xii
DYNAMICAL OCEANOGRAPHY
2.4.3 Special equatorial phenomena
44
2.4.4 Phenomena on the planetary scale
44
2.5 Exercises on chapter 2
47
3. MATHEMATICAL DESCRIPTION
51
3.1 A priori scales
52
3.1.1 Geometry
52
3.1.2 Coriolis acceleration
53
3.1.3 Stratification
56
3.1.4 Mixing of momentum, heat and salt
57
3.1.5 Ratio of scales
59
3.2 Large-scale balances
60
3.2.1 Equations of motion
61
3.2.2 Spherical coordinates
62
3.2.3 Boundary conditions
63
3.3 Dominant balances
65
3.4 Exercises on chapter 3
68
4. VORTICITY
71
4.1 The vorticity equation
72
4.2 Vorticity transport
73
4.2.1 Vortex stretching and tilting
73
4.2.2 Baroclinic vorticity production
74
4.2.3 Diffusion of vorticity
76
4.3 Potential vorticity
77
4.4 Shallow-water equations
79
4.4.1 Hydrostatic equilibrium
79
4.4.2 Inertial flows
81
4.5 Exercises on chapter 4
86
Part II Midlatitude circulation
5. WIND-DRIVEN CIRCULATION
91
5.1 The North Atlantic surface circulation
92
5.2 The barotropic circulation on the β-plane
94
5.2.1 The β-plane approximation
94
5.2.2 Boundary conditions
97
5.2.3 Model equations
98
5.3 Stationary solutions
99
5.3.1 The geostrophic flow
103
5.3.2 The bottom Ekman layer
105
5.3.3 The free surface Ekman layer
110
5.3.4 Continuity of the vertical velocity
113