Introduction to Geophysical Fluid Dynamics

by Cushman-Roisin; Beckers

• ISBN13: 9780120887590
• ISBN10: 0120887592
• Edition: 2nd
• Format: Hardcover
• Copyright: 2011-08-26
• Publisher: Elsevier Science

Summary

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. *long-awaited second edition of the classic text *combines both physical and numerical aspects of geophysical fluid dynamics into a single affordable volume *includes CD-ROM with MatLab codes *explores contemporary topics such as the Greenhouse Effect, global warming and the El Nino Southern Oscillation *biographical and historical notes at the ends of chapters trace the intellectual development of the field

Table of Contents

Foreword	p. xiii
Preface	p. xv
Preface of the First Edition	p. xvii
	p. Fundamentals
Introduction
Objective	p. 3
Importance of Geophysical Fluid Dynamics	p. 4
	p. 6
Scales of Motions	p. 8
Importance of Rotation	p. 10
Importance of Stratification	p. 12
Distinction between the Atmosphere and Oceans	p. 14
Data Acquisition	p. 17
The Emergence of Numerical Simulations	p. 19
Scales Analysis and Finite Differences	p. 23
Higher-Order Methods	p. 28
Aliasing	p. 33
Analytical Problems	p. 35
Numerica Exercises	p. 35
The Coriolis Force
Rotating Framework of Reference	p. 41
Unimportance of the Centrifugal Force	p. 44
Free Motion on a Rotating Plane	p. 47
Analogy and Physical Interpretation	p. 50
Acceleration on a Three-Dimensional Rotating Planet	p. 52
Numerical Approach to Oscillatory Motions	p. 55
Numerical Convergence and Stability	p. 59
Predictor-Corrector Methods	p. 63
Higher-Order Schemes	p. 65
Analytical Problems	p. 69
Equations of Fluid Motion
Mass Budget	p. 77
Momentum Budget78
Equation of State	p. 79
Energy Budget	p. 80
Salt and Moisture Budgets	p. 82
Summary of Governing Equations	p. 83
Boussinesq Approximation	p. 83
Flux Formulation and Conservative Form	p. 87
Finite-Volume Discretization	p. 88
Analytical Problems	p. 92
Numerical Exercises
Equations Governing Geophysical Flows
Reynolds-Averaged Equations	p. 99
Eddy Coefficients	p. 101
Scales of Motion	p. 103
Recapitulation of Equations Governing Geophysical Flows	p. 106
important Dimensionless Numbers	p. 107
Boundary Conditions	p. 109
Numerical Implementation of Boundary Conditions	p. 117
Accuracy and Errors	p. 120
Analytical Problems	p. 125
Numerical Exercises	p. 126
Diffusive Processes
Sotropic, Homogeneous Turbulence	p. 131
Turbulent Diffusion	p. 137
One-Dimensional Numerical Scheme	p. 140
Numerical Stability Analysis	p. 144
Other One-.Dimensional Schemes	p. 150
Multi-Dimensional Numerical Schemes	p. 154
	p. 157
Numerical Exercises	p. 158
Transport and Fate
Combination of Advection and Diffusion	p. 163
Relative Importance of Advection: The Peclet Number	p. 167
Highly Advective Situations	p. 168
Centered and Upwind Advection Schemes	p. 169
Advection-Diffusion with Sources and Sinks	p. 183
Multidimensional Approach	p. 186
Analytical Problems	p. 196
Numerical Exercises	p. 198
Rotation Effects
Geostrophic Flows and Vorticity Dynamics
Homogeneous Geostrophic Flows	p. 205
Homogeneous Geostrophic Flows over an Irregular Bottom	p. 208
Generalization to Nongeostrophic Flows	p. 210
Vorticity Dynamics	p. 212
Rigid-Lid Approximation	p. 215
Numerical Solution of the Rigid-Lid Pressure Equation	p. 217
Numerical Solution of the Streamfunction Equation	p. 221
Laplacian Inversion	p. 224
Analytical Problems	p. 231
Numerical Exercises	p. 233
The Ekman Layer
Shear Turbulence	p. 239
Friction and Rotation	p. 243
The Bottom Ekman Layer	p. 245
Generalization to Nonuniform Currents	p. 247
The Ekman Layer over Uneven Terrain	p. 250
The Surface Ekman Layer	p. 251
The Ekman Layer in Real Geophysical Flows	p. 254
Numerical Simulation of Shallow Flows	p. 257
Analytical Problems	p. 265
Numerical Exercises	p. 267
Barotropic Waves
Linear Wave Dynamics	p. 271
The Kelvin Wave	p. 273
Inertia-Gravity Waves (Poincaré Waves)	p. 276
Planetary Waves (Rossby Waves)	p. 278
Topographic Waves	p. 283
Analogy between Planetary and Topographic Waves	p. 287
Arakawa's Grids	p. 289
Numerical Simulation of Tides and Storm Surges	p. 300
Analytical Problems	p. 309
Numerical Exercises	p. 312
Barotropic Instability
What Makes a Wave Grow Unstable?	p. 317
Waves on a Shear Flow	p. 318
Bounds on Wave Speeds and Growth Rates	p. 322
A Simple Example	p. 324
Nonlinearities	p. 328
Filtering	p. 331
Contour Dynamics	p. 334
Analytical Problems	p. 340
Numerical Exercises	p. 341
Stratification Effects
Stratification
Introduction	p. 347
Static Stability	p. 348
A Note on Atmospheric Stratification	p. 349
Convective Adjustment	p. 354
The Importance of Stratification; The Froude Number	p. 356
Combination of Rotation and Stratification	p. 358
Analytical Problems	p. 361
Numerical Exercises	p. 361
Layered Models
From Depth to Density	p. 365
Layered Models	p. 369
Potential Vorticity	p. 374
Two-Layer Models	p. 374
Wind-Induced Seiches in Lakes	p. 379
Energy Conservation	p. 381
Numerical Layered Models	p. 383
Lagrangian Approach	p. 387
Analytical Problems	p. 390
Numerical Exercises	p. 391
Interna! Waves
From Surface to Internal Waves	p. 395
Internal-Wave Theory	p. 397
Structure of an Internal Wave	p. 399
Vertical Modes and Eigenvalue Problems	p. 401
Lee Waves!	p. 412
Nonlinear Effects	p. 416
Analytical Problems	p. 419
Numerical Exercise	p. 421
Turbulence in Stratified Fluids
Mixing of Stratified Fluids	p. 425
Instability of a Stratified Shear Flow: The Richardson Number	p. 429
TurbulencelClosure: k-Models	p. 435
Other Closures: k- ¿ and k-klm	p. 449
Mixed-Layer Modeling	p. 450
Patankar-Type Discretizations	p. 455
Wind Mixing and Penetrative Convection	p. 458
Analytical Problems	p. 466
Numerical Exercises	p. 467
Combined Rotation and Stratification Effects
Dynamics of Stratified Rotating Flows
Thermal Wind	p. 473
Geostrophic Adjustment	p. 475
Energetics of Geostrophic Adjustment	p. 480
Coastal Upwelling	p. 482
Atmospheric Frontogenesis	p. 490
Numerical Handling of Large Gradients	p. 502
Nonlinear Advection Schemes	p. 507
Analytical Problems	p. 512
Numerical Exercises	p. 516
Quasi-Geostrophic Dynamics
Simplifying Assumption	p. 521
Governing Equation	p. 522
Length and Timescale	p. 527
Energetics	p. 530
Planetary Waves in a Stratified Fluid	p. 532
Some Nonlinear Effects	p. 539
Quasi-Geostrophic Ocean Modeling	p. 542
Analytical Problems	p. 546
Numerical Exercises	p. 547
Instabilities of Rotating Stratified Flows
Two Types of Instability	p. 553
Inertial instability	p. 554
Baroclinic Instability-The Mechanism	p. 561
Linear Theory of Baroclinic Instability	p. 566
Heat Transport	p. 574
Bulk Criteria	p. 576
Finite-Amplitude Development	p. 579
Analytical Problems	p. 584
Numerical Exercises	p. 585
Fronts, jets and Vortices
Fronts and Jets	p. 589
Vortices	p. 601
Geostrophic Turbulence	p. 611
Simulations of Geostrophic Turbulence Analytical Problems Numerical Exercises	p. 613
Analytical Problems	p. 618
Numerical Exercises	p. 621
Special Topics
Atmospheric General Circulation
Climate Versus Weather	p. 627
Planetary Heat Budget	p. 627
Direct and Indirect Convective Cells	p. 631
Atmospheric Circulation Models	p. 637
Brief Remarks on Weather Forecasting	p. 642
Cloud Parameterizations	p. 642
Spectral Methods	p. 644
Semi-Lagrangian Methods	p. 649
Analitical Problems	p. 652
Numerical Exertises	p. 653
Oceanic General Circulation
What Drives the Oceanic Circulation	p. 657
Large-Scale Ocean Dynamics (Sverdrup Dynamics)	p. 660
Western Boundary Currents	p. 669
Thermohaiine Circulation	p. 673
Abyssal Circulation	p. 677
Oceanic Circulation Models	p. 681
Analytical Problems	p. 695
Numerical Exercises	p. 696
Equatorial Dynamics
Equatorial Beta Plane	p. 701
Linear Wave Theory	p. 703
El Nino - Southern Oscillation (ENSO)	p. 707
ENSO Forecasting	p. 716
Analytical Problems	p. 720
Numerical Exercises	p. 721
Data Assimilation
Need for Data Assimilation	p. 725
Nudging	p. 730
Optimallilnterpolation	p. 731
Kalman Filtering	p. 739
Inverse Methods	p. 743
Operational Models	p. 750
Analytical Problems	p. 754
Numerical Exercises	p. 756
Web site Information
Elements of Fluid Mechanics
Budgets	p. 763
Equations in Cylindrical Coordinates	p. 768
Equations in Spherical Coordinates	p. 769
Vorticity and Rotation	p. 770
Analytical Problems	p. 771
Numerical Exercise	p. 772
Wave Kinematics
Wavenumber and Wavelength	p. 773
Frequency, Phase Speed, and Dispersion	p. 776
Group Velocity and Energy Propagation	p. 778
Analytical Problems	p. 781
Numerical Exercises	p. 781
Recapitulation of Numerical Schemes
The Tridiagonal System Solver	p. 783
1D Finite-Difference Schemes of Various Orders	p. 785
Time-Stepping Algorithms	p. 786
Partial-Derivatives Finite Differences	p. 787
Discrete Fourier Transform and Fast Fourier Transform	p. 787
Analytical Problems	p. 792
Numerical Exercises	p. 793
References	p. 795
Index	p. 815
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