Preface 

ix  
PART I Fluid Mechanics Review 

1  (96) 


3  (20) 

Mass and Momentum Conservation 


23  (20) 


23  (1) 


23  (3) 


26  (3) 


29  (6) 

Dimensionless Equations and Ratios 


35  (8) 

Potential (Inviscid) Flow 


43  (14) 


43  (2) 

Stream Functions and Velocity Potentials 


45  (3) 

Flow Past a Circular Cylinder 


48  (5) 


53  (4) 

Boundary Layers and Turbulence 


57  (20) 

Introduction and Two Solutions by Stokes 


57  (3) 

Prandtl Boundary Layer Equations 


60  (4) 

Flat Plate and Cylinder Solutions 


64  (3) 

Momentum Integral Equation 


67  (3) 


70  (7) 


77  (20) 

Introduction and Definitions 


77  (7) 


84  (3) 


87  (6) 


93  (4) 
PART II Rotating Fluid Theory 

97  (136) 

Rotating Coordinate Systems 


99  (14) 

Intermediate Reference Frames 


99  (3) 

Fluids in a Rotating Frame 


102  (2) 


104  (2) 


106  (7) 


113  (14) 

Coriolis Forces vs. Accelerations 


113  (4) 

Coriolis and Angular Momentum 


117  (2) 

Coriolis ForceAcceleration Criteria 


119  (2) 


121  (6) 

Rotation, Vorticity, and Circulation 


127  (18) 


127  (1) 


128  (6) 

Circulation and Stokes Theorem 


134  (3) 


137  (8) 

Vorticity as the Variable 


145  (14) 

Vorticity in NavierStokes Equations 


145  (1) 

Viscous Production of Vorticity 


146  (4) 


150  (1) 


150  (9) 


159  (24) 

Vortex Interactions in Two Dimensions 


159  (4) 

Conservation of Vorticity and Circulation 


163  (6) 

The Formula of Biot and Savart 


169  (1) 

Rankine's Combined Vortex 


170  (3) 

Vortex Intensification by Stretching 


173  (3) 


176  (7) 


183  (18) 


183  (1) 

A Rotating Disk in a Stationary Fluid 


183  (5) 

A Rotating Fluid above a Stationary Surface 


188  (3) 


191  (3) 


194  (7) 


201  (14) 


201  (1) 


202  (7) 


209  (6) 

Rotation and Intertial Waves 


215  (18) 


215  (2) 

Stability of Circular Pathline Flows 


217  (2) 

Rossby Waves and Inertial Waves 


219  (3) 

Atmospheric Rossby Waves I 


222  (3) 

Instability and Turbulence 


225  (1) 


226  (7) 
PART III Rotating Fluid Applications 

233  (168) 

Pipes, Channels, and Rivers 


235  (16) 

Swirl in Straight Sections 


235  (4) 

Secondary Flow in Curved Sections 


239  (5) 


244  (1) 


245  (1) 

Study and Research Projects 


246  (5) 


251  (14) 


251  (3) 

Flow in a Cylindrical Annulus 


254  (1) 


255  (5) 


260  (1) 

Study and Research Projects 


261  (4) 


265  (14) 

Circulation and Lift (Inviscid) 


265  (2) 

Circulation and Lift (Viscous) 


267  (2) 


269  (1) 

Finite Wings and Vortices 


270  (3) 

Vertical Momentum and Induced Drag 


273  (2) 

Study and Research Projects 


275  (4) 


279  (26) 

Definitions and Classifications 


279  (8) 

Internal Flow Characteristics 


287  (2) 


289  (2) 


291  (7) 


298  (2) 

Study and Research Projects 


300  (5) 

Liquids in Precessing Spacecraft 


305  (14) 


305  (4) 

Energy Dissipation and Stability 


309  (2) 

Solution: Analysis and Computation 


311  (2) 

Solution: Scaled Experiments 


313  (3) 

Study and Research Projects 


316  (3) 


319  (14) 


319  (1) 

Earth and EarthSunMoon Dynamics 


320  (2) 

Motions in the Liquid Core 


322  (3) 


325  (2) 

Tides and EarthSunMoon Dynamics 


327  (2) 

Study and Research Projects 


329  (4) 


333  (16) 


333  (3) 


336  (2) 


338  (3) 


341  (2) 

Atmospheric Rossby Waves II 


343  (1) 

Study and Research Projects 


344  (5) 


349  (16) 

Flow Patterns and Energy Sources 


349  (3) 

Coriolis and Oceanic Gyres 


352  (1) 

Western Intensification and Elevated Centers 


353  (2) 


355  (2) 

Some Quantitative Analyses 


357  (4) 

Study and Research Projects 


361  (4) 

Intense Atmospheric Vortices 


365  (36) 

Whirlwinds and Dust Devils 


365  (1) 

LargeScale Vortex Storms 


366  (2) 


368  (5) 


373  (2) 

Study and Research Projects 


375  (4) 
Appendices 


A Mathematical Relationships 


379  (6) 


379  (1) 


379  (1) 

A.3 Direction Cosine Matrices 


380  (2) 


382  (1) 


382  (1) 


383  (2) 

B Stream Functions and Velocity Potentials 


385  (4) 


385  (1) 


385  (1) 


386  (1) 

B.4 Cylinders and Vortex Pairs 


387  (2) 


389  (4) 


389  (1) 


389  (1) 


390  (3) 


393  (4) 


393  (1) 


393  (1) 


394  (1) 

D.4 Common Gases and Liquids 


394  (1) 


395  (2) 


397  (4) 


397  (1) 


397  (1) 


397  (1) 


398  (1) 


398  (1) 

E.6 The Standard Atmosphere 


399  (2) 
References 

401  (14) 
Index 

415  