Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects

✍ Scribed by Cushman-Roisin B., Beckers J.-M.

• Year: 2006
• Tongue: English
• Leaves: 739
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Науки о Земле;Метеорология и климатология;