Rotating Fluids in Engineering and Science (eBook)

Front Cover 1
Rotating Fluids in Engineering and Science 2
Copyright Page 3
Table of Contents 4
Preface 10
PART I: Fluid Mechanics Review 12
Chapter 1. Rotating Fluid Phenomena 14
Chapter 2. Mass and Momentum Conservation 34
2.1 Eulerian Mechanics 34
2.2 Mass Conservation 34
2.3 Force and Momentum 37
2.4 Navier-Stokes Equations 40
2.5 Dimensionless Equations and Ratios 46
Chapter 3. Potential (Inviscid) Flow 54
3.1 Bernoulli Equation 54
3.2 Stream Functions and Velocity Potentials 56
3.3 Row Past a Circular Cylinder 59
3.4 Pressure Components 64
Chapter 4. Boundary Layers and Turbulence 68
4.1 Introduction and Two Solutions by Stokes 68
4.2 Prandtl Boundary Layer Equations 71
4.3 Flat Plate and Cylinder Solutions 75
4.4 Momentum Integral Equation 78
4.5 Turbulence and Stability 81
Chapter 5. Wave Theory 88
5.1 Introduction and Definitions 88
5.2 Longitudinal Waves 95
5.3 Transverse Waves 98
5.4 Mach Cones 104
PART II: Rotating Fluid Theory 108
Chapter 6. Rotating Coordinate Systems 110
6.1 Intermediate Reference Frames 110
6.2 Fluids in a Rotating Frame 113
6.3 Ekman and Rossby Numbers 115
6.4 Application Examples 117
Chapter 7. Coriolis Phenomena 124
7.1 Coriolis Forces vs. Accelerations 124
7.2 Coriolis and Angular Momentum 128
7.3 Coriolis Force-Acceleration Criteria 130
7.4 Application Examples 132
Chapter 8. Rotation, Vorticity, and Circulation 138
8.1 Rotation 138
8.2 Vorticity 139
8.3 Circulation and Stokes Theorem 145
8.4 Application Examples 148
Chapter 9. Vorticity as the Variable 156
9.1 Vorticity in Navier-Stokes Equations 156
9.2 Viscous Production of Vorticity 157
9.3 Relative Vorticity 161
9.4 Application Examples 161
Chapter 10. 
170 
10.1 Vortex Interactions in Two Dimensions 170
10.2 Conservation of Vorticity and Circulation 174
10.3 The Formula of Biot and Savart 180
10.4 Rankine's Combined Vortex 181
10.5 Vortex Intensification by Stretching 184
10.6 Application Examples 187
Chapter 11. Secondary Flows 194
11.1 Boundary Layer Review 194
11.2 A Rotating Disk in a Stationary Fluid 194
11.3 A Rotating Fluid above a Stationary Surface 199
11.4 Enclosed Secondary Rows 202
11.5 Application Examples 205
Chapter 12. Circular Pathline Flows 212
12.1 Theoretical Criteria 212
12.2 Some Important Rows 213
12.3 Application Examples 220
Chapter 13. Rotation and Inertial Waves 226
13.1 Rayleigh Instability 226
13.2 Stability of Circular Pathüne Flows 228
13.3 Rossby Waves and Inertial Waves 230
13.4 Atmospheric Rossby Waves I 233
13.5 Instability and Turbulence 236
13.6 Application Examples 237
PART III: Rotating Fluid Applications 244
Chapter 14. Pipes, Channels, and Rivers 246
14.1 Swirl in Straight Sections 246
14.2 Secondary Flow in Curved Sections 250
14.3 River Meandering 255
14.4 Abutment Undercutting 256
14.5 Study and Research Projects 257
Chapter 15. Rotors and Centrifuges 262
15.1 Thin Disk in a Housing 262
15.2 Row in a Cylindrical Annulus 265
15.3 Centrifuges 266
15.4 Cyclone Separators 271
15.5 Study and Research Projects 272
Chapter 16. Wings, Lift, and Drag 276
16.1 Circulation and Lift (Inviscid) 276
16.2 Circulation and Lift (Viscous) 278
16.3 Kutta-Zhukowskii Theory 280
16.4 Finite Wings and Vortices 281
16.5 Vertical Momentum and Induced Drag 284
16.6 Study and Research Projects 286
Chapter 17. Turbomachinery 290
17.1 Definitions and Classifications 290
17.2 Internal Flow Characteristics 298
17.3 Torque and Power Output 300
17.4 Row Calculations 302
17.5 Performance Criteria 309
17.6 Study and Research Projects 311
Chapter 18. Liquids in Precessing Spacecraft 316
18.1 Rigid-Body Dynamics 316
18.2 Energy Dissipation and Stability 320
18.3 Solution: Analysis and Computation 322
18.4 Solution: Scaled Experiments 324
18.5 Study and Research Projects 327
Chapter 19. The Earth, Sun, and Moon 330
19.1 Introduction 330
19.2 Earth and Earth-Sun-Moon Dynamics 331
19.3 Motions in the Liquid Core 333
19.4 Chandler Wobble 336
19.5 Tides and Earth-Sun-Moon Dynamics 338
19.6 Study and Research Projects 340
Chapter 20. Atmospheric Circulation 344
20.1 Introduction 344
20.2 Convective Flow Patterns 347
20.3 Coriolis Phenomena 349
20.4 Planetary Flow Dynamics 352
20.5 Atmospheric Rossby Waves II 354
20.6 Study and Research Projects 355
Chapter 21. Oceanic Circulation 360
21.1 Flow Patterns and Energy Sources 360
21.2 Coriolis and Oceanic Gyres 363
21.3 Western Intensification and Elevated 364
21.4 Localized Flow Phenomena 366
21.5 Some Quantitative Analyses 368
21.6 Study and Research Projects 372
Chapter 22. Intense Atmospheric Vortices 376
22.1 Whirlwinds and Dust Devils 376
22.2 Large-Scale Vortex Storms 377
22.3 Hurricanes (Typhoons) 379
22.4 Tornadoes 384
22.5 Study and Research Projects 386
Appendices 390
Appendix A: Mathematical Relationships 390
A.1 Vectors 390
A.2 Matrices 390
A.3 Direction Cosine Matrices 391
A.4 Dyadics and Tensors 393
A.5 The Del Operator V 393
A.6 Operations Using V 394
Appendix B: Stream Functions and Velocity Potentials 396
B.l Summary 396
B.2 Basic Flows 396
B.3 Sums of Two Flows 397
B.4 Cylinders and Vortex Pairs 398
Appendix C: Equations of Motion 400
C.l Cartesian 400
C.2 Cylindrical 400
C.3 Spherical 401
Appendix D: Fluid Properties 404
D.l Units 404
D.2 Properties of Air 404
D.3 Properties of Water 405
D.4 Common Gases and Liquids 405
D.5 Compressible Fluids 406
Appendix E: Geophysical Data 408
E.l The Earth 408
E.2 The Sun 408
E.3 The Moon 408
E.4 The Planets 409
E.5 The Oceans 409
E.6 The Standard Atmosphere 410
References 412
Index 426