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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