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Foreword | p. xiii |
Preface | p. xv |
Preface of the First Edition | p. xvii |
p. Fundamentals | |
Introduction | |
Objective | p. 3 |
Importance of Geophysical Fluid Dynamics | p. 4 |
p. 6 | |
Scales of Motions | p. 8 |
Importance of Rotation | p. 10 |
Importance of Stratification | p. 12 |
Distinction between the Atmosphere and Oceans | p. 14 |
Data Acquisition | p. 17 |
The Emergence of Numerical Simulations | p. 19 |
Scales Analysis and Finite Differences | p. 23 |
Higher-Order Methods | p. 28 |
Aliasing | p. 33 |
Analytical Problems | p. 35 |
Numerica Exercises | p. 35 |
The Coriolis Force | |
Rotating Framework of Reference | p. 41 |
Unimportance of the Centrifugal Force | p. 44 |
Free Motion on a Rotating Plane | p. 47 |
Analogy and Physical Interpretation | p. 50 |
Acceleration on a Three-Dimensional Rotating Planet | p. 52 |
Numerical Approach to Oscillatory Motions | p. 55 |
Numerical Convergence and Stability | p. 59 |
Predictor-Corrector Methods | p. 63 |
Higher-Order Schemes | p. 65 |
Analytical Problems | p. 69 |
Equations of Fluid Motion | |
Mass Budget | p. 77 |
Momentum Budget78 | |
Equation of State | p. 79 |
Energy Budget | p. 80 |
Salt and Moisture Budgets | p. 82 |
Summary of Governing Equations | p. 83 |
Boussinesq Approximation | p. 83 |
Flux Formulation and Conservative Form | p. 87 |
Finite-Volume Discretization | p. 88 |
Analytical Problems | p. 92 |
Numerical Exercises | |
Equations Governing Geophysical Flows | |
Reynolds-Averaged Equations | p. 99 |
Eddy Coefficients | p. 101 |
Scales of Motion | p. 103 |
Recapitulation of Equations Governing Geophysical Flows | p. 106 |
important Dimensionless Numbers | p. 107 |
Boundary Conditions | p. 109 |
Numerical Implementation of Boundary Conditions | p. 117 |
Accuracy and Errors | p. 120 |
Analytical Problems | p. 125 |
Numerical Exercises | p. 126 |
Diffusive Processes | |
Sotropic, Homogeneous Turbulence | p. 131 |
Turbulent Diffusion | p. 137 |
One-Dimensional Numerical Scheme | p. 140 |
Numerical Stability Analysis | p. 144 |
Other One-.Dimensional Schemes | p. 150 |
Multi-Dimensional Numerical Schemes | p. 154 |
p. 157 | |
Numerical Exercises | p. 158 |
Transport and Fate | |
Combination of Advection and Diffusion | p. 163 |
Relative Importance of Advection: The Peclet Number | p. 167 |
Highly Advective Situations | p. 168 |
Centered and Upwind Advection Schemes | p. 169 |
Advection-Diffusion with Sources and Sinks | p. 183 |
Multidimensional Approach | p. 186 |
Analytical Problems | p. 196 |
Numerical Exercises | p. 198 |
Rotation Effects | |
Geostrophic Flows and Vorticity Dynamics | |
Homogeneous Geostrophic Flows | p. 205 |
Homogeneous Geostrophic Flows over an Irregular Bottom | p. 208 |
Generalization to Nongeostrophic Flows | p. 210 |
Vorticity Dynamics | p. 212 |
Rigid-Lid Approximation | p. 215 |
Numerical Solution of the Rigid-Lid Pressure Equation | p. 217 |
Numerical Solution of the Streamfunction Equation | p. 221 |
Laplacian Inversion | p. 224 |
Analytical Problems | p. 231 |
Numerical Exercises | p. 233 |
The Ekman Layer | |
Shear Turbulence | p. 239 |
Friction and Rotation | p. 243 |
The Bottom Ekman Layer | p. 245 |
Generalization to Nonuniform Currents | p. 247 |
The Ekman Layer over Uneven Terrain | p. 250 |
The Surface Ekman Layer | p. 251 |
The Ekman Layer in Real Geophysical Flows | p. 254 |
Numerical Simulation of Shallow Flows | p. 257 |
Analytical Problems | p. 265 |
Numerical Exercises | p. 267 |
Barotropic Waves | |
Linear Wave Dynamics | p. 271 |
The Kelvin Wave | p. 273 |
Inertia-Gravity Waves (Poincaré Waves) | p. 276 |
Planetary Waves (Rossby Waves) | p. 278 |
Topographic Waves | p. 283 |
Analogy between Planetary and Topographic Waves | p. 287 |
Arakawa's Grids | p. 289 |
Numerical Simulation of Tides and Storm Surges | p. 300 |
Analytical Problems | p. 309 |
Numerical Exercises | p. 312 |
Barotropic Instability | |
What Makes a Wave Grow Unstable? | p. 317 |
Waves on a Shear Flow | p. 318 |
Bounds on Wave Speeds and Growth Rates | p. 322 |
A Simple Example | p. 324 |
Nonlinearities | p. 328 |
Filtering | p. 331 |
Contour Dynamics | p. 334 |
Analytical Problems | p. 340 |
Numerical Exercises | p. 341 |
Stratification Effects | |
Stratification | |
Introduction | p. 347 |
Static Stability | p. 348 |
A Note on Atmospheric Stratification | p. 349 |
Convective Adjustment | p. 354 |
The Importance of Stratification; The Froude Number | p. 356 |
Combination of Rotation and Stratification | p. 358 |
Analytical Problems | p. 361 |
Numerical Exercises | p. 361 |
Layered Models | |
From Depth to Density | p. 365 |
Layered Models | p. 369 |
Potential Vorticity | p. 374 |
Two-Layer Models | p. 374 |
Wind-Induced Seiches in Lakes | p. 379 |
Energy Conservation | p. 381 |
Numerical Layered Models | p. 383 |
Lagrangian Approach | p. 387 |
Analytical Problems | p. 390 |
Numerical Exercises | p. 391 |
Interna! Waves | |
From Surface to Internal Waves | p. 395 |
Internal-Wave Theory | p. 397 |
Structure of an Internal Wave | p. 399 |
Vertical Modes and Eigenvalue Problems | p. 401 |
Lee Waves! | p. 412 |
Nonlinear Effects | p. 416 |
Analytical Problems | p. 419 |
Numerical Exercise | p. 421 |
Turbulence in Stratified Fluids | |
Mixing of Stratified Fluids | p. 425 |
Instability of a Stratified Shear Flow: The Richardson Number | p. 429 |
TurbulencelClosure: k-Models | p. 435 |
Other Closures: k- ¿ and k-kl_{m} | p. 449 |
Mixed-Layer Modeling | p. 450 |
Patankar-Type Discretizations | p. 455 |
Wind Mixing and Penetrative Convection | p. 458 |
Analytical Problems | p. 466 |
Numerical Exercises | p. 467 |
Combined Rotation and Stratification Effects | |
Dynamics of Stratified Rotating Flows | |
Thermal Wind | p. 473 |
Geostrophic Adjustment | p. 475 |
Energetics of Geostrophic Adjustment | p. 480 |
Coastal Upwelling | p. 482 |
Atmospheric Frontogenesis | p. 490 |
Numerical Handling of Large Gradients | p. 502 |
Nonlinear Advection Schemes | p. 507 |
Analytical Problems | p. 512 |
Numerical Exercises | p. 516 |
Quasi-Geostrophic Dynamics | |
Simplifying Assumption | p. 521 |
Governing Equation | p. 522 |
Length and Timescale | p. 527 |
Energetics | p. 530 |
Planetary Waves in a Stratified Fluid | p. 532 |
Some Nonlinear Effects | p. 539 |
Quasi-Geostrophic Ocean Modeling | p. 542 |
Analytical Problems | p. 546 |
Numerical Exercises | p. 547 |
Instabilities of Rotating Stratified Flows | |
Two Types of Instability | p. 553 |
Inertial instability | p. 554 |
Baroclinic Instability-The Mechanism | p. 561 |
Linear Theory of Baroclinic Instability | p. 566 |
Heat Transport | p. 574 |
Bulk Criteria | p. 576 |
Finite-Amplitude Development | p. 579 |
Analytical Problems | p. 584 |
Numerical Exercises | p. 585 |
Fronts, jets and Vortices | |
Fronts and Jets | p. 589 |
Vortices | p. 601 |
Geostrophic Turbulence | p. 611 |
Simulations of Geostrophic Turbulence Analytical Problems Numerical Exercises | p. 613 |
Analytical Problems | p. 618 |
Numerical Exercises | p. 621 |
Special Topics | |
Atmospheric General Circulation | |
Climate Versus Weather | p. 627 |
Planetary Heat Budget | p. 627 |
Direct and Indirect Convective Cells | p. 631 |
Atmospheric Circulation Models | p. 637 |
Brief Remarks on Weather Forecasting | p. 642 |
Cloud Parameterizations | p. 642 |
Spectral Methods | p. 644 |
Semi-Lagrangian Methods | p. 649 |
Analitical Problems | p. 652 |
Numerical Exertises | p. 653 |
Oceanic General Circulation | |
What Drives the Oceanic Circulation | p. 657 |
Large-Scale Ocean Dynamics (Sverdrup Dynamics) | p. 660 |
Western Boundary Currents | p. 669 |
Thermohaiine Circulation | p. 673 |
Abyssal Circulation | p. 677 |
Oceanic Circulation Models | p. 681 |
Analytical Problems | p. 695 |
Numerical Exercises | p. 696 |
Equatorial Dynamics | |
Equatorial Beta Plane | p. 701 |
Linear Wave Theory | p. 703 |
El Nino - Southern Oscillation (ENSO) | p. 707 |
ENSO Forecasting | p. 716 |
Analytical Problems | p. 720 |
Numerical Exercises | p. 721 |
Data Assimilation | |
Need for Data Assimilation | p. 725 |
Nudging | p. 730 |
Optimallilnterpolation | p. 731 |
Kalman Filtering | p. 739 |
Inverse Methods | p. 743 |
Operational Models | p. 750 |
Analytical Problems | p. 754 |
Numerical Exercises | p. 756 |
Web site Information | |
Elements of Fluid Mechanics | |
Budgets | p. 763 |
Equations in Cylindrical Coordinates | p. 768 |
Equations in Spherical Coordinates | p. 769 |
Vorticity and Rotation | p. 770 |
Analytical Problems | p. 771 |
Numerical Exercise | p. 772 |
Wave Kinematics | |
Wavenumber and Wavelength | p. 773 |
Frequency, Phase Speed, and Dispersion | p. 776 |
Group Velocity and Energy Propagation | p. 778 |
Analytical Problems | p. 781 |
Numerical Exercises | p. 781 |
Recapitulation of Numerical Schemes | |
The Tridiagonal System Solver | p. 783 |
1D Finite-Difference Schemes of Various Orders | p. 785 |
Time-Stepping Algorithms | p. 786 |
Partial-Derivatives Finite Differences | p. 787 |
Discrete Fourier Transform and Fast Fourier Transform | p. 787 |
Analytical Problems | p. 792 |
Numerical Exercises | p. 793 |
References | p. 795 |
Index | p. 815 |
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