~~huplt1? r1.n troduction121. Fluid Mechanics.. ............................................2. Units of Measurement. ........................................3. Solids, Liquids, and Gases. .................................... 34. Continuum Hypothesis ........................................ 45. Transport Phmomena .........................................6. Surfacc Tension ..............................................7. FluidStatics 98. Classical Thcrmodynamics .................................... 129. Perfcct: Gas ..................................................10. Static Equilibrium of a Compressible Medium ................... 17Exercises .................................................... 22Literature Cited .............................................. 23Supplemcntal Reading ........................................ 2358.................................................16Uiqter 2(lartcsian X:nsors1. ScalarsandVeclors ........................................... 242. Rotation of Axes: Formal Dcfinition of a Vector ................. 25vi i3 .4 .5 .6 .7 .8 .9 .10 .11 .12 .13 .14 .15 .16 .Multiplication of Matices .....................................Second-Order Tensor .........................................Contraction and Multiplication .................................Force on a Surface ............................................

Kronecker Delta and Alternating Tensor ........................Dot Product ..................................................Cross Product ................................................Operator V: Gradient. Divergence. and Curl .....................Symmetric and Antisymmetric Tensors .........................Eigenvalues and Eigenvectors of a Symmetric Tensor .............Gauss’ Theorem ..............................................Stokes’ Theorem .............................................Comma Notation .............................................Boldface versus hdicial Notation ..............................Exercises ....................................................Literature Cited ..............................................Supplemental Reading ........................................Chapter 3Kinematics1 .2 .3 .4 .5 .6 .7 .8 .9 .10 .11 .12 .13 .14 .Introduction ..................................................Lagrangian and Eulerian Specifications .........................Material Derivative ...........................................Stredine. Path Line. and Streak Line ..........................Reference Frame and Streamline Pattern ........................Linear Strain Rate ............................................Shear Strain Rate .............................................Vorticity and Circulation ......................................Relative Motion near a Point: Principal Axes ....................Kinematic Considerations of Parallel Shear Flows ................Kinematic Considerations of Vortex Flows ......................One.. Two.. and Three-Dimensional Flows ......................The Stxamfunction ...........................................

Polar Coordinates .............................................Exercises ....................................................Supplemental Reading ........................................2829313235363637384042454647474949505152535656585860636568697273751 .2 .3 .4 .5 .6 .7 .8 .9 .10 .11 .12 .13 .14 .15 .16 .

I7 .18 .19 .Tntmduction ..................................................Timc Derivatives of Volume lntegrals ...........................Conservation of Mass .........................................Streamfunctions: Revisited and Generalized .....................Stress at a Point ..............................................Conservation of Momcntum ...................................Angular Momentum Principle for a Fixed Volume ...............Constitutivc Equation for Newtonian Fluid ......................NavierStokcs Equation .......................................Rotating Frame ...............................................Origin of Forces in Fluid ......................................Momentum Principle for a Fixed Volume .......................Mcchmical Energy Equation ..................................First Law of Thermodynamics: Thermal Energy Equation .........BcrnouUi Equation ............................................Applications of Bernoulli's Equation ...........................Boussincsq Approximation ....................................Boundary Conditions .........................................Exercjscs ....................................................Lileraturc Cited ..............................................Second Law or Thermodynamics: Entropy Production ............Supplemcntal Reading ........................................1 .2 .3 .4 .5 .6 .7 .8 .Tntroduc tion ..................................................Vortex Lines and Vortcx Tubes .................................Role of Viscosity in Rotational and Irrotational Vortices ..........Kclvin's Circulation Theorem ..................................Vorticity Equation in a Nonrotating Fmme ......................Vorticity Equation in a Rotating Frame ..........................Intcraction ol Vortices .........................................Vortcx Shect .................................................Excrcises ....................................................767779

818284868892949799104108109110114117121122124124125126126130134136141144145Literature Cited .............................................. 146Supplemental Reading ........................................ 147Ctuqter 61rrotati.onal Flow1 .2 .3 .4 .5 .6 .7 .8 .9 .10 .11 .12 .13 .14 .15 .16 .1.7.18 .

19 .20 .21 .22 .Relevance of Irrotational Flow Theory ..........................Velocity Potential: Laplace Equation ............................Application of Complex Variables ..............................Flow at a Wall Angle ..........................................Sources and Sinks ............................................Irrotational Vortex ............................................Doublet ......................................................Flow past a Half-Body ........................................Flow past a Circular Cylinder without Circulation ................Flow past a Circular Cylinder with Circulation ...................Forces on a lbo-Dimensional Body ............................Source near a Wall: Method of Images ..........................Flow around an Elliptic Cylinder with Circulation ................Uniqueness of Trrotational Flows ...............................Numerical Solution of Plane Trrotational Flow ...................Axisymmetric Irrotational Flow ................................Streamfunction and Velocity Potential for hisymmetric Flow ....Simple Examples of Axisymmetric Flows .......................Flow around a Streamlined Body of Revolution ..................Flow around an Arbitrary Body of Revolution ...................Concluding Remarks ..........................................Exercises ....................................................Literam Cited ..............................................Supplemental Reading ........................................Confonnal Mapping ..........................................148150152154156157157159160163166170171173175176181184

185187188.I 89190192192chi!pter 7Gravity Waves1 . Introduction .................................................. 1942 . TheWaveEquation ........................................... 1943 . WavcParameters ............................................. 1964 . SurfaceGravity Waves ........................................ 199

5 . Some Features of Surface Gravity Waves ........................ 2036 .7 .8 .9 .10 .1 I .12 .13 .14 .15 .16 .17 .18 .19 .20 .21 .Approximalions for Deep and Shallow Water ....................Tnfluence of Surface Tension ...................................Standing Wavcs ..............................................Group Velocity and Energy Flux ...............................Group Vclocity and Wave Dispersion ...........................Nonlinear Steepening in a Nondispersive Medium ...............Hydraulic Jump ..............................................Finite Amplitude Waves of Unchanging Form ina Dispersive Medium .........................................Stokes' Dri It .................................................Wavcs at a Density Interrace between Infinitely Decp Fluids ......Waves in a Finitc Layer Overlying an Infinitely Deep Fluid .......Shallow Layer Overlying an Inhitcly Deep Fluid ................Equations of Motion for a Continuously Stratified Fluid ..........Internal Wavcs in a Continuously Stratificd Fluid ................

Dispersion of Jntcrnal Wavcs in a Stratified Fluid ................Encrgy Considerations of Internal Wavcs in a Stratified Fluid ......Exercises ....................................................Litcrature Cited ..............................................1 . Tntroduction ..................................................2 . Nondimensional Parameters Determined from Differential Equations3 . Dimensional Matrix ...........................................4 . Buckingham's Pi Theorem .....................................5 .6 .7 .Nondimensional Parameters and Dynamic Similarity .............Commcnls on Model Testing ..................................Significance of Common Nondimensional Parametcrs ............Exerciscs ....................................................Litcrature Cited ..............................................Supplemcnlal Reading ........................................I . Introduction ..................................................2 . Analogy between Heat and Vorticity Diffusion ...................3 . Pressure Change Due to Dynamic Effects .......................20921321621822122522723023223423824024224524a250254255256257261262264266268270270270271273273xii CMtml8

4 .5 .6 .7 .8 .9 .10 .11 .12 .13 .14 .15 .Steady Flow between Parallel Plates ............................Steady Flow in a Pipe .........................................Steady Flow between Concentric Cylinders .....................Impulsively Started Plate: Similarity Solutions ...................Diffusion of a Vortex Sheet ....................................Decay of a Line Vortex ........................................Flow Due to an Oscillating Plate ...............................High and Low Reynolds Number Flows .........................Creeping Flow around a Sphere ................................Nonuniformity of Stokes’ Solution and Oseen’s Improvement .....Hele-Shaw Flow ..............................................Final Remarks ................................................Exercises ....................................................Literature Cited ..............................................Supplemental Reading ........................................(Xapter 10Boundary Layers and Related Topics1 .2 .3 .4 .5 .6 .7 .8 .9 .10 .11 .

12 .13 .14 .15 .16 .17 .Introduction ..................................................Boundary Layer Approximation ................................Different Measures of Boundary Layer Thickness ................Boundary Layer on a Flat plate with a Sink at the Leading Edge ...Boundary Layer on a Flat Plate: Blasius Solution ................von Karman Momentum Integral ...............................Effects of Pressure Gradient ...................................Separation ...................................................Description of Flow past a Circular Cylinder ....................Description of Flow past a Sphere ..............................Dynamics of Sports Balls ......................................Two-Dimensional Jets .........................................Secondary Flows .............................................Perturbation Techniques .......................................An Example of a Regular Perturbation Problem ..................An Example of a Singular Perturbation Problem .................Decay of a Laminar Shear Layer ...............................Exercises ....................................................Literature Cited ..............................................Supplemental Reading ........................................274277279282289290292295297302306308309311311312313318321323332335

336339346347350358359364366371374376377Chpter 3 IComputational Fluid Dynamics by Hom7arcl€I . Hu1 . Tntroduction ..................................................2 . Finite Differcnce Method ......................................3 . Finite Element Method ........................................4 . Incomprcssible Viscous Fluid Flow .............................5 . Two Examples ...............................................6 . Concluding Remarks ..........................................Exercises ....................................................Literature Cited ..............................................1 .2 .3 .4 .5 .6 .8 .9 .10 .11 .12 .‘I 3 .14 .TI I .Tntroduction ..................................................Method of Normal Modes .....................................Thermal Instabilily: The Bknard Problem .......................Double-Diffusive Instability ...................................Ccncrifugal Instability: Taylor Problem .........................Kelvin-Helmholtz Instability ..................................Instability of Continuously Stratified Parallel Flows ..............Squids Theorem and Orr-Sommerfeld Equation ................Tnviscid Stability of Parallel Flows .............................

Some Results of Parallel Viscous Flows .........................Experimental Verification of Boundary Layer Instability ..........Comments on Nonlinear Effects ................................Transition ....................................................Deterministic Chaos ..........................................Exercises ....................................................Literature Cited ..............................................Uurpler 13‘li.xhmlcncc‘1 . Tiitroduction ..................................................2 . Historical Notes ..............................................3 . Avcrages ....................................................4 . Correlations and Spectra ......................................5 . Averaged Equations of Motion .................................3783803853934064244274284304314324444484534614674714754804824834854934954%4984995025066 .7 .8 .9 .10 .11 .12 .13 .

14 .15 .Kinetic Energy Budget of Mean How ........................... 512Kinetic Energy Budget of Turbulent Flow ....................... 514Turbulence Production and Cascade ............................ 517Spectrum of Turbulence in Inertial Subrange .................... 524Wall-Free Shear Flow ......................................... 522Wall-Bounded Shear Flow ..................................... 528Eddy Viscosity and Mixing Length ............................. 536Coherent Structures in a Wall Layer ............................ 539Turbulence in a Stratified Medium .............................. 540Taylor’s Theory of nrbulent Dispersion ........................ 546Exercises .................................................... 552Literature Ciled .............................................. 553Supplemental Reading ........................................ 554Chapter I4Geophysical Fluid Dynamks1 .2 .3 .4 .5 .6 .7 .8 .9 .10 .11 .12 .13 .14 .15 .16 .17 .18 .Introduction ..................................................Vertical Variation of Density in Atmosphere and Ocean ...........Equations of Motion ..........................................Approximate Equations for a Thin Layer on a Rotating Sphere ....Geostrophic Flow .............................................Ekman Layer at a Frec Surface .................................Ekman Layer on a Rigid Surface ...............................

Shallow-Water Equations ......................................Normal Modes in a Continuously Stratified Layer ................High- and Low-Frequency Regimes in Shallow-Water Equations . .Gravity Wavcs with Rotation ...................................Kelvin Wave .................................................Potential Vorticity Conservation in Shallow-Water Thcory ........Internal Waves ...............................................Rossby Wave .................................................Barotropic Instability .........................................Baroclinic Instability ..........................................Geostrophic Turbulence .......................................Exercises ....................................................Literature Cited ..............................................555557559562564569574577579586588591595598(1086136156236266271 .2 .3 .4 .5 .6 .7 .E .9 .10 .1 1 .12 .13 .14 .d

I ntroduc Lion ..................................................The Aircraft and Tts Controls ...................................

Airfoil Geometry .............................................Forces on an M o i l ...........................................Kutta Condition ..............................................Generation of Circulation ......................................Conformal Transformation for Generating Airfoil Shape ..........Lift of Zhukhovsky Airroil ....................................Wing of Finite Span ..........................................Lifting Line Theory of Prandtl and Lanchester ...................Rcsults for Elliptic Circulation Distribution .....................Li.ft and Drag Characteristics of Airfoils ........................Pmpulsive Mechanisms of Fish and Birds .......................Sailing against the Wind .......................................Exercises ....................................................Litcrahre Cited ..............................................Supplemental Reading ........................................(.'hplm 16Compressihle Flow1 .2 .3 .4 .5 .6 .7 .8 .9 .IO .11 .12 .Introduction ..................................................Speed of Sound ..............................................Basic Equations for One-Dimensional Flow .....................Stagnation and Sonic Propcrties ................................Area-Velocity Relations in One-Dimensional Isentropic Flow .....Normal Shock Wave ..........................................Operdtion of Nozzlcs at Dimerent Back Pressures ................Effects of Friction and Heating in Constant-Area Ducts ...........Oblique Shock Wave ..........................................Expansion and Compression in Supersonic Flow .................Mach Cone ..................................................Thin Airfoil Thcory in Supersonic Flow .........................Exerci scs ....................................................629630

633633635636638642645646651653655656658660660661665667671676680685690694696700702704xvi Ctrnteith

Literature Cited ..............................................Supplemental Reading ........................................+pen& ASome Properties of Common FluidsA1 . Useful Conversion Factors ....................................A2 . Properties of Pure Water at Atmospheric Pressure ...............A3 . Properties of Dry Air at Atmospheric Pressure ..................A4 . Properties of Standard Atmosphere ............................Appendix BCurvilinear Coordi.natesB 1 . Cylindrical Polar Coordinates .................................B2 . Plane Polar Coordinates ......................................B3 . Spherical Polar Coordinates ..................................+per& CFounders of Modern Fluid DynamicsLudwig Prandtl(l875-1953) ..................................Geofli-ey Ingram Taylor (1886-1975) ..........................Supplemental Reading .......................................Index705706707

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