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| Foreword | |
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| Preface | |
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| Preface of the First Edition | |
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| Introduction | |
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| Objective | |
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| Importance of Geophysical Fluid Dynamics | |
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| Scales of Motions | |
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| Importance of Rotation | |
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| Importance of Stratification | |
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| Distinction between the Atmosphere and Oceans | |
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| Data Acquisition | |
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| The Emergence of Numerical Simulations | |
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| Scales Analysis and Finite Differences | |
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| Higher-Order Methods | |
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| Aliasing | |
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| Analytical Problems | |
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| Numerica Exercises | |
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| The Coriolis Force | |
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| Rotating Framework of Reference | |
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| Unimportance of the Centrifugal Force | |
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| Free Motion on a Rotating Plane | |
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| Analogy and Physical Interpretation | |
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| Acceleration on a Three-Dimensional Rotating Planet | |
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| Numerical Approach to Oscillatory Motions | |
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| Numerical Convergence and Stability | |
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| Predictor-Corrector Methods | |
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| Higher-Order Schemes | |
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| Analytical Problems | |
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| Equations of Fluid Motion | |
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| Mass Budget | |
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| Momentum Budget78 | |
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| Equation of State | |
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| Energy Budget | |
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| Salt and Moisture Budgets | |
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| Summary of Governing Equations | |
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| Boussinesq Approximation | |
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| Flux Formulation and Conservative Form | |
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| Finite-Volume Discretization | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Equations Governing Geophysical Flows | |
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| Reynolds-Averaged Equations | |
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| Eddy Coefficients | |
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| Scales of Motion | |
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| Recapitulation of Equations Governing Geophysical Flows | |
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| important Dimensionless Numbers | |
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| Boundary Conditions | |
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| Numerical Implementation of Boundary Conditions | |
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| Accuracy and Errors | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Diffusive Processes | |
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| Sotropic, Homogeneous Turbulence | |
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| Turbulent Diffusion | |
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| One-Dimensional Numerical Scheme | |
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| Numerical Stability Analysis | |
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| Other One-.Dimensional Schemes | |
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| Multi-Dimensional Numerical Schemes | |
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| Numerical Exercises | |
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| Transport and Fate | |
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| Combination of Advection and Diffusion | |
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| Relative Importance of Advection: The Peclet Number | |
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| Highly Advective Situations | |
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| Centered and Upwind Advection Schemes | |
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| Advection-Diffusion with Sources and Sinks | |
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| Multidimensional Approach | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Rotation Effects | |
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| Geostrophic Flows and Vorticity Dynamics | |
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| Homogeneous Geostrophic Flows | |
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| Homogeneous Geostrophic Flows over an Irregular Bottom | |
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| Generalization to Nongeostrophic Flows | |
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| Vorticity Dynamics | |
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| Rigid-Lid Approximation | |
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| Numerical Solution of the Rigid-Lid Pressure Equation | |
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| Numerical Solution of the Streamfunction Equation | |
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| Laplacian Inversion | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| The Ekman Layer | |
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| Shear Turbulence | |
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| Friction and Rotation | |
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| The Bottom Ekman Layer | |
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| Generalization to Nonuniform Currents | |
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| The Ekman Layer over Uneven Terrain | |
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| The Surface Ekman Layer | |
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| The Ekman Layer in Real Geophysical Flows | |
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| Numerical Simulation of Shallow Flows | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Barotropic Waves | |
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| Linear Wave Dynamics | |
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| The Kelvin Wave | |
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| Inertia-Gravity Waves (Poincar� Waves) | |
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| Planetary Waves (Rossby Waves) | |
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| Topographic Waves | |
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| Analogy between Planetary and Topographic Waves | |
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| Arakawa's Grids | |
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| Numerical Simulation of Tides and Storm Surges | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Barotropic Instability | |
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| What Makes a Wave Grow Unstable? | |
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| Waves on a Shear Flow | |
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| Bounds on Wave Speeds and Growth Rates | |
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| A Simple Example | |
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| Nonlinearities | |
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| Filtering | |
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| Contour Dynamics | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Stratification Effects | |
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| Stratification | |
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| Introduction | |
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| Static Stability | |
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| A Note on Atmospheric Stratification | |
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| Convective Adjustment | |
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| The Importance of Stratification; The Froude Number | |
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| Combination of Rotation and Stratification | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Layered Models | |
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| From Depth to Density | |
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| Layered Models | |
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| Potential Vorticity | |
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| Two-Layer Models | |
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| Wind-Induced Seiches in Lakes | |
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| Energy Conservation | |
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| Numerical Layered Models | |
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| Lagrangian Approach | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Interna! Waves | |
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| From Surface to Internal Waves | |
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| Internal-Wave Theory | |
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| Structure of an Internal Wave | |
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| Vertical Modes and Eigenvalue Problems | |
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| Lee Waves! | |
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| Nonlinear Effects | |
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| Analytical Problems | |
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| Numerical Exercise | |
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| Turbulence in Stratified Fluids | |
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| Mixing of Stratified Fluids | |
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| Instability of a Stratified Shear Flow: The Richardson Number | |
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| TurbulencelClosure: k-Models | |
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| Other Closures: k- � and k-kl<sub>m</sub> | |
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| Mixed-Layer Modeling | |
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| Patankar-Type Discretizations | |
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| Wind Mixing and Penetrative Convection | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Combined Rotation and Stratification Effects | |
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| Dynamics of Stratified Rotating Flows | |
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| Thermal Wind | |
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| Geostrophic Adjustment | |
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| Energetics of Geostrophic Adjustment | |
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| Coastal Upwelling | |
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| Atmospheric Frontogenesis | |
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| Numerical Handling of Large Gradients | |
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| Nonlinear Advection Schemes | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Quasi-Geostrophic Dynamics | |
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| Simplifying Assumption | |
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| Governing Equation | |
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| Length and Timescale | |
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| Energetics | |
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| Planetary Waves in a Stratified Fluid | |
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| Some Nonlinear Effects | |
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| Quasi-Geostrophic Ocean Modeling | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Instabilities of Rotating Stratified Flows | |
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| Two Types of Instability | |
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| Inertial instability | |
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| Baroclinic Instability-The Mechanism | |
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| Linear Theory of Baroclinic Instability | |
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| Heat Transport | |
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| Bulk Criteria | |
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| Finite-Amplitude Development | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Fronts, jets and Vortices | |
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| Fronts and Jets | |
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| Vortices | |
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| Geostrophic Turbulence | |
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| Simulations of Geostrophic Turbulence Analytical Problems Numerical Exercises | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Special Topics | |
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| Atmospheric General Circulation | |
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| Climate Versus Weather | |
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| Planetary Heat Budget | |
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| Direct and Indirect Convective Cells | |
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| Atmospheric Circulation Models | |
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| Brief Remarks on Weather Forecasting | |
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| Cloud Parameterizations | |
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| Spectral Methods | |
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| Semi-Lagrangian Methods | |
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| Analitical Problems | |
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| Numerical Exertises | |
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| Oceanic General Circulation | |
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| What Drives the Oceanic Circulation | |
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| Large-Scale Ocean Dynamics (Sverdrup Dynamics) | |
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| Western Boundary Currents | |
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| Thermohaiine Circulation | |
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| Abyssal Circulation | |
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| Oceanic Circulation Models | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Equatorial Dynamics | |
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| Equatorial Beta Plane | |
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| Linear Wave Theory | |
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| El Nino - Southern Oscillation (ENSO) | |
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| ENSO Forecasting | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Data Assimilation | |
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| Need for Data Assimilation | |
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| Nudging | |
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| Optimallilnterpolation | |
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| Kalman Filtering | |
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| Inverse Methods | |
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| Operational Models | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Web site Information | |
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| Elements of Fluid Mechanics | |
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| Budgets | |
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| Equations in Cylindrical Coordinates | |
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| Equations in Spherical Coordinates | |
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| Vorticity and Rotation | |
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| Analytical Problems | |
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| Numerical Exercise | |
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| Wave Kinematics | |
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| Wavenumber and Wavelength | |
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| Frequency, Phase Speed, and Dispersion | |
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| Group Velocity and Energy Propagation | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| Recapitulation of Numerical Schemes | |
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| The Tridiagonal System Solver | |
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| 1D Finite-Difference Schemes of Various Orders | |
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| Time-Stepping Algorithms | |
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| Partial-Derivatives Finite Differences | |
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| Discrete Fourier Transform and Fast Fourier Transform | |
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| Analytical Problems | |
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| Numerical Exercises | |
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| References | |
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| Index | |