The theory of large-scale ocean circulation

Cover
......Page 1
THE THEORY OF LARGE-SCALE OCEAN CIRCULATION......Page 3
Title
......Page 5
Copyright......Page 6
Large-Scale Vertical Momentum Balance......Page 9
Preface......Page 13
1.1 The Large-Scale Ocean Circulation......Page 17
1.2 Physical Variables......Page 20
1.3 Fluid Motion and the Material Derivative......Page 22
1.4 Mass Conservation......Page 24
1.5 Momentum Balance......Page 25
1.8 Equation of State......Page 26
1.9 Seawater Equations of Motion......Page 27
1.10 Fluid Parcel Trajectories......Page 28
1.11 Notes......Page 29
2.1 Scaling......Page 30
2.2 Spherical Polar Coordinates......Page 32
2.3 The Hydrostatic Approximation......Page 34
Pressure Effect on Density......Page 36
Incompressibility......Page 38
Entropy and Pressure Heating......Page 39
Large Thermal Variations......Page 40
Potential Temperature......Page 41
Gravitational Stability and Buoyancy Frequency......Page 44
2.6 Inviscid, Nondiffusive, Adiabatic Flow......Page 47
2.7 The Primitive Equations for the Ocean......Page 49
2.8 Thermohaline Planetary Geostrophic Equations......Page 50
2.9 Notes......Page 52
3.1 Vorticity Balance......Page 53
3.2 The β-Plane......Page 54
3.3 Boundary Conditions on Vertical Velocity......Page 56
3.5 The Wind-Driven Surface Ekman Layer......Page 57
3.6 Sverdrup Transport......Page 59
3.7 Depth-Integrated Wind-Driven Gyre Circulation......Page 61
3.8 Topographic Effects on the Depth-Integrated Flow......Page 66
3.9 Notes......Page 67
4.1 Planetary Geostrophic Equations for a Simplified Equation of State......Page 68
4.2 Linear Theory......Page 70
4.4 Long Planetary Waves......Page 71
4.5 Vertical Modes for Constant Stratification......Page 75
4.6 Planetary Geostrophic Conservation Laws......Page 77
4.7 Representation of Small-Scale Turbulent Heat Diffusion......Page 78
4.8 The M Equation......Page 79
4.9 Reduced-Gravity Layer Models......Page 80
4.10 Notes......Page 84
5.1 Domain and Boundary Conditions......Page 85
5.2 Planetary Geostrophic Energetics......Page 87
5.3 Thermocline Scaling......Page 90
5.4 The One-Layer Model......Page 94
A Two-Layer Model......Page 96
The Ventilated Regime......Page 98
Western Pool......Page 101
N-Layer Models......Page 104
5.6 Internal Boundary Layer Theory......Page 105
5.7 Diffusively Driven Circulation......Page 110
5.8 Meridional Overturning Cells......Page 111
5.10 Notes......Page 112
6.1 Homogenization of Scalars in Recirculating Flow......Page 115
A Quasi-Geostrophic Approximation......Page 117
A Mid-Ocean Gyre Example......Page 119
Potential Vorticity Diffusion......Page 121
Vorticity Drag......Page 122
6.3 Potential Vorticity Homogenization: Planetary Geostrophic Theory......Page 123
6.4 Notes......Page 127
7.1 The Geostrophic Constraint......Page 128
7.2 Depth-Integrated Flow with Linear Frictional Closure......Page 130
7.3 Circumpolar Flow over a Topographic Sill......Page 131
7.4 A Baroclinic Model of Circumpolar Flow......Page 135
7.5 Circumpolar Flow in Sverdrup Balance......Page 139
7.6 Abyssal Circulation......Page 142
7.7 Notes......Page 143
8.1 Meridional Overturning Circulations......Page 144
8.2 A Model of the Warm-Water Branch......Page 146
8.3 Weak Friction and Diabatic Forcing......Page 151
8.4 Steady Solutions......Page 154
8.5 Time-Dependent Solutions......Page 158
8.6 Notes......Page 161
9.1 Seawater as a Two-Component Fluid......Page 162
9.2 Thermohaline Surface Boundary Conditions......Page 164
9.3 Multiple Equilibria for a Thermohaline Exchange Flow......Page 166
9.4 Thermohaline Potential Vorticity......Page 168
9.5 Pressure Coordinates......Page 170
9.6 Thermohaline Planetary Geostrophic Equations in Pressure Coordinates......Page 173
9.7 A Simple Nonlinear Equation of State......Page 175
9.8 Notes......Page 179
10.1 A Perturbation-Theoretical Perspective......Page 180
10.2 Degeneracy of the Large-Scale Theory......Page 181
10.3 Numerical Simulations of Large-Scale Circulation......Page 182
10.4 The Observational Record......Page 184
10.5 Notes......Page 185
Exercises for Chapter 1......Page 187
Exercises for Chapter 2......Page 188
Exercises for Chapter 3......Page 189
Exercises for Chapter 4......Page 192
Exercises for Chapter 5......Page 193
Exercises for Chapter 6......Page 196
Exercises for Chapter 7......Page 199
Exercises for Chapter 9......Page 200
References......Page 203
Index......Page 207