Cushman-Roisin B., Beckers J.-M. Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects

Academic Press, 2006. XIV, 721 p.Foreword.Preface of the first edition.
Fundamentals.Objective.
Importance of geophysical fluid dynamics.
Distinguishing attributes of geophysical flows.
Scales of motions.
Importance of rotation.
Importance of stratification.
Distinction between the atmosphere and oceans.
Data acquisition.
The emergence of numerical simulations.
Scales analysis and finite differences.
Higher-order methods.
Aliasing.
Physical Problems.
Numerical Exercises.
Walsh Cottage , Woods Hole, Massachusetts.
UK Meteorological Office, Exeter, England.
The Coriolis Force.
Rotating framework of reference.
Unimportance of the centrifugal force.
Free motion on a rotating plane.
Analogies and physical interpretations.
Acceleration on a three-dimensional rotating planet.
Numerical approach to oscillatory motions.
Numerical convergence and stability.
Predictor-corrector methods.
Higher-order schemes.
Analytical Problems.
Numerical Exercises.
Biography: Pierre Simon Marquis de Laplace.
Biography: Gaspard Gustave de Coriolis.
Equations of Fluid Motion.
Mass budget.
Momentum budget.
Equation of state.
Energy budget.
Salt and moisture budgets.
Summary of governing equations.
Boussinesq approximation.
Flux formulation and conservative form.
Finite-volume discretization.
Analytical Problems.
Numerical Exercises.
Biography: Joseph Valentin Boussinesq.
Biography: Vilhelm Bjerknes.
Equations Governing Geophysical Flows.
Reynolds-averaged equations.
Eddy coefficients.
Scales of motion.
Recapitulation of equations governing geophysical flows.
Important dimensionless numbers.
Boundary conditions.
Numerical implementation of boundary conditions.
Accuracy and errors.
Analytical Problems.
Numerical Exercises.
Biography: Osborne Reynolds.
Biography: Carl-Gustaf Arvid Rossby.
Diffusive Processes.
Isotropic, homogeneous turbulence.
Turbulent diffusion.
One-dimensional numerical scheme.
Numerical stability analysis.
Other one-dimensional schemes.
Multi-dimensional numerical schemes.
Analytical Problems.
Numerical Exercises.
Biography: Andrey Nikolaevich Kolmogorov.
Biography: John von Neumann.
Transport and Fate.
Combination of advection and diffusion.
Relative importance of advection: The Peclet number.
Highly advective situations.
Centered and upwind advection schemes.
Advection-diffusion with sources and sinks.
Multi-dimensional approach.
Analytical Problems.
Numerical Exercises.
Biography: Richard Courant.
Biography: Peter Lax.
Rotation Effects.
Geostrophic Flows and Vorticity Dynamics.
Homogeneous geostrophic flows.
Homogeneous geostrophic flows over an irregular bottom.
Non-geostrophic flows.
Vorticity dynamics.
Rigid-lid approximation.
Numerical solution of the rigid-lid pressure equation.
Numerical solution of the streamfunction equation.
Laplacian inversion.
Analytical Problems.
Numerical Exercises.
Biography: Geoffrey Ingram Taylor.
Biography: James Cyrus McWilliams.
Ekman layer.
Shear turbulence.
Friction and rotation.
The bottom Ekman layer.
Generalization to non-uniform currents.
The Ekman layer over uneven terrain.
The surface Ekman layer.
The Ekman layer in real geophysical flows.
Numerical simulation of shallow flows.
Analytical Problems.
Numerical Exercises.
Biography: VagnWalfrid Ekman.
Biography: Ludwig Prandtl.
Barotropic Waves.
Linear wave dynamics.
The Kelvin wave.
Inertia-gravity waves (Poincar´e waves).
Planetary waves (Rossby waves).
Topographic waves.
Analogy between planetary and topographic waves.
Arakawa’s grids.
Numerical simulation of tides and storm surges.
Analytical Problems.
Numerical Exercises.
Biography: William Thomson, Lord Kelvin.
Biography: Akio Arakawa.
Barotropic Instability.
Mechanism.
Waves on a shear flow.
Bounds on wave speeds and growth rates.
A simple example.
Nonlinearities.
Filtering.
Contour dynamics.
Analytical Problems.
Numerical Exercises.
Biography: Louis Norberg Howard.
Biography: Norman J. Zabusky.
Stratification Effects.
Stratification.Static stability.
A note on atmospheric stratification.
Convective adjustment.
The importance of stratification: The Froude number.
Combination of rotation and stratification.
Analytical Problems.
Numerical Exercises.
Biography: David Brunt.
Biography: Vilho V¨ais¨al¨a.
Layered Models.
From depth to density.
Layered models.
Potential vorticity.
Two-layer models.
Wind-induced seiches and resonance in lakes.
Energy conservation.
Numerical layered models.
Lagrangian approach.
Analytical Problems.
Numerical Exercises.
Biography: Raymond Braislin Montgomery.
Biography: J¨org Imberger.
InternalWaves.
From surface to internal waves.
Internal-wave theory.
Structure of an internal wave.
ertical modes and eigenvalue problems.
Waves concentrated at a pycnocline.
Lee waves.
Nonlinear effects.
The Garrett-Munk Spectrum.
Analytical Problems.
Numerical Exercises.
Biography: Walter Heinrich Munk.
Biography: Adrian Edmund Gill.
Turbulence in Stratified Fluids.
Mixing of stratified fluids.
Instability of a stratified shear flow: The Richardson number.
Turbulence closure: k-models.
Other closures: k − or k − klm.
Mixed-layer modeling.
Patankar-type discretizations.
Penetrative convection.
Analytical Problems.
Numerical Exercises.
Biography: Lewis Fry Richardson.
Biography: George Mellor.
Combined Rotation and Stratification Effects.
Dynamics of Stratified Rotating Flows.
Thermal wind.
Geostrophic adjustment.
Energetics of geostrophic adjustment.
Coastal upwelling.
Atmospheric frontogenesis.
Numerical handling of large gradients.
Nonlinear advection schemes.
Analytical Problems.
Numerical Exercises.
Biography: George Veronis.
Biography: Kozo Yoshida.
Quasi-Geostrophic Dynamics.
Simplifying assumption.
Governing equation.
Length and time scales.
Energetics.
Planetary waves in a stratified fluid.
Quasi-geostrophic ocean modeling.
Analytical Problems.
Numerical Exercises.
Biography: Jule Gregory Charney.
Biography: Allan Richard Robinson.
Instabilities of Rotating Stratified Flows.
Two types of instability.
Inertial instability.
Baroclinic instability – The mechanism.
Linear theory of baroclinic instability.
Heat transport.
Bulk criteria.
Finite-amplitude development.
Analytical Problems.
Numerical Exercises.
Biography: Joseph Pedlosky.
Biography: Peter Broomell Rhines.
Fronts, Jets and Vortices.
Front and jets.
Vortices.
Geostrophic turbulence.
Simulations of geostrophic turbulence.
Analytical Problems.
Numerical Exercises.
Biography: Melvin Ernest Stern.
Biography: Peter Douglas Killworth.
Special Topics.
Atmospheric General Circulation.
Climate versus weather.
Planetary heat budget.
Direct and indirect convective cells.
Atmospheric circulation models.
Weather forecasting.
Cloud parameterizations.
Spectral methods.
Semi-Lagrangian methods.
Analytical Problems.
Numerical Exercises.
Biography: Edward Norton Lorenz.
Biography: Joseph Smagorinsky.
Oceanic General Circulation.
What drives the oceanic circulation.
Large-scale ocean dynamics (Sverdrup dynamics).
Thermohaline circulation.
Western boundary currents.
Abyssal circulation.
Oceanic circulation models.
Coordinate systems.
Parameterization of subgrid-scale processes.
Analytical Problems.
Numerical Exercises.
Biography: Henry Melson Stommel.
Biography: Kirk Bryan.
Equatorial Dynamics.
Equatorial beta plane.
Linear wave theory.
El Ni ˜no – Southern Oscillation (ENSO).
ENSO forecasting.
Analytical Problems.
Numerical Exercises.
Biography: James Jay O’Brien.
Biography: Paola Malanotte Rizzoli.
Data Assimilation.
Need for data assimilation.
Nudging.
Optimal interpolation.
Kalman filtering.
Inverse methods.
Operational models.
Analytical Problems.
Numerical Exercises.
Biography: Michael Ghil.
Biography: Eugenia Kalnay.
Appendix A: Elements of Fluid Mechanics.
Budgets.
Spherical coordinates.
Appendix B:Wave Kinematics.
Wavenumber and wavelength.
Frequency, phase speed, and dispersion.
Group velocity and energy propagation.
Analytical Problems.
Numerical Exercises.
Appendix C: Recapitulation of Numerical schemes.
The tridiagonal system solver.
1D finite-difference schemes of various orders.
Time-stepping algorithms.
Partial-derivatives finite differences.
Discrete Fourier Transform and Fast Fourier Transform.
Analytical Problems.
Numerical Exercises.