Introduction to Geophysical Fluid Dynamics book cover

Introduction to Geophysical Fluid Dynamics

Physical and Numerical Aspects

This book provides an introductory-level exploration of geophysical fluid dynamics (GFD), the principles governing air and water flows on large terrestrial scales. Physical principles are illustrated with the aid of the simplest existing models, and the computer methods are shown in juxtaposition with the equations to which they apply. It explores contemporary topics of climate dynamics and equatorial dynamics, including the Greenhouse Effect, global warming, and the El Nino Southern Oscillation.

Audience
first-year graduate students and upper-level undergraduates in meteorology, oceanography, civil/environmental engineering, along with researchers and professionals in related fields who require a solid introduction to geophysical fluid dynamics

Included in series
International Geophysics

Hardbound, 875 Pages

Published: August 2011

Imprint: Academic Press

ISBN: 978-0-12-088759-0

Reviews

  • "This book…is one of the best books introducing the subject matter. The physics underlying the different phenomena of interest to geophysical fluid dynamics is concisely explained…Several problems, questions and exercises are given at the end of each chapter. I highly recommend this to undergraduate students, however, graduate students will also benefit from the material presented."--Contemporary Physics, January 29, 2013
    "…Introduction to Geophysical Fluid Dynamics is one of the best books introducing the subject matter. The physics underlying the different phenomena of interest to geophysical fluid dynamics is concisely explained…I highly recommend this to undergraduate students, however, graduate students will also benefit from the material presented."--Contemporary Physics, Volume 54, Issue 1


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
    Walsh Cottage, Woods Hole, Massachusetts
    UK Meteorological Office, Exeter, England
    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
    2.8 Predictor-corrector methods
    2.9 Higher-order schemes
    Analytical Problems
    Numerical Exercises
    Biography: Pierre Simon Marquis de Laplace
    Biography: Gaspard Gustave de Coriolis
    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
    Biography: Joseph Valentin Boussinesq
    Biography: Vilhelm Bjerknes
    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
    4.7 Numerical implementation of boundary conditions
    4.8 Accuracy and errors
    Analytical Problems
    Numerical Exercises
    Biography: Osborne Reynolds
    Biography: Carl-Gustaf Arvid Rossby
    5 Diffusive Processes
    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
    Biography: Andrey Nikolaevich Kolmogorov
    Biography: John von Neumann
    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 Multi-dimensional approach
    Analytical Problems
    Numerical Exercises
    Biography: Richard Courant
    Biography: Peter Lax
    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 Non-geostrophic 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
    Biography: Geoffrey Ingram Taylor
    Biography: James Cyrus McWilliams
    8 Ekman layer
    8.1 Shear turbulence
    8.2 Friction and rotation
    8.3 The bottom Ekman layer
    8.4 Generalization to non-uniform 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
    Biography: VagnWalfrid Ekman
    Biography: Ludwig Prandtl
    9 BarotropicWaves
    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
    Biography: William Thomson, Lord Kelvin
    Biography: Akio Arakawa
    10 Barotropic Instability
    10.1 Mechanism
    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
    Biography: Louis Norberg Howard
    Biography: Norman J. Zabusky
    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
    Biography: David Brunt
    Biography: Vilho Väisälä
    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
    Biography: Raymond Braislin Montgomery
    Biography: James Joseph O’Brien
    13 InternalWaves
    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
    Biography: Walter Heinrich Munk
    Biography: Adrian Edmund Gill
    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 − ǫ and k − klm
    14.5 Mixed-layer modeling
    14.6 Patankar-type discretizations
    14.7 Wind mixing and penetrative convection
    Analytical Problems
    Numerical Exercises
    Biography: Lewis Fry Richardson
    Biography: George Mellor
    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
    15.5 Atmospheric frontogenesis
    15.6 Numerical handling of large gradients
    15.7 Nonlinear advection schemes
    Analytical Problems
    Numerical Exercises
    Biography: George Veronis
    Biography: Kozo Yoshida
    16 Quasi-Geostrophic Dynamics
    16.1 Simplifying assumption
    16.2 Governing equation
    16.3 Length and time scales
    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
    Biography: Jule Gregory Charney
    Biography: Allan Richard Robinson
    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
    Biography: Joseph Pedlosky
    Biography: Peter Broomell Rhines
    18 Fronts, Jets and Vortices
    18.1 Fronts and jets
    18.2 Vortices
    18.3 Geostrophic turbulence
    18.4 Simulations of geostrophic turbulence
    Analytical Problems 
    Numerical Exercises
    Biography: Melvin Ernest Stern
    Biography: Peter Douglas Killworth
    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
    Biography: Edward Norton Lorenz
    Biography: Joseph Smagorinsky
    20 Oceanic General Circulation
    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
    Biography: Henry Melson Stommel
    Biography: Kirk Bryan
    21 Equatorial Dynamics
    21.1 Equatorial beta plane
    21.2 Linear wave theory
    21.3 El Niño - Southern Oscillation (ENSO)
    21.4 ENSO forecasting
    Analytical Problems
    Numerical Exercises
    Biography: George Philander
    Biography: Paola Malanotte Rizzoli
    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
    Biography: Michael Ghil8
    Biography: Eugenia Kalnay
    VI Web-site information
    Appendix A: Elements of Fluid Mechanics
    A.1 Budgets
    A.2 Spherical coordinates
    A.3 Cylindrical coordinates
    A.4 Vorticity and rotation
    Analytical Problems
    Numerical Exercises
    Appendix 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
    Appendix C: Recapitulation of Numerical schemes
    C.1 The tridiagonal system solver
    C.2 1D finite-difference schemes of various orders
    C.3 Time-stepping algorithms
    C.4 Partial-derivatives finite differences
    C.5 Discrete Fourier Transform and Fast Fourier Transform
    Analytical Problems
    Numerical Exercises
    References
    Index

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