Lectures on geophysical fluid dynamics

Contents......Page 12
1 Fundamentals......Page 18
1. Eulerian and Lagrangian Descriptions......Page 20
2. Mass Conservation......Page 21
3. Functionals and Variational Principles......Page 22
4. Hamilton's Principle for Point Masses......Page 23
5. Hamilton's Principle for a Barotropic Fluid......Page 24
6. Nonhomentropic Flow......Page 26
7. Variable Composition......Page 27
8. Equations of Motion for an Ideal Fluid......Page 28
9. The Method of Averaging......Page 31
10. Momentum Equation by the Method of Averaging......Page 34
11. An Example of Kinetic Theory......Page 38
12. Thermodynamic Constraints on Molecular Diffusion......Page 41
13. Macroscopic Averages of the Equations of Motion......Page 46
14. Stirring and Mixing......Page 49
15. Static Stability......Page 54
16. Potential Density and Potential Temperature......Page 55
17. The Equation of State for Seawater......Page 57
18. Statistical Mechanics: The Ideal Gas......Page 60
1. Equations Of Motion in Rotating Coordinates......Page 65
2. Geostrophic, Hydrostatic Flow......Page 69
3. The Shallow-water Equations......Page 72
4. Potential Vorticity......Page 76
5. The Quasigeostrophic Equation......Page 78
6. A Second Look at the Quasigeostrophic Equation......Page 80
7. Plane-wave Solutions of the Linear Equations......Page 83
8. A Practical Benefit Of Filtering Out Inertia-gravity Waves......Page 88
9. Geostrophic Adjustment......Page 91
10. A Third Look at the Quasigeostrophic Equation......Page 96
11. Rigid-lid Approximation......Page 98
12. Two-layer Equations......Page 99
13. Two-layer Rossby Waves......Page 102
14. Available Potential Energy......Page 105
15. Baroclinic Instability......Page 108
16. Primitive Equations for the Ocean......Page 114
17. Primitive Equations for the Atmosphere......Page 117
18. Primitive Equations in Isentropic Coordinates......Page 120
19. Quasigeostrophic Equations for Continuously Stratified Flow......Page 122
20. Two-level Quasigeostrophic Equations......Page 125
21. Quasigeostrophic Flow over Topography......Page 127
1. Overview......Page 135
2. Rotating Sector Models......Page 139
3. Boundary-layer Methods......Page 142
4. Theory of the Depth-averaged Circulation......Page 146
5. Ekman Layers......Page 152
6. A Second Look at Ekman Layers......Page 157
7. Spin-up in the Laboratory......Page 161
8. Simplified Inertia-less Equations......Page 165
9. Linear Solutions of the Simplified Equations......Page 168
10. The Case of Homogeneous Fluid......Page 172
11. The Case of Stratified Fluid......Page 176
12. Spin-up in the Ocean......Page 181
13. The Effect Of Bottom Topography......Page 185
14. Stratified Flow over Bottom Topography......Page 191
15. A Nonlinear Model......Page 197
16. The Thermocline......Page 203
1. The Vorticity Equation......Page 212
2. Ertel's Theorem......Page 214
3. A Deeper Look at Potential Vorticity......Page 216
4. Alternative Statements of the Vorticity Law......Page 218
5. Turbulence......Page 222
6. Kolmogorov's Theory......Page 223
7. Intermittency and the Beta-model......Page 228
8. Two-dimensional Turbulence......Page 232
9. More Two-dimensional Turbulence......Page 236
10. Energy Transfer in Two and Three Dimensions......Page 241
5 Statistical Fluid Dynamics......Page 247
1. The Closure Problem of Turbulence......Page 248
2. The Eddy-damped Markovian Model......Page 250
3. Stochastic Model Representation......Page 255
4. Entropy......Page 257
5. The Entropy Principle......Page 261
6. Equilibrium Statistical Mechanics......Page 266
7. The Meaning of Absolute Equilibrium......Page 271
6 Geostrophic Turbulence......Page 278
1. Quasigeostrophic Flow over Topography......Page 279
2. The Statistical Mechanics of Flow over Topography......Page 284
3. Flow on the Beta-plane......Page 288
4. Stratified Quasigeostrophic Flow......Page 294
5. Two-layer Turbulence......Page 301
1. Symmetry and Conservation Laws......Page 310
2. The Particle-relabeling Symmetry Property......Page 314
3. Sound Waves in One Dimension: The Conservation of Wave Action......Page 319
4. Sound Waves in One Dimension: The Equations for the Mean Flow......Page 322
5. Sound Waves in Three Dimensions: Particle-relabeling and Nonacceleration......Page 324
6. Approximations and Constraints......Page 328
7. The Canonical Equations......Page 333
8. Eulerian Forms of Hamilton's Principle......Page 341
9. The Geometrical View of Dynamics......Page 347
10. Noncanonical Hamiltonian Dynamics......Page 351
11. Poisson Brackets for Fluids......Page 354
12. Pseudoenergy, Stability, and Available Energy......Page 359
13. Dynamical Approximations: The Semigeostrophic Equations......Page 367
References......Page 378
C......Page 388
E......Page 389
K......Page 390
P......Page 391
S......Page 392
W......Page 393