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Preface page xi

Part I Introduction 1

1 Description of the world's oceans 3

1.1 Surface forcing for the world's oceans 3

1.1.1 Surface wind forcing 3

1.1.2 Surface thermohaline forcing 6

1.1.3 Other external forcing 15

1.2 Temperature, salinity, and density distribution in the world's oceans 17

1.2.1 Surface distribution of temperature, salinity, and density 17

1.2.2 Meridional distribution of temperature, salinity, and density

1.2.3 Distribution of potential temperature, salinity, and density in the Southern Ocean 36

1.3 Various types of motion in the oceans 38

1.3.1 Introduction 38

1.3.2 Two types of circulation 40

1.4 A survey of oceanic circulation theory 45

1.4.1 Introduction 45

1.4.2 Thermal structure and circulation in the upper ocean 47

1.4.3 Early theories for the wind-driven circulation 50

1.4.4 Theoretical framework for the barotropic circulation 52

1.4.5 Theories of the baroclinic wind-driven circulation 55

1.4.6 Theory of thermohaline circulation 57

1.4.7 Mixing and energetics of the oceanic circulation 60

2 Dynamical foundations 63

2.1 Dynamical and thermodynamic laws 63

2.1.1 Basic equations 63

2.1.2 Integral properties 65

2.2 Dimensional analysis and nondimensional numbers 67

2.2.1 Dimensions of the commonly used variables in physical oceanography 67

2.2.2 Dimensional homogeneity 69

2.2.3 The nondimensional parameters 70

2.2.4 A few simple applications of dimensional analysis 70

2.2.5 Important nondimensional numbers in dynamical oceanography 72

2.3 Basic concepts in thermodynamics 73

2.3.1 Temperature 74

2.3.2 Energy 74

2.3.3 Entropy 76

2.3.4 The second law of thermodynamics

2.3.5 Energy versus entropy 82

2.4 Thermodynamics of seawater 83

2.4.1 Basic differential relations of thermodynamics 83

2.4.2 Basic relations for seawater thermodynamic functions 87

2.4.3 Density, thermal expansion coefficient, and saline contraction coefficient 88

2.4.4 Specific heat capacity 90

2.4.5 Compressibility and adiabatic temperature gradient 91

2.4.6 Adiabatic lapse rate 91

2.4.7 Potential temperature 93

2.4.8 Potential density 94

2.4.9 Thermobaric effect 97

2.4.10 Cabbeling 100

2.4.11 Neutral surface and neutral density 100

2.4.12 Spiciness 101

2.4.13 Stability and Brunt-Vaisala frequency 101

2.4.14 Thermodynamics of seawater based on the Gibbs function 103

2.4.15 Entropy of seawater 103

2.4.16 Relation between internal energy, enthalpy, and free enthalpy 105

2.5 A hierarchy of equations of state for seawater 109

2.5.1 Introduction 109

2.5.2 Simple equations of state 109

2.6 Scaling and different approximations 112

2.6.1 Hydrostatic approximation 112

2.6.2 The traditional approximation 115

2.6.3 Scaling of the horizontal momentum equations 115

2.6.4 Geostrophy and the thermal wind relation 118

2.7 Boussinesq approximations and buoyancy fluxes 119

2.7.1 Boussinesq approximations 119

2.7.2 Potential problems associated with Boussinesq approximations 122

2.7.3 Buoyancy fluxes 122

2.7.4 Pitfalls of using the buoyancy flux to diagnose energetics of oceanic circulation 123

2.7.5 Balance of buoyancy in a model with a nonlinear equation of state 124

2.8 Various vertical coordinates 125

2.8.1 Vertical coordinate transformation 126

2.8.2 Commonly used vertical coordinates in oceanography 127

2.9 Ekman layer 130

2.9.1 Classical theory of Ekman layer below a free surface 131

2.9.2 Ekman spiral with inhomogeneous diffusivity 135

2.10 Sverdrup relation, island rule, and the f-spiral 137

2.10.1 Sverdrup relation 138

2.10.2 The island rule 138

2.10.3 Vertical structure of the horizontal velocity field 140 3 Energetics of the oceanic circulation 149

3.1 Introduction 149

3.1.1 Energetic view of the ocean 149

3.1.2 Different views of the oceanic circulation 150

3.2 Sandstrom's theorem 151

3.2.1 The oceanic circulation as a thermodynamic cycle 151

3.2.2 Where does Sandstrom's theorem stand? 156

3.2.3 Laboratory experiments testing Sandstrom's theorem 159

3.3 Seawater as a two-component mixture 162

3.3.1 Description in coordinates moving with the center of mass 163

3.3.2 Natural boundary condition for salinity balance 164

3.3.3 A one-dimensional model with evaporation 165

3.4 Balance of mass, energy, and entropy 167

3.4.1 Mass conservation 167

3.4.2 Momentum conservation 167

3.4.3 Gravitational potential energy conservation 168

3.4.4 Kinetic energy conservation 168

3.4.5 Internal energy conservation 168

3.4.6 Entropy balance 170

3.5 Energy equations for the world's oceans 171

3.5.1 Three types of time derivative for the property integral in the ocean 171

3.5.2 The generalized Leibnitz theorem and generalized Reynolds transport theorem 173

3.5.3 Energetics of the barotropic tides 175

3.5.4 Energy equations for the oceans 176

3.5.5 Interpretation of energy integral equations 180

3.5.6 An energy diagram for the world's oceans 183

3.6 Mechanical energy balance in the ocean 185 3.6.1 Mechanical energy sources/sinks in the world's oceans 185

3.6.2 Source of chemical potential energy 202

3.6.3 A tentative scheme for balancing the mechanical energy in the ocean 203

3.6.4 Remaining challenges in the energetics of the world's oceans 204

3.7 Gravitational potential energy and available potential energy 207

3.7.1 Gravitational potential energy 207

3.7.2 Available potential energy 213

3.7.3 Balance of gravitational potential energy in a model ocean 226

3.7.4 Balance of GPE/AGPE during the adjustment of circulations 236

3.8 Entropy balance in the oceans 240

3.8.1 Entropy production due to freshwater mixing 240

3.8.2 Balance of entropy in the world's oceans 248 Appendix: Source/sink of GPE due to heating/cooling 256

Part II Wind-driven and thermohaline circulation 259

4 Wind-driven circulation 261

4.1 Simple layered models 261

4.1.1 Pressure gradient and continuity equations in layered models 261

4.1.2 Reduced-gravity models 266

4.1.3 The physics of wind-driven circulation 285

4.1.4 The Parsons model 294

4.1.5 The puzzles about motions in the subsurface layers 300

4.1.6 Theory of potential vorticity homogenization 307

4.1.7 The ventilated thermocline 315

4.1.8 Multi-layer inertial western boundary currents 336

4.1.9 Thermocline theory applied to the world's oceans 346

4.2 Thermocline models with continuous stratification 350

4.2.1 Diffusive versus ideal-fluid thermocline 350

4.2.2 Models with continuous stratification 357

4.3 Structure of circulation in a subpolar gyre 369

4.3.1 Introduction 369

4.3.2 A2j-layer model 372

4.3.3 A continuously stratified model 374

4.4 Recirculation 385

4.4.1 Motivation 385

4.4.2 Fofonoff solution 387

4.4.3 Veronis model 389

4.4.4 Potential vorticity homogenization applied to recirculation 391

4.4.5 The role of bottom pressure torque 393

4.4.6 Final remarks 396

4.5 Layer models coupling thermocline and thermohaline circulation 397

4.5.1 Introduction 397

4.5.2 A2j-layer model 398

4.6 Equatorial thermocline 401

4.6.1 Introduction 401

4.6.2 The extra-equatorial solution 404

4.6.3 The Equatorial Undercurrent as an inertial boundary current 406

4.6.4 The asymmetric nature of the Equatorial Undercurrent in the Pacific 407

4.7 Communication between subtropics and tropics 416

4.7.1 Introduction 416

4.7.2 Interior communication window between subtropics and tropics 420

4.7.3 Communication windows in the world's oceans 426

4.7.4 Communication and pathways on different isopycnal surfaces 432

4.8 Adjustment of thermocline and basin-scale circulation 435

4.8.1 Geostrophic adjustment 435

4.8.2 Basin-scale adjustment 445

4.9 Climate variability inferred from models of the thermocline 452

4.9.1 Multi-layer model formulation 453

4.9.2 Continuously stratified model 463

4.9.3 Decadal climate variability diagnosed from data and numerical models 468

4.10 Inter-gyre communication due to regional climate variability 472

4.10.1 Introduction 472

4.10.2 Model formulation 472 5 Thermohaline circulation 480

5.1 Water mass formation/erosion 480

5.1.1 Sources of deep water in the world's oceans 480

5.1.2 Bottom/deepwater formation 487

5.1.3 Overflow of deep water 491

5.1.4 Mode water formation/erosion 508

5.1.5 Subduction and obduction 512

5.2 Deep circulation 536

5.2.1 Observations 536

5.2.2 Simple theory of the deep circulation 542

5.2.3 Generalized theories of deep circulation 553

5.2.4 Mixing-enhanced deep circulation 570

5.2.5 Mid-depth circulation 582

5.3 Haline circulation 585

5.3.1 Hydrological cycle and poleward heat flux 585

5.3.2 Surface boundary conditions for salinity 604

5.3.3 Haline circulation induced by evaporation and precipitation 615

5.3.4 Double diffusion 628

5.4 Theories for the thermohaline circulation 633

5.4.1 Conceptual models for the thermohaline circulation 633

5.4.2 Thermohaline circulation based on box models 641

5.4.3 Thermohaline circulation based on loop models 663

5.4.4 Two-dimensional thermohaline circulation 668

5.4.5 Thermal circulation in a three-dimensional basin 677

5.4.6 Thermohaline circulation: multiple states and catastrophe 685

5.4.7 Thermohaline oscillations 695

5.5 Combining wind-driven and thermohaline circulation 707

5.5.1 Scaling of pycnocline and thermohaline circulation 707

5.5.2 Interaction between wind-driven and deep circulations 723

5.5.3 Global adjustment of the thermocline 738

5.5.4 Dynamical role of the mixed layer in regulating meridional mass/heat fluxes 749

Appendix: Definition of the oceanic sensible heat flux 758

References 761

Suggested reading 782

Index 784 Colour plates between pages 148 and 149

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