Introduction to Geophysical Fluid Dynamics

Part I: Fundamentals

Chapter 1. Introduction

• Abstract
• 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
• Walsh Cottage, Woods Hole, Massachusetts 1962–present
• UK Meteorological Office, Exeter, England 1854–present

Chapter 2. The Coriolis Force

• Abstract
• 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
• 2.8 Predictor-Corrector Methods
• 2.9 Higher-Order Schemes
• Analytical Problems
• Numerical Exercises
• Pierre Simon Marquis de Laplace 1749–1827
• Gaspard Gustave de Coriolis 1792–1843

Chapter 3. Equations of Fluid Motion

• Abstract
• 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
• Joseph Valentin Boussinesq 1842–1929
• Vilhelm Frimann Koren Bjerknes 1862–1951

Chapter 4. Equations Governing Geophysical Flows

• Abstract
• 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
• 4.7 Numerical Implementation of Boundary Conditions
• 4.8 Accuracy and Errors
• Analytical Problems
• Numerical Exercises
• Osborne Reynolds 1842–1912
• Carl-Gustaf Arvid Rossby 1898–1957

Chapter 5. Diffusive Processes

• Abstract
• 5.1 Isotropic, Homogeneous Turbulence
• 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
• Andrey Nikolaevich Kolmogorov 1903–1987
• John Louis von Neumann 1903–1957

Chapter 6. Transport and Fate

• Abstract
• 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
• Richard Courant 1888–1972
• Peter David Lax 1926–

Part II: Rotation Effects

Chapter 7. Geostrophic Flows and Vorticity Dynamics

• Abstract
• 7.1 Geostrophy 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
• Geoffrey Ingram Taylor 1886–1975
• James Cyrus McWilliams 1946–

Chapter 8. The Ekman Layer

• Abstract
• 8.1 Shear Turbulence
• 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
• Vagn Walfrid Ekman 1874–1954
• Ludwig Prandtl 1875–1953

Chapter 9. Barotropic Waves

• Abstract
• 9.1 Linear Wave Dynamics
• 9.2 The Kelvin Wave
• 9.3 Inertia-Gravity Waves (Poincaré 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
• William Thomson, Lord Kelvin 1824–1907
• Akio Arakawa 1927–2010

Chapter 10. Barotropic Instability

• Abstract
• 10.1 What Makes a Wave Grow Unstable?
• 10.2 Waves on a 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
• Louis Norberg Howard 1929–
• Norman Julius Zabusky 1929–

Part III: Stratification Effects

Chapter 11. Stratification

• Abstract
• 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
• David Brunt 1886–1965
• Vilho Väisälä 1889–1969

Chapter 12. Layered Models

• Abstract
• 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
• Raymond Braislin Montgomery 1910–1988
• James Joseph O’Brien 1935–

Chapter 13. Internal Waves

• Abstract
• 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
• 13.5 Lee Waves
• 13.6 Nonlinear Effects
• Analytical Problems
• Numerical Exercises
• Walter Heinrich Munk 1917–
• Adrian Edmund Gill 1937–1986

Chapter 14. Turbulence in Stratified Fluids

• Abstract
• 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 – and k – kl_m
• 14.5 Mixed-Layer Modeling
• 14.6 Patankar-Type Discretizations
• 14.7 Wind Mixing and Penetrative Convection
• Analytical Problems
• Numerical Exercises
• Lewis Fry Richardson 1881–1953
• George Lincoln Mellor 1929–

Part IV: Combined Rotation and Stratification Effects

Chapter 15. Dynamics of Stratified Rotating Flows

• Abstract
• 15.1 Thermal Wind
• 15.2 Geostrophic Adjustment
• 15.3 Energetics of Geostrophic Adjustment
• 15.4 Coastal Upwelling
• 15.5 Atmospheric Frontogenesis
• 15.6 Numerical Handling of Large Gradients
• 15.7 Nonlinear Advection Schemes
• Analytical Problems
• Numerical Exercises
• George Veronis 1926–
• Kozo Yoshida 1922–1978

Chapter 16. Quasi-Geostrophic Dynamics

• Abstract
• 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
• Jule Gregory Charney 1917–1981
• Allan Richard Robinson 1932–2009

Chapter 17. Instabilities of Rotating Stratified Flows

• Abstract
• 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
• Joseph Pedlosky 1938–
• Peter Broomell Rhines 1942–

Chapter 18. Fronts, Jets and Vortices

• Abstract
• 18.1 Fronts and Jets
• 18.2 Vortices
• 18.3 Geostrophic Turbulence
• 18.4 Simulations of Geostrophic Turbulence
• Analytical Problems
• Numerical Exercises
• Melvin Ernest Stern 1929–2010
• Peter Douglas Killworth 1946–2008

Part V: Special Topics

Chapter 19. Atmospheric General Circulation

• Abstract
• 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
• Edward Norton Lorenz 1917–2008
• Joseph Smagorinsky 1924–2005

Chapter 20. Oceanic General Circulation

• Abstract
• 20.1 What Drives the Oceanic Circulation
• 20.2 Large-Scale Ocean Dynamics (Sverdrup Dynamics)
• 20.3 Western Boundary Currents
• 20.4 Thermohaline Circulation
• 20.5 Abyssal Circulation
• 20.6 Oceanic Circulation Models
• Analytical Problems
• Numerical Exercises
• Henry Melson Stommel 1920–1992
• Kirk Bryan 1929–

Chapter 21. Equatorial Dynamics

• Abstract
• 21.1 Equatorial Beta Plane
• 21.2 Linear Waves Theory
• 21.3 El Niño – Southern Oscillation (ENSO)
• 21.4 ENSO Forecasting
• Analytical Problems
• Numerical Exercises
• S. George H. Philander 1942–
• Paola Malanotte Rizzoli

Chapter 22. Data Assimilation

• Abstract
• 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
• Michael Ghil 1944–
• Eugenia Kalnay 1942–

Part VI: Web site Information

• Introduction
• Appendix A. Elements of Fluid Mechanics
• Appendix B. Wave Kinematics
• Appendix C. Recapitulation of Numerical Schemes