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. Preface of the first edition......Page 5 I Fundamentals......Page 19 Objective......Page 21 Importance of geophysical fluid dynamics......Page 22 Distinguishing attributes of geophysical flows......Page 23 Scales of motions......Page 25 Importance of rotation......Page 28 Importance of stratification......Page 30 Distinction between the atmosphere and oceans......Page 31 Data acquisition......Page 34 The emergence of numerical simulations......Page 35 Scales analysis and finite differences......Page 39 Higher-order methods......Page 44 Aliasing......Page 48 Numerical Exercises......Page 50 Walsh Cottage , Woods Hole, Massachusetts......Page 52 UK Meteorological Office, Exeter, England......Page 53 Rotating framework of reference......Page 55 Unimportance of the centrifugal force......Page 58 Free motion on a rotating plane......Page 60 Analogies and physical interpretations......Page 63 Acceleration on a three-dimensional rotating planet......Page 65 Numerical approach to oscillatory motions......Page 68 Numerical convergence and stability......Page 72 Predictor-corrector methods......Page 76 Higher-order schemes......Page 78 Analytical Problems......Page 81 Numerical Exercises......Page 84 Biography: Pierre Simon Marquis de Laplace......Page 86 Biography: Gaspard Gustave de Coriolis......Page 87 Mass budget......Page 89 Momentum budget......Page 90 Equation of state......Page 91 Energy budget......Page 92 Boussinesq approximation......Page 94 Flux formulation and conservative form......Page 98 Finite-volume discretization......Page 99 Analytical Problems......Page 103 Numerical Exercises......Page 105 Biography: Joseph Valentin Boussinesq......Page 106 Biography: Vilhelm Bjerknes......Page 107 Reynolds-averaged equations......Page 109 Eddy coefficients......Page 111 Scales of motion......Page 113 Recapitulation of equations governing geophysical flows......Page 116 Important dimensionless numbers......Page 117 Boundary conditions......Page 119 Numerical implementation of boundary conditions......Page 125 Accuracy and errors......Page 128 Analytical Problems......Page 133 Numerical Exercises......Page 134 Biography: Osborne Reynolds......Page 136 Biography: Carl-Gustaf Arvid Rossby......Page 137 Isotropic, homogeneous turbulence......Page 139 Turbulent diffusion......Page 144 One-dimensional numerical scheme......Page 147 Numerical stability analysis......Page 151 Other one-dimensional schemes......Page 155 Multi-dimensional numerical schemes......Page 160 Analytical Problems......Page 162 Numerical Exercises......Page 163 Biography: Andrey Nikolaevich Kolmogorov......Page 165 Biography: John von Neumann......Page 166 Combination of advection and diffusion......Page 167 Relative importance of advection: The Peclet number......Page 170 Highly advective situations......Page 171 Centered and upwind advection schemes......Page 172 Advection-diffusion with sources and sinks......Page 184 Multi-dimensional approach......Page 187 Analytical Problems......Page 195 Numerical Exercises......Page 198 Biography: Richard Courant......Page 201 Biography: Peter Lax......Page 202 II Rotation Effects......Page 203 Homogeneous geostrophic flows......Page 205 Homogeneous geostrophic flows over an irregular bottom......Page 207 Non-geostrophic flows......Page 210 Vorticity dynamics......Page 212 Rigid-lid approximation......Page 215 Numerical solution of the rigid-lid pressure equation......Page 216 Numerical solution of the streamfunction equation......Page 220 Laplacian inversion......Page 222 Analytical Problems......Page 229 Numerical Exercises......Page 231 Biography: Geoffrey Ingram Taylor......Page 235 Biography: James Cyrus McWilliams......Page 236 Shear turbulence......Page 237 Friction and rotation......Page 241 The bottom Ekman layer......Page 242 Generalization to non-uniform currents......Page 245 The Ekman layer over uneven terrain......Page 247 The surface Ekman layer......Page 248 The Ekman layer in real geophysical flows......Page 251 Numerical simulation of shallow flows......Page 254 Analytical Problems......Page 261 Numerical Exercises......Page 263 Biography: Vagn Walfrid Ekman......Page 264 Biography: Ludwig Prandtl......Page 265 Linear wave dynamics......Page 267 The Kelvin wave......Page 269 Inertia-gravity waves (Poincaré waves)......Page 272 Planetary waves (Rossby waves)......Page 274 Topographic waves......Page 277 Analogy between planetary and topographic waves......Page 281 Arakawa's grids......Page 283 Numerical simulation of tides and storm surges......Page 294 Analytical Problems......Page 302 Numerical Exercises......Page 304 Biography: William Thomson, Lord Kelvin......Page 306 Biography: Akio Arakawa......Page 307 Mechanism......Page 309 Waves on a shear flow......Page 310 Bounds on wave speeds and growth rates......Page 313 A simple example......Page 316 Nonlinearities......Page 320 Filtering......Page 322 Contour dynamics......Page 324 Analytical Problems......Page 330 Numerical Exercises......Page 331 Biography: Louis Norberg Howard......Page 333 Biography: Norman J. Zabusky......Page 334 III Stratification Effects......Page 335 Introduction......Page 337 Static stability......Page 338 A note on atmospheric stratification......Page 339 Convective adjustment......Page 344 The importance of stratification: The Froude number......Page 345 Combination of rotation and stratification......Page 348 Analytical Problems......Page 350 Numerical Exercises......Page 351 Biography: David Brunt......Page 352 Biography: Vilho Väisälä......Page 353 From depth to density......Page 355 Layered models......Page 358 Potential vorticity......Page 364 Two-layer models......Page 365 Wind-induced seiches and resonance in lakes......Page 368 Energy conservation......Page 370 Numerical layered models......Page 372 Lagrangian approach......Page 377 Analytical Problems......Page 379 Numerical Exercises......Page 381 Biography: Raymond Braislin Montgomery......Page 383 Biography: Jörg Imberger......Page 384 From surface to internal waves......Page 385 Internal-wave theory......Page 386 Structure of an internal wave......Page 389 Vertical modes and eigenvalue problems......Page 391 Waves concentrated at a pycnocline......Page 399 Lee waves......Page 403 Nonlinear effects......Page 407 Analytical Problems......Page 409 Numerical Exercises......Page 410 Biography: Walter Heinrich Munk......Page 412 Biography: Adrian Edmund Gill......Page 413 Mixing of stratified fluids......Page 415 Instability of a stratified shear flow: The Richardson number......Page 419 Turbulence closure: k-models......Page 425 Other closures: k- or k-klm......Page 436 Mixed-layer modeling......Page 438 Patankar-type discretizations......Page 440 Penetrative convection......Page 444 Analytical Problems......Page 450 Numerical Exercises......Page 451 Biography: Lewis Fry Richardson......Page 453 Biography: George Mellor......Page 454 IV Combined Rotation and Stratification Effects......Page 455 Thermal wind......Page 457 Geostrophic adjustment......Page 459 Energetics of geostrophic adjustment......Page 462 Coastal upwelling......Page 465 Atmospheric frontogenesis......Page 472 Numerical handling of large gradients......Page 474 Nonlinear advection schemes......Page 479 Analytical Problems......Page 483 Numerical Exercises......Page 486 Biography: George Veronis......Page 488 Biography: Kozo Yoshida......Page 489 Simplifying assumption......Page 491 Governing equation......Page 492 Length and time scales......Page 496 Energetics......Page 498 Planetary waves in a stratified fluid......Page 501 Quasi-geostrophic ocean modeling......Page 507 Analytical Problems......Page 510 Numerical Exercises......Page 511 Biography: Jule Gregory Charney......Page 514 Biography: Allan Richard Robinson......Page 515 Two types of instability......Page 517 Inertial instability......Page 518 Baroclinic instability -- The mechanism......Page 526 Linear theory of baroclinic instability......Page 529 Heat transport......Page 537 Bulk criteria......Page 539 Finite-amplitude development......Page 541 Analytical Problems......Page 543 Numerical Exercises......Page 544 Biography: Joseph Pedlosky......Page 545 Biography: Peter Broomell Rhines......Page 546 Front and jets......Page 547 Vortices......Page 559 Geostrophic turbulence......Page 567 Simulations of geostrophic turbulence......Page 570 Analytical Problems......Page 575 Numerical Exercises......Page 576 Biography: Melvin Ernest Stern......Page 577 Biography: Peter Douglas Killworth......Page 578 V Special Topics......Page 579 Planetary heat budget......Page 581 Direct and indirect convective cells......Page 585 Atmospheric circulation models......Page 589 Weather forecasting......Page 593 Spectral methods......Page 594 Semi-Lagrangian methods......Page 598 Analytical Problems......Page 600 Numerical Exercises......Page 601 Biography: Edward Norton Lorenz......Page 602 Biography: Joseph Smagorinsky......Page 603 What drives the oceanic circulation......Page 605 Large-scale ocean dynamics (Sverdrup dynamics)......Page 608 Thermohaline circulation......Page 611 Abyssal circulation......Page 616 Oceanic circulation models......Page 617 Coordinate systems......Page 620 Parameterization of subgrid-scale processes......Page 627 Analytical Problems......Page 629 Numerical Exercises......Page 630 Biography: Henry Melson Stommel......Page 632 Biography: Kirk Bryan......Page 633 Equatorial beta plane......Page 635 Linear wave theory......Page 637 El Niño -- Southern Oscillation (ENSO)......Page 641 ENSO forecasting......Page 645 Analytical Problems......Page 647 Numerical Exercises......Page 648 Biography: James Jay O'Brien......Page 650 Biography: Paola Malanotte Rizzoli......Page 651 Need for data assimilation......Page 653 Nudging......Page 657 Optimal interpolation......Page 658 Kalman filtering......Page 664 Inverse methods......Page 668 Operational models......Page 674 Analytical Problems......Page 678 Numerical Exercises......Page 681 Biography: Michael Ghil......Page 683 Biography: Eugenia Kalnay......Page 684 A.2 Spherical coordinates......Page 685 B.1 Wavenumber and wavelength......Page 687 B.2 Frequency, phase speed, and dispersion......Page 689 B.3 Group velocity and energy propagation......Page 691 Analytical Problems......Page 694 Numerical Exercises......Page 695 C.1 The tridiagonal system solver......Page 697 C.2 1D finite-difference schemes of various orders......Page 699 C.3 Time-stepping algorithms......Page 700 C.5 Discrete Fourier Transform and Fast Fourier Transform......Page 702 Numerical Exercises......Page 707 Index......Page 709 VI CD-ROM informations......Page 737