ocean Circulation
151(74)
Phenomena
152(5)
Mean circulation
152(2)
Variability
154(2)
Central questions
156(1)
Models of the Midlatitude Ocean Circulation
157(6)
The homogeneous model
157(2)
Dominant balances
159(2)
The multi-layer model
161(2)
Intermediate Complexity Models
163(7)
Shallow water models
163(1)
The β-plane model
164(3)
Quasi-geostrophic β-plane models
167(2)
Overview of the intermediate models
169(1)
Classical Results
170(14)
The Sverdrup-Munk-Stommel theory
171(4)
Temporal variability
175(1)
Rossby waves
175(1)
Rossby basin modes
176(2)
Basic instability mechanisms
178(6)
Flows in Small Rectangular Basins
184(18)
Quasi-geostrophic barotropic flows
184(8)
The two-layer case
192(3)
The (equivalent) barotropic shallow water case
195(5)
Connection: SW- and QG-models
200(2)
Continental Geometry
202(8)
Continents within a β-plane model
203(1)
Continents on the sphere
204(4)
Summary
208(2)
High Resolution OGCM's
210(6)
Typical results
211(2)
Gulf Stream separation in POCM
213(3)
Temporal variability in POCM
216(1)
Observations
216(3)
Signatures of different separation patterns?
216(3)
Subannual variability
219(1)
Synthesis
219(6)
Analysis of observations
221(1)
Analysis of GCM results
222(1)
Bifurcation analysis
222(3)
The Thermohaline Ocean Circulation
225(96)
Phenomena
226(5)
Mean state
226(1)
Variability
227(4)
Central questions and approach
231(1)
Potential Mechanisms
231(9)
Advective feedback
232(1)
Convective feedback
233(3)
The flip-flop oscillation
236(2)
The loop oscillation
238(1)
Models of the thermohaline circulation
239(1)
Two-dimensional Boussinesq Models
240(3)
Formulation
240(2)
Nondimensional equations
242(1)
Diffusive Thermohaline Flows
243(25)
Basic bifurcation diagram
243(4)
Physical mechanisms
247(1)
Symmetry breaking
247(2)
Transition to time-dependence
249(3)
Model-model comparison
252(6)
Imperfections: flux-correction
258(3)
Perfect case
261(3)
Flux-correction procedure
264(1)
Solutions under flux-correction
264(4)
Summary
268(1)
Convective Thermohaline Flows
268(11)
Basic bifurcation diagrams
269(3)
Imperfections
272(1)
Coupled model
273(1)
Asymmetric air sea interaction
274(3)
Regime diagram
277(2)
Zonally Averaged Models
279(14)
Scaling of the equations
280(2)
Zonal averaging
282(1)
Procedure
283(3)
Convective adjustment
286(1)
The 'geostrophic' closure
287(4)
The 'frictional' closure
291(2)
Three-dimensional models
293(5)
Low resolution OGCM's
298(19)
Single hemispheric basin
299(1)
Multiple equilibria
299(4)
Decadal variability
303(1)
Interdedacal variability
304(2)
Centennial (and longer) time scale
306(2)
Multi basin models
308(3)
Global models
311(3)
Coupled ocean-atmosphere models
314(3)
Synthesis
317(4)
Different mean thermohaline flows?
317(2)
Temporal variability through instabilities?
319(2)
The Dynamics and Physics of ENSO
321(105)
Basic Phenomena
322(9)
The annual mean state
323(1)
The seasonal cycle
324(3)
Interannual variability
327(3)
Central questions and Approach
330(1)
Models of the Equatorial Ocean
331(14)
Constant density ocean model
331(1)
The reduced gravity model
332(2)
Equatorial waves
334(4)
Forced response in a basin
338(7)
Physics of Coupling
345(14)
Atmospheric response to diabatic heating
345(5)
Adjustment of the ocean
350(4)
Processes determining the SST
354(2)
Feedbacks
356(1)
Thermocline feedback
356(2)
Upwelling feedback
358(1)
Strength of the feedbacks
358(1)
The Zebiak-Cane Model
359(6)
Formulation
359(3)
Results
362(3)
Towards the Delayed Oscillator
365(29)
Coupled modes: periodic ocean basin
365(5)
Coupled modes: bounded basin
370(1)
The near equatorial behavior
371(5)
The fast wave limit
376(3)
The weak-coupling limit
379(2)
Modes in the full problem
381(5)
Conceptual models of the ENSO oscillation
386(1)
The two-strip model
386(3)
The delayed oscillator
389(3)
The coupled wave oscillator
392(1)
The recharge oscillator
392(2)
Coupled Processes and the Annual Mean State
394(10)
Constructed versus coupled mean states
394(1)
Demise of multiple equilibria
395(4)
The position of the cold tongue
399(5)
Unifying Mean State and Variability
404(8)
The warm pool/cold tongue state
404(2)
The ENSO mode
406(5)
Model reductions
411(1)
Presence of the Seasonal Cycle
412(10)
Coupled processes and the seasonal cycle
413(1)
Interaction of seasonal cycle and ENSO
414(5)
The irregularity of ENSO
419(3)
Synthesis
422(4)
Simulation of the mean state
422(4)
Simulation of ENSO
426