Preface ........................................................ xi
1 Basic Physical Principles and Equations ...................... 1
1.1 The Large-Scale Ocean Circulation ....................... 1
1.2 Physical Variables ...................................... 4
1.3 Fluid Motion and the Material Derivative ................ 6
1.4 Mass Conservation ....................................... 8
1.5 Momentum Balance ........................................ 9
1.6 Salt Conservation ...................................... 10
1.7 Thermodynamic Energy Balance ........................... 10
1.8 Equation of State ...................................... 10
1.9 Seawater Equations of Motion ........................... 11
1.10 Fluid Parcel Trajectories .............................. 12
1.11 Notes .................................................. 13
2 Reduced Equations for Large-Scale Motion .................... 14
2.1 Scaling ................................................ 14
2.2 Spherical Polar Coordinates ............................ 16
2.3 The Hydrostatic Approximation .......................... 18
2.4 The Boussinesq Approximation ........................... 22
2.5 Pressure-Corrected Temperatures and Densities .......... 25
2.6 Inviscid, Nondiffusive, Adiabatic Flow ................. 31
2.7 The Primitive Equations for the Ocean .................. 33
2.8 Thermohaline Planetary Geostrophic Equations ........... 34
2.9 Notes .................................................. 36
3 Planetary Geostrophic Vorticity Dynamics .................... 37
3.1 Vorticity Balance ...................................... 37
3.2 The β-Plane ............................................ 38
3.3 Boundary Conditions on Vertical Velocity ............... 40
3.4 The Transport Stream Function .......................... 41
3.5 The Wind-Driven Surface Ekman Layer .................... 41
3.6 Sverdrup Transport ..................................... 43
3.7 Depth-Integrated Wind-Driven Gyre Circulation .......... 45
3.8 Topographic Effects on the Depth-Integrated Flow ....... 50
3.9 Notes .................................................. 51
4 Stratified Large-Scale Flow ................................. 52
4.1 Planetary Geostrophic Equations for a Simplified
Equation of State ...................................... 52
4.2 Linear Theory .......................................... 54
4.3 Breakdown of Steady Linear Theory ...................... 55
4.4 Long Planetary Waves ................................... 55
4.5 Vertical Modes for Constant Stratification ............. 59
4.6 Planetary Geostrophic Conservation Laws ................ 61
4.7 Representation of Small-Scale Turbulent Heal
Diffusion .............................................. 62
4.8 The M Equation ......................................... 63
4.9 Reduced-Gravity Layer Models ........................... 64
4.10 Notes .................................................. 68
5 Circulation in a Simple Rectangular Basin ................... 69
5.1 Domain and Boundary Conditions ......................... 69
5.2 Planetary Geostrophic Energetics ....................... 71
5.3 Thermocline Scaling .................................... 74
5.4 The One-Layer Model .................................... 78
5.5 Multilayer Models: The Ventilated Thermocline .......... 80
5.6 Internal Boundary Layer Theory ......................... 89
5.7 Diffusively Driven Circulation ......................... 94
5.8 Meridional Overturning Cells ........................... 95
5.9 Summary ................................................ 96
5.10 Notes .................................................. 96
6 Eddy-Driven Subsurface Motion ............................... 99
6.1 Homogenization of Scalars in Recirculating Flow ........ 99
6.2 Potential Vorticity Homogenization: Quasi-Geostrophic
Theory ................................................ 101
6.3 Potential Vorticity Homogenization: Planetary
Geostrophic Theory .................................... 107
6.4 Notes ................................................. 111
7 Circumpolar Flow ........................................... 112
7.1 The Geostrophic Constraint ............................ 112
7.2 Depth-Integrated Flow with Linear Frictional Closure .. 114
7.3 Circumpolar Flow over a Topographic Sill .............. 115
7.4 A Baroclinic Model of Circumpolar Flow ................ 119
7.5 Circumpolar Flow in Sverdrup Balance .................. 123
7.6 Abyssal Circulation ................................... 126
7.7 Notes ................................................. 127
8 Mid-Depth Meridional Overturning ........................... 128
8.1 Meridional Overturning Circulations ................... 128
8.2 A Model of the Warm-Water Branch ...................... 130
8.3 Weak Friction and Diabatic Forcing .................... 135
8.4 Steady Solutions ...................................... 138
8.5 Time-Dependent Solutions .............................. 142
8.6 Notes ................................................. 145
9 Thermohaline Effects ....................................... 146
9.1 Seawater as a Two-Component Fluid ..................... 146
9.2 Thermohaline Surface Boundary Conditions .............. 148
9.3 Multiple Equilibria for a Thermohaline Exchange
Flow .................................................. 150
9.4 Thermohaline Potential Vorticity ...................... 152
9.5 Pressure Coordinates .................................. 154
9.6 Thermohaline Planetary Geostrophic Equations in
Pressure Coordinates .................................. 157
9.7 A Simple Nonlinear Equation of State .................. 159
9.8 Notes ................................................. 163
10 Theory and Observation ..................................... 164
10.1 A Perturbation-Theoretical Perspective ................ 164
10.2 Degeneracy of the Large-Scale Theory .................. 165
10.3 Numerical Simulations of Large-Scale Circulation ...... 166
10.4 The Observational Record .............................. 168
10.5 Notes ................................................. 169
Exercises .................................................. 171
References ................................................. 187
Index ......................................................... 191
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