Fundamentals of Geophysical Fluid Dynamics / Edition 1

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Fundamentals of Geophysical Fluid Dynamics is a concise and accessible introduction to GFD for intermediate to advanced students of the physics, chemistry, and/or biology of Earth's fluid environment. This textbook was developed from the author's many years of teaching a first-year graduate course at the Department of Atmospheric and Oceanic Sciences, University of California, LOS Angeles. Readers are expected to be familiar with physics and mathematics at the level of general dynamics (mechanics) and partial differential equations.

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Editorial Reviews

From the Publisher
' … a very good introductory text to geophysical fluid dynamics. Explanations of complex subjects are clear, concise, and insightful. Distracting and unnecessary details are avoided in discussions, and the organization of the material is well thought-out and logical … ideal for use as a first exposure to the subject matter.' - Dr Leif Thomas, School of Oceanography , University of Washington

'Jim McWilliams' introductory book to the fundamentals of Geophysical Fluid Dynamics is clearly written and well posed. The author relies on examples based on jets and vortices to introduce concepts such as turbulence, chaotic dynamics, bolus velocities, boundary layers, etc. that have not been extensively covered by existing textbooks. This book will therefore be very useful not only to graduate students, but also to scientists who are looking for a well-written reference book that is complementary to what is presently available.' Dr Eric P. Chassignet, Rosenstiel School of Marine and Atmospheric Science, Division of Meteorology and Physical Oceanography, University of Miami

'McWilliams shows how the simplified models of Geophysical Fluid Dynamics (GFD) can be used to explain the underlying physics in the complex turbulent flows in the Earth's atmosphere and oceans.' Professor John A Johnson, School of Mathematics, University of East Anglia

Pre-publication praise: ' … a delightfully refreshing introduction to graduate-level geophysical fluid dynamics. This well-written text includes a concise review of the needed applied mathematics, physics and fluid dynamics. The text pulls examples not only from the atmospheres and oceans but also from recent numerical studies and laboratory experiments in nonlinear dynamics, solitons, chaos and 2- and 3-dimensional turbulence, with an appropriate emphasis on their relevance to geophysical fluid dynamics. Some topics, for example geostrophic adjustment, are more clearly explained and are better physically motivated here than in any other text I have read. This book should not only be on the shelves of all geophysical fluid dynamicists, but also physicists, astronomers, and applied mathematicians.' Professor Philip Marcus, Department of Mechanical Engineering, University of California, Berkeley

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Product Details

  • ISBN-13: 9780521856379
  • Publisher: Cambridge University Press
  • Publication date: 7/31/2006
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 266
  • Product dimensions: 6.85 (w) x 9.72 (h) x 0.71 (d)

Meet the Author

James C. McWilliams is Louis B. Slichter Professor of Earth Sciences in the Department of Atmospheric and Oceanic Sciences, Institute of Geophysics and Planetary Physics, University of California at Los Angeles.

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Table of Contents

Preface ix

Symbols xi

1 Purposes and value of geophysical fluid dynamics 1

2 Fundamental dynamics 8

2.1 Fluid dynamics 8

2.1.1 Representations 8

2.1.2 Governing equations 9

2.1.3 Boundary and initial conditions 13

2.1.4 Energy conservation 14

2.1.5 Divergence, vorticity, and strain rate 16

2.2 Oceanic approximations 18

2.2.1 Mass and density 19

2.2.2 Momentum 22

2.2.3 Boundary conditions 24

2.3 Atmospheric approximations 27

2.3.1 Equation of state for an ideal gas 27

2.3.2 A stratified resting state 29

2.3.3 Buoyancy oscillations and convection 31

2.3.4 Hydrostatic balance 34

2.3.5 Pressure coordinates 35

2.4 Earth's rotation 39

2.4.1 Rotating coordinates 41

2.4.2 Geostrophic balance 43

2.4.3 Inertial oscillations 47

3 Barotropic and vortex dynamics 49

3.1 Barotropic equations 50

3.1.1 Circulation 51

3.1.2 Vorticity and potential vorticity 54

3.1.3 Divergence and diagnostic force balance 57

3.1.4 Stationary, inviscid flows 59

3.2 Vortex movement 64

3.2.1 Point vortices 64

3.2.2 Chaos and limits of predictability 72

3.3 Barotropic and centrifugal instability 73

3.3.1 Rayleigh's criterion for vortex stability 73

3.3.2 Centrifugal instability 75

3.3.3 Barotropic instability of parallel flows 76

3.4 Eddy-mean interaction 80

3.5 Eddy viscosity and diffusion 83

3.6 Emergence of coherent vortices 86

3.7 Two-dimensional turbulence 88

4 Rotating shallow-water and wave dynamics 95

4.1 Rotating shallow-water equations 97

4.1.1 Integral and parcel invariants 101

4.2 Linear wave solutions 104

4.2.1 Geostrophic mode 106

4.2.2 Inertia-gravity waves 107

4.2.3 Kelvin waves 109

4.3 Geostrophic adjustment 111

4.4 Gravity wave steepening: bores and breakers 120

4.5 Stokes drift and material transport 126

4.6 Quasigeostrophy 129

4.7 Rossby waves 133

4.8 Rossby-wave emission 134

4.8.1 Vortex propagation on the β-plane 135

4.8.2 Eastern boundary Kelvin wave 138

5 Baroclinic and jet dynamics 141

5.1 Layered hydrostatic model 143

5.1.1 Two-layer equations 143

5.1.2 N-layer equations 147

5.1.3 Vertical modes 149

5.2 Baroclinic instability 155

5.2.1 Unstable modes 156

5.2.2 Upshear phase tilt 160

5.2.3 Eddy heat flux 161

5.2.4 Effects on the mean flow 162

5.3 Turbulent baroclinic zonal jet 164

5.3.1 Posing the jet problem 164

5.3.2 Equilibrium velocity and buoyancy structure 167

5.3.3 Zonal momentum balance 171

5.3.4 Potential vorticity homogenization 177

5.3.5 Meridional overturning circulation and mass balance 177

5.3.6 Meridional heat balance 180

5.3.7 Maintenance of the general circulation 181

5.4 Rectification by Rossby-wave radiation 182

6 Boundary-layer and wind-gyre dynamics 186

6.1 Planetary boundary layer 186

6.1.1 Boundary-layer approximations 187

6.1.2 The shear boundary layer 192

6.1.3 Eddy-viscosity closure 196

6.1.4 Bottom Ekman layer 197

6.1.5 Oceanic surface Ekman layer 201

6.1.6 Vortex spin down 205

6.1.7 Turbulent Ekman layer 206

6.2 Oceanic wind gyre and western boundary layer 213

6.2.1 Posing the gyre problem 215

6.2.2 Interior and boundary-layer circulations 219

6.2.3 Application to real gyres 224

6.2.4 Turbulent baroclinic wind gyres 228

Afterword 233

Exercises 234

References 243

Index 245

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