Fluid Mechanics of the Atmosphere (eBook)

Front Cover 1
Fluid Mechanics of the Atmosphere 4
Copyright Page 5
Contents 6
Preface 10
Part I Fundamentals 14
Chapter 1 Fundamentals of Fluid Dynamics 20
1.1 Atmospheric Fluid Dynamics 21
1.2 Newton's Law in a Rotating Frame of Reference 23
1.3 The Laminar Flow Regime and Potential Flow 31
1.4 Waves, Vortices, and Instabilities 37
1.5 Turbulence and Transition 46
1.6 Boundary Layers 50
1.7 Historical Development 57
1.8 The Fluid Parcel 59
1.9 Continuum and Averaging 63
1.10 The Equation of State for a Perfect Gas 71
1.11 Viscosity 79
1.12 Summary 90
1.13 Glossary 91
1.14 Symbols 93
Problems 94
Chapter 2 Flow Parameters 97
2.1 Local Time and Spatial Changes (Differentiation at a Point) 98
2.2 The Advective Change and Index Notation 106
2.3 Divergence/Convergence 108
2.4 Vorticity 110
2.5 The Vortex 117
2.6 The Coriolis Term 121
2.7 Integral Theorems 123
2.8 Summary 128
Problems 129
Chapter 3 Methods of Analysis 132
3.1 Scaling 133
3.2 Dimensional Analysis 148
3.3 Similarity 162
3.4 Some Similarity Concepts 169
3.5 Summary 172
Problems 173
Chapter 4 Tensors and Relative Motion 176
4.1 Tensors 176
4.2 Relative Motion near a Point 193
4.3 An Arbitrary Division of the Velocity 202
Summary 203
Problems 204
Part II The Governing Equations for Fluid Flow 206
Chapter 5 Conservation of Mass—Continuity 210
5.1 The Parcel Derivation 210
5.2 A Lagrangian Perspective 214
5.3 Two-Dimensional Version of Continuity 219
5.4 The Integral Form of Continuity 221
5.5 Compressibility 226
5.6 Conservation Statement for the Quantity f 230
Problems 234
Chapter 6 Momentum Dynamics 238
6.1 Conservation of Momentum—Newton's Law 239
6.2 Derivation with Respect to the Infinitesimal Elementary Parcel—Lagrangian Perspective 248
6.3 The Stress Term—Liquids and Gases 249
6.4 The Coriolis Term 262
6.5 The Dimensionless Navier—Stokes Equations 266
6.6 Summary 268
Problems 271
Chapter 7 Conservation of Energy 273
7.1 The First Law of Thermodynamics 276
7.2 The Energy Equation 279
7.3 The Mechanical Energy Equation 281
7.4 The Internal Energy Equation 282
7.5 The Enthalpy Equation 283
7.6 The Moist Atmosphere Energy Equation 285
7.7 An Alternative Derivation 287
7.8 Flow along a Streamline 289
7.9 Summary 302
Problems 305
Chapter 8 Vorticity 307
8.1 Vorticity Characteristics 307
8.2 Arbitrary Separation of the Velocity Field 314
8.3 Kinematics of Vorticity 320
8.4 The Vorticity Tube 321
8.5 Vorticity Transport Equation 332
8.6 Vorticity Characteristics 342
8.7 Application of Momentum, Energy, and Vorticity Equations to Bernoulli's Law 345
8.8 Summary 352
Problems 353
Chapter 9 Potential Flow 355
9.1 Introduction 355
9.2 The Velocity Potential 357
9.3 The Stream Function for Two-Dimensional Flow 358
9.4 Potential Motion with Circulation Compared to Rotational Flow in a Free Vortex 363
9.5 Potential Flow (of an Ideal Fluid) 368
9.6 The Method of Singularities 373
9.7 The Idealized Vortex 383
9.8 Summary 391
Problems 392
Chapter 10 Perturbation Equations 394
10.1 The Mean Flow 394
10.2 Waves 399
10.3 Turbulence 402
10.4 Reynolds Averaging—Flux 404
10.5 The Set of Perturbed Navier–Stokes Equations 410
10.6 The Eddy Viscosity Assumption 417
10.7 Summary 419
Problems 422
Chapter 11 Boundary Layers 424
11.1 Introduction 424
11.2 The Boundary Layer Concept 430
11.3 Boundary Layer Equations 432
11.4 Ekman's Planetary Boundary Layer Solution 437
11.5 The Modified Ekman Solution 446
11.6 The Surface Layer 453
11.7 The Mixing Length 459
11.8 Summary 463
Problems 467
Suggested Reading 470
Answers to Selected Problems 474
Index 494
International Geophysics Series 500