Note: Front Cover -- Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects -- Copyright -- Table of Contents -- Foreword -- Preface -- Preface of the First Edition -- I Fundamentals -- 1 Introduction -- 1.1 Objective -- 1.2 Importance of Geophysical Fluid Dynamics -- 1.3 Distinguishing Attributes of Geophysical Flows -- 1.4 Scales of Motions -- 1.5 Importance of Rotation -- 1.6 Importance of Stratification -- 1.7 Distinction between the Atmosphere and Oceans -- 1.8 Data Acquisition -- 1.9 The Emergence of Numerical Simulations -- 1.10 Scales Analysis and Finite Differences -- 1.11 Higher-Order Methods -- 1.12 Aliasing -- Analytical Problems -- Numerical Exercises -- 2 The Coriolis Force -- 2.1 Rotating Framework of Reference -- 2.2 Unimportance of the Centrifugal Force -- 2.3 Free Motion on a Rotating Plane -- 2.4 Analogy and Physical Interpretation -- 2.5 Acceleration on a Three-Dimensional Rotating Planet -- 2.6 Numerical Approach to Oscillatory Motions -- 2.7 Numerical Convergence and Stability -- 2.7.1 Formal Stability Definition -- 2.7.2 Strict Stability -- 2.7.3 Choice of a Stability Criterion -- 2.8 Predictor-Corrector Methods -- 2.9 Higher-Order Schemes -- Analytical Problems -- Numerical Exercises -- 3 Equations of Fluid Motion -- 3.1 Mass Budget -- 3.2 Momentum Budget -- 3.3 Equation of State -- 3.4 Energy Budget -- 3.5 Salt and Moisture Budgets -- 3.6 Summary of Governing Equations -- 3.7 Boussinesq Approximation -- 3.8 Flux Formulation and Conservative Form -- 3.9 Finite-Volume Discretization -- Analytical Problems -- Numerical Exercises -- 4 Equations Governing Geophysical Flows -- 4.1 Reynolds-Averaged Equations -- 4.2 Eddy Coefficients -- 4.3 Scales of Motion -- 4.4 Recapitulation of Equations Governing Geophysical Flows -- 4.5 Important Dimensionless Numbers -- 4.6 Boundary Conditions -- 4.6.1 Kinematic Conditions. , 4.6.2 Dynamic Conditions -- 4.6.3 Heat, Salt, and Tracer Boundary Conditions -- 4.7 Numerical Implementation of Boundary Conditions -- 4.8 Accuracy and Errors -- 4.8.1 Discretization Error Estimates -- Analytical Problems -- Numerical Exercises -- 5 Diffusive Processes -- 5.1 Isotropic, Homogeneous Turbulence -- 5.1.1 Length and Velocity Scales -- 5.1.2 Energy Spectrum -- 5.2 Turbulent Diffusion -- 5.3 One-Dimensional Numerical Scheme -- 5.4 Numerical Stability Analysis -- 5.5 Other One-Dimensional Schemes -- 5.6 Multi-Dimensional Numerical Schemes -- Analytical Problems -- Numerical Exercises -- 6 Transport and Fate -- 6.1 Combination of Advection and Diffusion -- 6.2 Relative Importance of Advection: The Peclet Number -- 6.3 Highly Advective Situations -- 6.4 Centered and Upwind Advection Schemes -- 6.5 Advection-Diffusion with Sources and Sinks -- 6.6 Multidimensional Approach -- Analytical Problems -- Numerical Exercises -- II Rotation Effects -- 7 Geostrophic Flows and Vorticity Dynamics -- 7.1 Homogeneous Geostrophic Flows -- 7.2 Homogeneous Geostrophic Flows Over an Irregular Bottom -- 7.3 Generalization to Nongeostrophic Flows -- 7.4 Vorticity Dynamics -- 7.5 Rigid-Lid Approximation -- 7.6 Numerical Solution of the Rigid-Lid Pressure Equation -- 7.7 Numerical Solution of the Streamfunction Equation -- 7.8 Laplacian Inversion -- Analytical Problems -- Numerical Exercises -- 8 The Ekman Layer -- 8.1 Shear Turbulence -- 8.1.1 Logarithmic Profile -- 8.1.2 Eddy Viscosity -- 8.2 Friction and Rotation -- 8.3 The Bottom Ekman Layer -- 8.4 Generalization to Nonuniform Currents -- 8.5 The Ekman Layer over Uneven Terrain -- 8.6 The Surface Ekman Layer -- 8.7 The Ekman Layer in Real Geophysical Flows -- 8.8 Numerical Simulation of Shallow Flows -- Analytical Problems -- Numerical Exercises -- 9 Barotropic Waves -- 9.1 Linear wave dynamics. , 9.2 The Kelvin Wave -- 9.3 Inertia-Gravity Waves (Poincér Waves) -- 9.4 Planetary Waves (Rossby Waves) -- 9.5 Topographic Waves -- 9.6 Analogy between Planetary and Topographic Waves -- 9.7 Arakawa's Grids -- 9.8 Numerical Simulation of Tides and Storm Surges -- Analytical Problems -- Numerical Exercises -- 10 Barotropic Instability -- 10.1 What Makes a Wave Grow Unstable? -- 10.2 Waves on Shear Flow -- 10.3 Bounds on Wave Speeds and Growth Rates -- 10.4 A Simple Example -- 10.5 Nonlinearities -- 10.6 Filtering -- 10.7 Contour Dynamics -- Analytical Problems -- Numerical Exercises -- III Stratification Effects -- 11 Stratification -- 11.1 Introduction -- 11.2 Static Stability -- 11.3 A Note on Atmospheric Stratification -- 11.4 Convective Adjustment -- 11.5 The Importance of Stratification: The Froude Number -- 11.6 Combination of Rotation and Stratification -- Analytical Problems -- Numerical Exercises -- 12 Layered Models -- 12.1 From Depth to Density -- 12.2 Layered Models -- 12.3 Potential Vorticity -- 12.4 Two-Layer Models -- 12.5 Wind-Induced Seiches in Lakes -- 12.6 Energy Conservation -- 12.7 Numerical Layered Models -- 12.8 Lagrangian Approach -- Analytical Problems -- Numerical Exercises -- 13 Internal Waves -- 13.1 From Surface to Internal Waves -- 13.2 Internal-wave Theory -- 13.3 Structure of an Internal Wave -- 13.4 Vertical Modes and Eigenvalue Problems -- 13.4.1 Vertical Eigenvalue Problem -- 13.4.2 Bounds on Frequency -- 13.4.3 Simple Example of Constant N2 -- 13.4.4 Numerical Decomposition into Vertical Modes -- 13.4.5 Waves Concentration at a Pycnocline -- 13.5 Lee Waves -- 13.5.1 Radiating Waves -- 13.5.2 Trapped Waves -- 13.6 Nonlinear Effects -- Analytical Problems -- Numerical Exercises -- 14 Turbulence in Stratified Fluids -- 14.1 Mixing of Stratified Fluids -- 14.2 Instability of a Stratified Shear Flow: The Richardson Number. , 14.3 Turbulence Closure: k-Models -- 14.4 Other Closures: k-ε and k-klm -- 14.5 Mixed-layer Modeling -- 14.6 Patankar-Type Discretizations -- 14.7 Wind Mixing and Penetrative Convection -- 14.7.1 Wind Mixing -- 14.7.2 Penetrative Convection -- Analytical Problems -- Numerical Exercises -- IV Combined Rotation and Stratification Effects -- 15 Dynamics of Stratified Rotating Flows -- 15.1 Thermal Wind -- 15.2 Geostrophic Adjustment -- 15.3 Energetics of Geostrophic Adjustment -- 15.4 Coastal Upwelling -- 15.4.1 The Upwelling Process -- 15.4.2 A Simple Model of Coastal Upwelling -- 15.4.3 Finite-Amplitude Upwelling -- 15.4.4 Variability of the Upwelling Front -- 15.5 Atmospheric Frontogenesis -- 15.6 Numerical Handling of Large Gradients -- 15.7 Nonlinear Advection Schemes -- Analytical Problems -- Numerical Exercises -- 16 Quasi-Geostrophic Dynamics -- 16.1 Simplifying Assumption -- 16.2 Governing Equation -- 16.3 Length and Timescale -- 16.4 Energetics -- 16.5 Planetary Waves in a Stratified Fluid -- 16.6 Some Nonlinear Effects -- 16.7 Quasi-Geostrophic Ocean Modeling -- Analytical Problems -- Numerical Exercises -- 17 Instabilities of Rotating Stratified Flows -- 17.1 Two Types of Instability -- 17.2 Inertial Instability -- 17.3 Baroclinic Instability-the Mechanism -- 17.4 Linear Theory of Baroclinic Instability -- 17.5 Heat Transport -- 17.6 Bulk Criteria -- 17.7 Finite-Amplitude Development -- Analytical Problems -- Numerical Exercises -- 18 Fronts, Jets and Vortices -- 18.1 Fronts and Jets -- 18.1.1 Origin and Scales -- 18.1.2 Meanders -- 18.1.3 Multiple Equilibria -- 18.1.4 Stretching and Topographic Effects -- 18.1.5 Instabilities -- 18.2 Vortices -- 18.3 Turbulence -- 18.4 Simulations of Geostrophic Turbulence -- Analytical Problems -- Numerical Exercises -- V Special Topics -- 19 Atmospheric General Circulation -- 19.1 Climate Versus Weather. , 19.2 Planetary Heat Budget -- 19.3 Direct and Indirect Convective Cells -- 19.4 Atmospheric Circulation Models -- 19.5 Brief Remarks on Weather Forecasting -- 19.6 Cloud Parameterizations -- 19.7 Spectral Methods -- 19.8 Semi-Lagrangian Methods -- Analytical Problems -- Numerical Exercises -- 20 Oceanic General Circulation -- 20.1 What Drives the Oceanic Circulation -- 20.2 Large-Scale Ocean Dynamics (Sverdrup Dynamics) -- 20.2.1 Sverdrup Relation -- 20.2.2 Sverdrup Transport -- 20.2.3 Thermal Wind and Beta Spiral -- 20.2.4 A Bernoulli Function -- 20.2.5 Potential Vorticity -- 20.3 Western Boundary Currents -- 20.4 Thermohaline Circulation -- 20.4.1 Subduction -- 20.4.2 Ventilated Thermocline Theory -- 20.4.3 Scaling of the Main Thermocline -- 20.5 Abyssal Circulation -- 20.6 Models -- 20.6.1 Coordinate Systems -- 20.6.2 Subgrid-Scale Processes -- Analytical Problems -- Numerical Exercises -- 21 Equatorial Dynamics -- 21.1 Equatorial Beta Plane -- 21.2 Linear Waves Theory -- 21.3 El Niño - Southern Oscillation (ENSO) -- 21.3.1 The Ocean -- 21.3.2 The Atmosphere -- 21.3.3 The Coupled Model -- 21.4 ENSO Forecasting -- Analytical Problems -- Numerical Exercises -- 22 Data Assimilation -- 22.1 Need for Data Assimilation -- 22.2 Nudging -- 22.3 Optimal Interpolation -- 22.4 Kalman Filtering -- 22.5 Inverse Methods -- 22.6 Operational Models -- Analytical Problems -- Numerical Exercises -- VI Web site Information -- A. Elements of Fluid Mechanics -- A.1 Budgets -- A.2 Equations in Cylindrical Coordinates -- A.3 Equations in Spherical Coordinates -- A.4 Vorticity and Rotation -- Analytical Problems -- Numerical Exercise -- B. Wave Kinematics -- B.1 Wavenumber and Wavelength -- B.2 Frequency, Phase Speed, and Dispersion -- B.3 Group Velocity and Energy Propagation -- Analytical Problems -- Numerical Exercises -- C. Recapitulation of Numerical Schemes. , C.1 The Tridiagonal System Solver.

Note: Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke , Part 1, Fundamentals: Introduction ; The Coriolis force ; Equations of fluid motion ; Equations governing geophysical flows ; Diffusive processes ; Transport and fate -- Part 2, Rotation effects: Geostrophic flows and vorticity dynamics ; The Ekman layer ; Barotropic waves ; Barotropic instability -- Part 3, Stratification effects: Stratification ; Layered models ; Internal waves ; Turbulence in stratified fluids -- Part 4, Combined rotation and stratification effects: Dynamics of stratified rotating flows ; Quasi-geostrophic dynamics ; Instabilities of rotating stratified flows ; Fronts, jets and vortices -- Part 5, Special topics: Atmospheric general circulation ; Oceanic general circulation ; Equatorial dynamics ; Data assimilation -- Part 6, Web site information: Elements of fluid mechanics ; Wave kinematics ; Recapitulation of numerical schemes.