Cushman-Roisin / Beckers Introduction to Geophysical Fluid Dynamics

Physical and Numerical Aspects
2. Auflage 2011
ISBN: 978-0-08-091678-1
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, Band Volume 101, 875 Seiten

Reihe: International Geophysics

Introduction to Geophysical Fluid Dynamics 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. - Combines both physical and numerical aspects of geophysical fluid dynamics into a single affordable volume - 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 - Recipient of the 2010 Wernaers Prize, awarded each year by the National Fund for Scientific Research of Belgium (FNR-FNRS)

Benoit Cushman-Roisin is Professor of Engineering Sciences at Dartmouth College, where he has been on the faculty since 1990. His teaching includes a series of introductory, mid-level, and advanced courses in environmental engineering. He has also developed new courses in sustainable design and industrial ecology. Prof. Cushman-Roisin holds a B.S. in Engineering Physics, Summa Cum Laude, from the University of LiŠge, Belgium (1978) and a Ph.D. in Geophysical Fluid Dynamics from the Florida State University (1980). He is the author of two books and numerous refereed publications on various aspects of environmental fluid mechanics. In addition to his appointment at Dartmouth College, Prof. Cushman-Roisin maintains an active consultancy in environmental aspects of fluid mechanics and energy efficiency He is co-founder of e2fuel LLC, a startup dedicated to aviation and trucking fuel from clean sources. He is the founding editor of Environmental Fluid Mechanics.

Autoren/Hrsg.

Cushman-Roisin, Benoit

Beckers, Jean-Marie

Inhaltsverzeichnis

1;Front Cover;1
2;Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects;4
3;Copyright;5
4;Table of Contents;6
5;Foreword;14
6;Preface;16
7;Preface of the First Edition;18
8;I Fundamentals;20
8.1;1 Introduction;22
8.1.1;1.1 Objective;22
8.1.2;1.2 Importance of Geophysical Fluid Dynamics;23
8.1.3;1.3 Distinguishing Attributes of Geophysical Flows;25
8.1.4;1.4 Scales of Motions;27
8.1.5;1.5 Importance of Rotation;29
8.1.6;1.6 Importance of Stratification;31
8.1.7;1.7 Distinction between the Atmosphere and Oceans;33
8.1.8;1.8 Data Acquisition;36
8.1.9;1.9 The Emergence of Numerical Simulations;38
8.1.10;1.10 Scales Analysis and Finite Differences;42
8.1.11;1.11 Higher-Order Methods;47
8.1.12;1.12 Aliasing;52
8.1.13;Analytical Problems;54
8.1.14;Numerical Exercises;54
8.2;2 The Coriolis Force;60
8.2.1;2.1 Rotating Framework of Reference;60
8.2.2;2.2 Unimportance of the Centrifugal Force;63
8.2.3;2.3 Free Motion on a Rotating Plane;66
8.2.4;2.4 Analogy and Physical Interpretation;69
8.2.5;2.5 Acceleration on a Three-Dimensional Rotating Planet;71
8.2.6;2.6 Numerical Approach to Oscillatory Motions;74
8.2.7;2.7 Numerical Convergence and Stability;78
8.2.7.1;2.7.1 Formal Stability Definition;80
8.2.7.2;2.7.2 Strict Stability;80
8.2.7.3;2.7.3 Choice of a Stability Criterion;80
8.2.8;2.8 Predictor-Corrector Methods;82
8.2.9;2.9 Higher-Order Schemes;84
8.2.10;Analytical Problems;88
8.2.11;Numerical Exercises;91
8.3;3 Equations of Fluid Motion;96
8.3.1;3.1 Mass Budget;96
8.3.2;3.2 Momentum Budget;97
8.3.3;3.3 Equation of State;98
8.3.4;3.4 Energy Budget;99
8.3.5;3.5 Salt and Moisture Budgets;101
8.3.6;3.6 Summary of Governing Equations;102
8.3.7;3.7 Boussinesq Approximation;102
8.3.8;3.8 Flux Formulation and Conservative Form;106
8.3.9;3.9 Finite-Volume Discretization;107
8.3.10;Analytical Problems;111
8.3.11;Numerical Exercises;113
8.4;4 Equations Governing Geophysical Flows;118
8.4.1;4.1 Reynolds-Averaged Equations;118
8.4.2;4.2 Eddy Coefficients;120
8.4.3;4.3 Scales of Motion;122
8.4.4;4.4 Recapitulation of Equations Governing Geophysical Flows;125
8.4.5;4.5 Important Dimensionless Numbers;126
8.4.6;4.6 Boundary Conditions;128
8.4.6.1;4.6.1 Kinematic Conditions;131
8.4.6.2;4.6.2 Dynamic Conditions;133
8.4.6.3;4.6.3 Heat, Salt, and Tracer Boundary Conditions;135
8.4.7;4.7 Numerical Implementation of Boundary Conditions;136
8.4.8;4.8 Accuracy and Errors;139
8.4.8.1;4.8.1 Discretization Error Estimates;140
8.4.9;Analytical Problems;144
8.4.10;Numerical Exercises;145
8.5;5 Diffusive Processes;150
8.5.1;5.1 Isotropic, Homogeneous Turbulence;150
8.5.1.1;5.1.1 Length and Velocity Scales;151
8.5.1.2;5.1.2 Energy Spectrum;154
8.5.2;5.2 Turbulent Diffusion;156
8.5.3;5.3 One-Dimensional Numerical Scheme;159
8.5.4;5.4 Numerical Stability Analysis;163
8.5.5;5.5 Other One-Dimensional Schemes;169
8.5.6;5.6 Multi-Dimensional Numerical Schemes;173
8.5.7;Analytical Problems;176
8.5.8;Numerical Exercises;177
8.6;6 Transport and Fate;182
8.6.1;6.1 Combination of Advection and Diffusion;182
8.6.2;6.2 Relative Importance of Advection: The Peclet Number;186
8.6.3;6.3 Highly Advective Situations;187
8.6.4;6.4 Centered and Upwind Advection Schemes;188
8.6.5;6.5 Advection–Diffusion with Sources and Sinks;202
8.6.6;6.6 Multidimensional Approach;205
8.6.7;Analytical Problems;215
8.6.8;Numerical Exercises;217
9;II Rotation Effects;222
9.1;7 Geostrophic Flows and Vorticity Dynamics;224
9.1.1;7.1 Homogeneous Geostrophic Flows;224
9.1.2;7.2 Homogeneous Geostrophic Flows Over an Irregular Bottom;227
9.1.3;7.3 Generalization to Nongeostrophic Flows;229
9.1.4;7.4 Vorticity Dynamics;231
9.1.5;7.5 Rigid-Lid Approximation;234
9.1.6;7.6 Numerical Solution of the Rigid-Lid Pressure Equation;236
9.1.7;7.7 Numerical Solution of the Streamfunction Equation;240
9.1.8;7.8 Laplacian Inversion;243
9.1.9;Analytical Problems;250
9.1.10;Numerical Exercises;252
9.2;8 The Ekman Layer;258
9.2.1;8.1 Shear Turbulence;258
9.2.1.1;8.1.1 Logarithmic Profile;259
9.2.1.2;8.1.2 Eddy Viscosity;261
9.2.2;8.2 Friction and Rotation;262
9.2.3;8.3 The Bottom Ekman Layer;264
9.2.4;8.4 Generalization to Nonuniform Currents;266
9.2.5;8.5 The Ekman Layer over Uneven Terrain;269
9.2.6;8.6 The Surface Ekman Layer;270
9.2.7;8.7 The Ekman Layer in Real Geophysical Flows;273
9.2.8;8.8 Numerical Simulation of Shallow Flows;276
9.2.9;Analytical Problems;284
9.2.10;Numerical Exercises;286
9.3;9 Barotropic Waves;290
9.3.1;9.1 Linear wave dynamics;290
9.3.2;9.2 The Kelvin Wave;292
9.3.3;9.3 Inertia-Gravity Waves (Poincér Waves);295
9.3.4;9.4 Planetary Waves (Rossby Waves);297
9.3.5;9.5 Topographic Waves;302
9.3.6;9.6 Analogy between Planetary and Topographic Waves;306
9.3.7;9.7 Arakawa's Grids;308
9.3.8;9.8 Numerical Simulation of Tides and Storm Surges;319
9.3.9;Analytical Problems;328
9.3.10;Numerical Exercises;331
9.4;10 Barotropic Instability;336
9.4.1;10.1 What Makes a Wave Grow Unstable?;336
9.4.2;10.2 Waves on Shear Flow;337
9.4.3;10.3 Bounds on Wave Speeds and Growth Rates;341
9.4.4;10.4 A Simple Example;343
9.4.5;10.5 Nonlinearities;347
9.4.6;10.6 Filtering;350
9.4.7;10.7 Contour Dynamics;353
9.4.8;Analytical Problems;359
9.4.9;Numerical Exercises;360
10;III Stratification Effects;364
10.1;11 Stratification;366
10.1.1;11.1 Introduction;366
10.1.2;11.2 Static Stability;367
10.1.3;11.3 A Note on Atmospheric Stratification;368
10.1.4;11.4 Convective Adjustment;373
10.1.5;11.5 The Importance of Stratification: The Froude Number;375
10.1.6;11.6 Combination of Rotation and Stratification;377
10.1.7;Analytical Problems;380
10.1.8;Numerical Exercises;380
10.2;12 Layered Models;384
10.2.1;12.1 From Depth to Density;384
10.2.2;12.2 Layered Models;388
10.2.3;12.3 Potential Vorticity;393
10.2.4;12.4 Two-Layer Models;393
10.2.5;12.5 Wind-Induced Seiches in Lakes;398
10.2.6;12.6 Energy Conservation;400
10.2.7;12.7 Numerical Layered Models;402
10.2.8;12.8 Lagrangian Approach;406
10.2.9;Analytical Problems;409
10.2.10;Numerical Exercises;410
10.3;13 Internal Waves;414
10.3.1;13.1 From Surface to Internal Waves;414
10.3.2;13.2 Internal-wave Theory;416
10.3.3;13.3 Structure of an Internal Wave;418
10.3.4;13.4 Vertical Modes and Eigenvalue Problems;420
10.3.4.1;13.4.1 Vertical Eigenvalue Problem;423
10.3.4.2;13.4.2 Bounds on Frequency;423
10.3.4.3;13.4.3 Simple Example of Constant N2;424
10.3.4.4;13.4.4 Numerical Decomposition into Vertical Modes;426
10.3.4.5;13.4.5 Waves Concentration at a Pycnocline;429
10.3.5;13.5 Lee Waves;431
10.3.5.1;13.5.1 Radiating Waves;433
10.3.5.2;13.5.2 Trapped Waves;435
10.3.6;13.6 Nonlinear Effects;435
10.3.7;Analytical Problems;438
10.3.8;Numerical Exercises;440
10.4;14 Turbulence in Stratified Fluids;444
10.4.1;14.1 Mixing of Stratified Fluids;444
10.4.2;14.2 Instability of a Stratified Shear Flow: The Richardson Number;448
10.4.3;14.3 Turbulence Closure: k-Models;454
10.4.4;14.4 Other Closures: k-e and k-klm;468
10.4.5;14.5 Mixed-layer Modeling;469
10.4.6;14.6 Patankar-Type Discretizations;474
10.4.7;14.7 Wind Mixing and Penetrative Convection;477
10.4.7.1;14.7.1 Wind Mixing;478
10.4.7.2;14.7.2 Penetrative Convection;480
10.4.8;Analytical Problems;485
10.4.9;Numerical Exercises;486
11;IV Combined Rotation and Stratification Effects;490
11.1;15 Dynamics of Stratified Rotating Flows;492
11.1.1;15.1 Thermal Wind;492
11.1.2;15.2 Geostrophic Adjustment;494
11.1.3;15.3 Energetics of Geostrophic Adjustment;499
11.1.4;15.4 Coastal Upwelling;501
11.1.4.1;15.4.1 The Upwelling Process;501
11.1.4.2;15.4.2 A Simple Model of Coastal Upwelling;503
11.1.4.3;15.4.3 Finite-Amplitude Upwelling;505
11.1.4.4;15.4.4 Variability of the Upwelling Front;508
11.1.5;15.5 Atmospheric Frontogenesis;509
11.1.6;15.6 Numerical Handling of Large Gradients;521
11.1.7;15.7 Nonlinear Advection Schemes;526
11.1.8;Analytical Problems;531
11.1.9;Numerical Exercises;535
11.2;16 Quasi-Geostrophic Dynamics;540
11.2.1;16.1 Simplifying Assumption;540
11.2.2;16.2 Governing Equation;541
11.2.3;16.3 Length and Timescale;546
11.2.4;16.4 Energetics;549
11.2.5;16.5 Planetary Waves in a Stratified Fluid;551
11.2.6;16.6 Some Nonlinear Effects;558
11.2.7;16.7 Quasi-Geostrophic Ocean Modeling;561
11.2.8;Analytical Problems;565
11.2.9;Numerical Exercises;566
11.3;17 Instabilities of Rotating Stratified Flows;572
11.3.1;17.1 Two Types of Instability;572
11.3.2;17.2 Inertial Instability;573
11.3.3;17.3 Baroclinic Instability—the Mechanism;580
11.3.4;17.4 Linear Theory of Baroclinic Instability;585
11.3.5;17.5 Heat Transport;593
11.3.6;17.6 Bulk Criteria;595
11.3.7;17.7 Finite-Amplitude Development;598
11.3.8;Analytical Problems;603
11.3.9;Numerical Exercises;604
11.4;18 Fronts, Jets and Vortices;608
11.4.1;18.1 Fronts and Jets;608
11.4.1.1;18.1.1 Origin and Scales;608
11.4.1.2;18.1.2 Meanders;611
11.4.1.3;18.1.3 Multiple Equilibria;616
11.4.1.4;18.1.4 Stretching and Topographic Effects;616
11.4.1.5;18.1.5 Instabilities;619
11.4.2;18.2 Vortices;620
11.4.3;18.3 Turbulence;630
11.4.4;18.4 Simulations of Geostrophic Turbulence;632
11.4.5;Analytical Problems;637
11.4.6;Numerical Exercises;640
12;V Special Topics;644
12.1;19 Atmospheric General Circulation;646
12.1.1;19.1 Climate Versus Weather;646
12.1.2;19.2 Planetary Heat Budget;646
12.1.3;19.3 Direct and Indirect Convective Cells;650
12.1.4;19.4 Atmospheric Circulation Models;656
12.1.5;19.5 Brief Remarks on Weather Forecasting;661
12.1.6;19.6 Cloud Parameterizations;661
12.1.7;19.7 Spectral Methods;663
12.1.8;19.8 Semi-Lagrangian Methods;668
12.1.9;Analytical Problems;671
12.1.10;Numerical Exercises;672
12.2;20 Oceanic General Circulation;676
12.2.1;20.1 What Drives the Oceanic Circulation;676
12.2.2;20.2 Large-Scale Ocean Dynamics (Sverdrup Dynamics);679
12.2.2.1;20.2.1 Sverdrup Relation;681
12.2.2.2;20.2.2 Sverdrup Transport;682
12.2.2.3;20.2.3 Thermal Wind and Beta Spiral;683
12.2.2.4;20.2.4 A Bernoulli Function;685
12.2.2.5;20.2.5 Potential Vorticity;686
12.2.3;20.3 Western Boundary Currents;688
12.2.4;20.4 Thermohaline Circulation;692
12.2.4.1;20.4.1 Subduction;692
12.2.4.2;20.4.2 Ventilated Thermocline Theory;695
12.2.4.3;20.4.3 Scaling of the Main Thermocline;696
12.2.5;20.5 Abyssal Circulation;696
12.2.6;20.6 Models;700
12.2.6.1;20.6.1 Coordinate Systems;705
12.2.6.2;20.6.2 Subgrid-Scale Processes;712
12.2.7;Analytical Problems;714
12.2.8;Numerical Exercises;715
12.3;21 Equatorial Dynamics;720
12.3.1;21.1 Equatorial Beta Plane;720
12.3.2;21.2 Linear Waves Theory;722
12.3.3;21.3 El Niño – Southern Oscillation (ENSO);726
12.3.3.1;21.3.1 The Ocean;730
12.3.3.2;21.3.2 The Atmosphere;734
12.3.3.3;21.3.3 The Coupled Model;734
12.3.4;21.4 ENSO Forecasting;735
12.3.5;Analytical Problems;739
12.3.6;Numerical Exercises;740
12.4;22 Data Assimilation;744
12.4.1;22.1 Need for Data Assimilation;744
12.4.2;22.2 Nudging;749
12.4.3;22.3 Optimal Interpolation;750
12.4.4;22.4 Kalman Filtering;758
12.4.5;22.5 Inverse Methods;762
12.4.6;22.6 Operational Models;769
12.4.7;Analytical Problems;773
12.4.8;Numerical Exercises;775
13;VI Web site Information;780
13.1;A. Elements of Fluid Mechanics;782
13.1.1;A.1 Budgets;782
13.1.2;A.2 Equations in Cylindrical Coordinates;787
13.1.3;A.3 Equations in Spherical Coordinates;788
13.1.4;A.4 Vorticity and Rotation;789
13.1.5;Analytical Problems;790
13.1.6;Numerical Exercise;791
13.2;B. Wave Kinematics;792
13.2.1;B.1 Wavenumber and Wavelength;792
13.2.2;B.2 Frequency, Phase Speed, and Dispersion;795
13.2.3;B.3 Group Velocity and Energy Propagation;797
13.2.4;Analytical Problems;800
13.2.5;Numerical Exercises;800
13.3;C. Recapitulation of Numerical Schemes;802
13.3.1;C.1 The Tridiagonal System Solver;802
13.3.2;C.2 1D Finite-Difference Schemes of Various Orders;804
13.3.3;C.3 Time-Stepping Algorithms;805
13.3.4;C.4 Partial-Derivatives Finite Differences;806
13.3.5;C.5 Discrete Fourier Transform and Fast Fourier Transform;806
13.3.6;Analytical Problems;811
13.3.7;Numerical Exercises;812
14;References;814
15;Index;834
15.1;A;834
15.2;B;835
15.3;C;835
15.4;D;836
15.5;E;837
15.6;F;838
15.7;G;839
15.8;H;839
15.9;I;839
15.10;J;840
15.11;K;840
15.12;L;841
15.13;M;841
15.14;N;842
15.15;O;842
15.16;P;843
15.17;Q;843
15.18;R;844
15.19;S;844
15.20;T;846
15.21;U;846
15.22;V;846
15.23;W;847
15.24;Y;847
15.25;Z;847

Leseproben

Chapter 1 Introduction
Benoit Cushman-Roisin,    Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, USA Jean-Marie Beckers,    Département d’Astrophysique, Géophysique et Océanographie, Université de Liège, B-4000 Liège, Belgium Abstract
This opening chapter defines the discipline known as geophysical fluid dynamics, stresses its importance, and highlights its most distinctive attributes. A brief history of numerical simulations in meteorology and oceanography is also presented. Scale analysis and its relationship with finite differences are introduced to show how discrete numerical grids depend on the scales under investigation and how finite differences permit the approximation of derivatives at those scales. The problem of unresolved scales is introduced as an aliasing problem in discretization. Keywords
Aliasing; computational fluid dynamics (CFD); data acquisition; discretization; forecasting; hurricanes; Jupiter; Lewis Fry Richardson; meteorological office; numerical simulations; rotation; scales of motion; stratification; Walsh Cottage 1.1 Objective
The object of geophysical fluid dynamics is the study of naturally occurring, large-scale flows on Earth and elsewhere, but mostly on Earth. Although the discipline encompasses the motions of both fluid phases – liquids (waters in the ocean, molten rock in the outer core) and gases (air in our atmosphere, atmospheres of other planets, ionized gases in stars) – a restriction is placed on the scale of these motions. Only the large-scale motions fall within the scope of geophysical fluid dynamics. For example, problems related to river flow, microturbulence in the upper ocean, and convection in clouds are traditionally viewed as topics specific to hydrology, oceanography, and meteorology, respectively. Geophysical fluid dynamics deals exclusively with those motions observed in various systems and under different guises but nonetheless governed by similar dynamics. For example, large anticyclones of our weather are dynamically germane to vortices spun off by the Gulf Stream and to Jupiter’s Great Red Spot. Most of these problems, it turns out, are at the large-scale end, where either the ambient rotation (of Earth, planet, or star) or density differences (warm and cold air masses, fresh and saline waters), or both assume some importance. In this respect, geophysical fluid dynamics comprises rotating-stratified fluid dynamics. Typical problems in geophysical fluid dynamics concern the variability of the atmosphere (weather and climate dynamics), ocean (waves, vortices, and currents), and, to a lesser extent, the motions in the earth’s interior responsible for the dynamo effect, vortices on other planets (such as Jupiter’s Great Red Spot and Neptune’s Great Dark Spot), and convection in stars (the sun, in particular). 1.2 Importance of Geophysical Fluid Dynamics
Without its atmosphere and oceans, it is certain that our planet would not sustain life. The natural fluid motions occurring in these systems are therefore of vital importance to us, and their understanding extends beyond intellectual curiosity—it is a necessity. Historically, weather vagaries have baffled scientists and laypersons alike since times immemorial. Likewise, conditions at sea have long influenced a wide range of human activities, from exploration to commerce, tourism, fisheries, and even wars. Thanks in large part to advances in geophysical fluid dynamics, the ability to predict with some confidence the paths of hurricanes (Figs. 1.1 and 1.2) has led to the establishment of a warning system that, no doubt, has saved numerous lives at sea and in coastal areas (Abbott, 2004). However, warning systems are only useful if sufficiently dense observing systems are implemented, fast prediction capabilities are available, and efficient flow of information is ensured. A dreadful example of a situation in which a warning system was not yet adequate to save lives was the earthquake off Indonesia’s Sumatra Island on 26 December 2004. The tsunami generated by the earthquake was not detected, its consequences not assessed, and authorities not alerted within the 2 h needed for the wave to reach beaches in the region. On a larger scale, the passage every 3–5 years of an anomalously warm water mass along the tropical Pacific Ocean and the western coast of South America, known as the El-Niño event, has long been blamed for serious ecological damage and disastrous economical consequences in some countries (Glantz, 2001; O’Brien, 1978). Now, thanks to increased understanding of long oceanic waves, atmospheric convection, and natural oscillations in air–sea interactions (D’Aleo, 2002; Philander, 1990), scientists have successfully removed the veil of mystery on this complex event, and numerical models (e.g., Chen, Cane, Kaplan, Zebiak & Huang, 2004) offer reliable predictions with at least one year of lead time, that is, there is a year between the moment the prediction is made and the time to which it applies.
Figure 1.1 Hurricane Frances during her passage over Florida on 5 September 2004. The diameter of the storm was about 830 km, and its top wind speed approached 200 km per hour. Courtesy of NOAA, Department of Commerce, Washington, D.C.
Figure 1.2 Computer prediction of the path of Hurricane Frances. The calculations were performed on Friday, 3 September 2004, to predict the hurricane path and characteristics over the next 5 days (until Wednesday, 8 September). The outline surrounding the trajectory indicates the level of uncertainty. Compare the position predicted for Sunday, 5 September, with the actual position shown on Fig. 1.1. Courtesy of NOAA, Department of Commerce, Washington, D.C. Having acknowledged that our industrial society is placing a tremendous burden on the planetary atmosphere and consequently on all of us, scientists, engineers, and the public are becoming increasingly concerned about the fate of pollutants and greenhouse gases dispersed in the environment and especially about their cumulative effect. Will the accumulation of greenhouse gases in the atmosphere lead to global climatic changes that, in turn, will affect our lives and societies? What are the various roles played by the oceans in maintaining our present climate? Is it possible to reverse the trend toward depletion of the ozone in the upper atmosphere? Is it safe to deposit hazardous wastes on the ocean floor? Such pressing questions cannot find answers without, first, an in-depth understanding of atmospheric and oceanic dynamics and, second, the development of predictive models. In this twin endeavor, geophysical fluid dynamics assumes an essential role, and the numerical aspects should not be underestimated in view of the required predictive tools. 1.3 Distinguishing Attributes of Geophysical Flows
Two main ingredients distinguish the discipline from traditional fluid mechanics: the effects of rotation and those of stratification. The controlling influence of one, the other, or both leads to peculiarities exhibited only by geophysical flows. In a nutshell, this book can be viewed as an account of these peculiarities. The presence of an ambient rotation, such as that due to the earth’s spin about its axis, introduces in the equations of motion two acceleration terms that, in the rotating framework, can be interpreted as forces. They are the Coriolis force and the centrifugal force. Although the latter is the more palpable of the two, it plays no role in geophysical flows; however, surprising this may be.1 The former and less intuitive of the two turns out to be a crucial factor in geophysical motions. For a detailed explanation of the Coriolis force, the reader is referred to the following chapter in this book or to the book by Stommel and Moore (1989). A more intuitive explanation and laboratory illustrations can be found in Chapter 6 of Marshall and Plumb (2008). In anticipation of the following chapters, it can be mentioned here (without explanation) that a major effect of the Coriolis force is to impart a certain vertical rigidity to the fluid. In rapidly rotating, homogeneous fluids, this effect can be so strong that the flow displays strict columnar motions; that is, all particles along the same vertical evolve in concert, thus retaining their vertical alignment over long periods of time. The discovery of this property is attributed to Geoffrey I. Taylor, a British physicist famous for his varied contributions to fluid dynamics. (See the short biography at the end of Chapter 7.) It is said that Taylor first arrived at the rigidity property with mathematical arguments alone. Not believing that this could be correct, he then performed laboratory experiments that revealed, much to his amazement, that the theoretical prediction was indeed correct. Drops of dye released in such rapidly rotating, homogeneous fluids form vertical streaks, which, within a few rotations, shear laterally to form spiral sheets of dyed fluid (Fig. 1.3). The vertical coherence of these sheets is truly fascinating!
Figure 1.3 Experimental evidence of the rigidity of a rapidly rotating, homogeneous fluid. In a spinning vessel filled with clear water, an initially amorphous cloud of aqueous dye is transformed in the course of several rotations into perfectly vertical sheets,...