Preface to the Ninth English Edition	5
	Preface to the Eighth English Edition	6
	Preface to the Ninth German Edition	7
	Contents	9
	Introduction	19
	Abstract	24
	Part I Fundamentals of Viscous Flows	26
	1. Some Features of Viscous Flows	27
	1.1 Real and Ideal Fluids	27
	1.2 Viscosity	28
	1.3 Reynolds Number	30
	1.4 Laminar and Turbulent Flows	36
	1.5 Asymptotic Behaviour at Large Reynolds Numbers	38
	1.6 Comparison of Measurements Using the Inviscid Limiting Solution	38
	1.7 Summary	50
	2. Fundamentals of Boundary–Layer Theory	52
	2.1 Boundary–Layer Concept	52
	2.2 Laminar Boundary Layer on a Flat Plate at Zero Incidence	53
	2.3 Turbulent Boundary Layer on a Flat Plate at Zero Incidence	56
	2.4 Fully Developed Turbulent Flow in a Pipe	59
	2.5 Boundary Layer on an Airfoil	61
	2.6 Separation of the Boundary Layer	62
	2.7 Overview of the Following Material	71
	3. Field Equations for Flowsof Newtonian Fluids	73
	3.1 Description of Flow Fields	73
	3.2 Continuity Equation	74
	3.3 Momentum Equation	74
	3.4 General Stress State of Deformable Bodies	75
	3.5 General State of Deformation of Flowing Fluids	79
	3.6 Relation Between Stresses and Rate of Deformation	84
	3.7 Stokes Hypothesis	87
	3.8 Bulk Viscosity and Thermodynamic Pressure	88
	3.9 Navier–Stokes Equations	90
	3.10 Energy Equation	91
	3.11 Equations of Motion for Arbitrary Coordinate Systems (Summary)	95
	3.12 Equations of Motion for Cartesian Coordinates in Index Notation	98
	3.13 Equations of Motion in Different Coordinate Systems	101
	4. General Propertiesof the Equations of Motion	105
	4.1 Similarity Laws	105
	4.2 Similarity Laws for Flow with Buoyancy Forces (Mixed Forced and Natural Convection)	108
	4.3 Similarity Laws for Natural Convection	112
	4.4 Vorticity Transport Equation	113
	4.5 Limit of Very Small Reynolds Numbers	115
	4.6 Limit of Very Large Reynolds Numbers	116
	4.7 Mathematical Example of the Limit Re??	118
	4.8 Non–Uniqueness of Solutions of the Navier–Stokes Equations	121
	5. Exact Solutionsof the Navier–Stokes Equations	122
	5.1 Steady Plane Flows	122
	5.1.1 Couette–Poiseuille Flows	122
	5.1.2 Jeffery–Hamel Flows (Fully Developed Nozzle and Diffuser Flows)	125
	5.1.3 Plane Stagnation–Point Flow	131
	5.1.4 Flow Past a Parabolic Body	136
	5.1.5 Flow Past a Circular Cylinder	136
	5.2 Steady Axisymmetric Flows	137
	5.2.1 Circular Pipe Flow (Hagen–Poiseuille Flow)	137
	5.2.2 Flow Between Two Concentric Rotating Cylinders	138
	5.2.3 Axisymmetric Stagnation–Point Flow	139
	5.2.4 Flow at a Rotating Disk	140
	5.2.5 Axisymmetric Free Jet	145
	5.3 Unsteady Plane Flows	147
	5.3.1 Flow at a Wall Suddenly Set into Motion (First Stokes Problem)	147
	5.3.2 Flow at an Oscillating Wall (Second Stokes Problem)	150
	5.3.3 Start–up of Couette Flow	151
	5.3.4 Unsteady Asymptotic Suction	152
	5.3.5 Unsteady Plane Stagnation–Point Flow	152
	5.3.6 Oscillating Channel Flow	158
	5.4 Unsteady Axisymmetric Flows	160
	5.4.1 Vortex Decay	160
	5.4.2 Unsteady Pipe Flow	160
	5.5 Summary	162
	Part IILaminar Boundary Layers	164
	6. Boundary–Layer Equations in Plane Flow	165
	6.1 Setting up the Boundary–Layer Equations	165
	6.2 Wall Friction, Separation and Displacement	170
	6.3 Dimensional Representation of the Boundary–Layer Equations	172
	6.4 Friction Drag	175
	6.5 Plate Boundary Layer	176
	7. General Properties and Exact Solutions of the Boundary–Layer Equationsfor Plane Flows	185
	7.1 Compatibility Condition at the Wall	186
	7.2 Similar Solutions of the Boundary–Layer Equations	187
	7.2.1 Derivation of the Ordinary Differential Equation	187
	7.2.2 Wedge Flows	192
	7.2.3 Flow in a Convergent Channel	194
	7.2.4 Mixing Layer	195
	7.2.5 Moving Plate	196
	7.2.6 Free Jet	197
	7.2.7 Wall Jet	200
	7.3 Coordinate Transformation	202
	7.3.1 G¨ortler Transformation	202
	7.3.2 v. Mises Transformation	203
	7.3.3 Crocco Transformation	204
	7.4 Series Expansion of the Solutions	204
	7.4.1 Blasius Series	204
	7.4.2 G¨ortler Series	206
	7.5 Asymptotic Behaviour of Solutions Downstream	207
	7.5.1 Wake Behind Bodies	207
	7.5.2 Boundary Layer at a Moving Wall	210
	7.6 Integral Relations of the Boundary Layer	211
	7.6.1 Momentum–Integral Equation	211
	7.6.2 Energy–Integral Equation	212
	7.6.3 Moment–of–Momentum Integral Equations	214
	8. Approximate Methods for Solving the Boundary–Layer Equationsfor Steady Plane Flows	215
	8.1 Integral Methods	216
	8.2 Stratford’s Separation Criterion	222
	8.3 Comparison of the Approximate Solutions with Exact Solutions	222
	8.3.1 Retarded Stagnation–Point Flow	222
	8.3.2 Divergent Channel (Diffuser)	224
	8.3.3 Circular Cylinder Flow	225
	8.3.4 Symmetric Flow past a Joukowsky Airfoil	227
	9. Thermal Boundary Layers without Coupling of the Velocity Fieldto the Temperature Field	229
	9.1 Boundary–Layer Equations for the Temperature Field	229
	9.2 Forced Convection for Constant Properties	231
	9.3 Effect of the Prandtl Number	235
	9.4 Similar Solutions of the Thermal Boundary Layer	238
	9.5 Integral Methods for Computing the Heat Transfer	243
	9.6 Effect of Dissipation	246
	10. Thermal Boundary Layers with Coupling of the Velocity Fieldto the Temperature Field	251
	10.1 Remark	251
	10.2 Boundary–Layer Equations	251
	10.3 Boundary Layers with Moderate Wall Heat Transfer (Without Gravitational Effects)	253
	10.3.1 Perturbation Calculation	253
	10.3.2 Property Ratio Method (Temperature Ratio Method)	257
	10.3.3 Reference Temperature Method	260
	10.4 Compressible Boundary Layers (Without Gravitational Effects)	261
	10.4.1 Physical Property Relations	261
	10.4.2 Simple Solutions of the Energy Equation	264
	10.4.3 Transformations of the Boundary–Layer Equations	266
	10.4.4 Similar Solutions	269
	10.4.5 Integral Methods	278
	10.4.6 Boundary Layers in Hypersonic Flows	283
	10.5 Natural Convection	285
	10.5.1 Boundary–Layer Equations	285
	10.5.2 Transformation of the Boundary–Layer Equations	290
	10.5.3 Limit of Large Prandtl Numbers (	291
	10.5.4 Similar Solutions	293
	10.5.5 General Solutions	297
	10.5.6 Variable Physical Properties	298
	10.5.7 Effect of Dissipation	300
	10.6 Indirect Natural Convection	301
	10.7 Mixed Convection	304
	11. Boundary–Layer Control(Suction/Blowing)	311
	11.1 Different Kinds of Boundary–Layer Control	311
	11.2 Continuous Suction and Blowing	315
	11.2.1 Fundamentals	315
	11.2.2 Massive Suction (vw ???)	317
	11.2.3 Massive Blowing (vw ? +?)	319
	11.2.4 Similar Solutions	322
	11.2.5 General Solutions	327
	11.2.6 Natural Convection with Blowing and Suction	330
	11.3 Binary Boundary Layers	331
	11.3.1 Overview	331
	11.3.2 Basic Equations	332
	11.3.3 Analogy Between Heat and Mass Transfer	336
	11.3.4 Similar Solutions	337
	12. Axisymmetric and Three–DimensionalBoundary Layers	341
	12.1 Axisymmetric Boundary Layers	341
	12.1.1 Boundary–Layer Equations	341
	12.1.2 Mangler Transformation	343
	12.1.3 Boundary Layers on Non–Rotating Bodies of Revolution	344
	12.1.4 Boundary Layers on Rotating Bodies of Revolution	347
	12.1.5 Free Jets and Wakes	351
	12.2 Three–Dimensional Boundary Layers	355
	12.2.1 Boundary–Layer Equations	355
	12.2.2 Boundary Layer at a Cylinder	361
	12.2.3 Boundary Layer at a Yawing Cylinder	362
	12.2.4 Three–Dimensional Stagnation Point	364
	12.2.5 Boundary Layers in Symmetry Planes	365
	12.2.6 General Configurations	365
	13. Unsteady Boundary Layers	368
	13.1 Fundamentals	368
	13.1.1 Remark	368
	13.1.2 Boundary–Layer Equations	369
	13.1.3 Similar and Semi–Similar Solutions	370
	13.1.4 Solutions for Small Times (High Frequencies)	371
	13.1.5 Separation of Unsteady Boundary Layers	372
	13.1.6 Integral Relations and Integral Methods	373
	13.2 Unsteady Motion of Bodies in a Fluid at Rest	374
	13.2.1 Start–Up Processes	374
	13.2.2 Oscillation of Bodies in a Fluid at Rest	381
	13.3 Unsteady Boundary Layers in a Steady Basic Flow	384
	13.3.1 Periodic Outer Flow	384
	13.3.2 Steady Flow with a Weak Periodic Perturbation	386
	13.3.3 Transition Between Two Slightly Different Steady Boundary Layers	388
	13.4 Compressible Unsteady Boundary Layers	389
	13.4.1 Remark	389
	13.4.2 Boundary Layer Behind a Moving Normal Shock Wave	390
	13.4.3 Flat Plate at Zero Incidence with Variable Free Stream Velocity and Wall Temperature	392
	14. Extensions to the Prandtl Boundary–LayerTheory	395
	14.1 Remark	395
	14.2 Higher Order Boundary–Layer Theory	397
	14.3 Hypersonic Interaction	407
	14.4 Triple–Deck Theory	410
	14.5 Marginal Separation	421
	14.6 Massive Separation	426
	Part IIILaminar–Turbulent Transition	430
	15. Onset of Turbulence (Stability Theory)	431
	15.1 Some Experimental Results on the Laminar–Turbulent Transition	431
	15.1.1 Transition in the Pipe Flow	431
	15.1.2 Transition in the Boundary Layer	435
	15.2 Fundamentals of Stability Theory	440
	15.2.1 Remark	440
	15.2.2 Fundamentals of Primary Stability Theory	441
	15.2.3 Orr–Sommerfeld Equation	443
	15.2.4 Curve of Neutral Stability and the Indifference Reynolds Number	450
	15.2.4a Plate Boundary Layer	452
	15.2.4b Effect of Pressure Gradient	461
	15.2.4c Effect of Suction	473
	15.2.4d Effect of Wall Heat Transfer	476
	15.2.4e Effect of Compressibility	479
	15.2.4f Effect of Wall Roughness	483
	15.2.4g Further Effects	488
	15.3 Instability of the Boundary Layer for Three–Dimensional Perturbations	489
	15.3.1 Remark	489
	15.3.2 Fundamentals of Secondary Stability Theory	492
	15.3.3 Boundary Layers at Curved Walls	497
	15.3.4 Boundary Layer at a Rotating Disk	501
	15.3.5 Three–Dimensional Boundary Layers	503
	15.4 Local Perturbations	509
	Part IVTurbulent Boundary Layers	513
	16. Fundamentals of Turbulent Flows	514
	16.1 Remark	514
	16.2 Mean Motion and Fluctuations	516
	16.3 Basic Equations for the Mean Motion of Turbulent Flows	519
	16.3.1 Continuity Equation	519
	16.3.2 Momentum Equations (Reynolds Equations)	520
	16.3.3 Equation for the Kinetic Energy of the Turbulent Fluctuations (	522
	Equation)	522
	16.3.4 Thermal Energy Equation	525
	16.4 Closure Problem	526
	16.5 Description of the Turbulent Fluctuations	527
	16.5.1 Correlations	527
	16.5.2 Spectra and Eddies	528
	16.5.3 Turbulence of the Outer Flow	530
	16.5.4 Edges of Turbulent Regions and Intermittence	530
	16.6 Boundary–Layer Equations for Plane Flows	531
	17. Internal Flows	534
	17.1 Couette Flow	534
	17.1.1 Two–Layer Structure of the Velocity Field and the Logarithmic Overlap Law	534
	17.1.2 Universal Laws of the Wall	539
	17.1.3 Friction Law	551
	17.1.4 Turbulence Models	553
	17.1.5 Heat Transfer	556
	17.2 Fully Developed Internal Flows (A = const)	558
	17.2.1 Channel Flow	558
	17.2.2 Couette–Poiseuille Flows	559
	17.2.3 Pipe Flow	564
	17.3 Slender–Channel Theory	569
	18. Turbulent Boundary Layers without Coupling of the Velocity Fieldto the Temperature Field	572
	18.1 Turbulence Models	572
	18.1.1 Remark	572
	18.1.2 Algebraic Turbulence Models	574
	18.1.3 Turbulent Energy Equation	575
	18.1.4 Two–Equation Models	577
	18.1.5 Reynolds Stress Models	580
	18.1.6 Heat Transfer Models	583
	18.1.7 Low–Reynolds–Number Models	585
	18.1.8 Large–Eddy Simulation and Direct Numerical Simulation	586
	18.2 Attached Boundary Layers (?w = 0)	587
	18.2.1 Layered Structure	587
	18.2.2 Boundary–Layer Equations Using the Defect Formulation	589
	18.2.3 Friction Law and Characterisitic Quantities of the Boundary Layer	592
	18.2.4 Equilibrium Boundary Layers	595
	18.2.5 Boundary Layer on a Plate at Zero Incidence	597
	18.3 Boundary Layers with Separation	604
	18.3.1 Stratford Flow	604
	18.3.2 Quasi–Equilibrium Boundary Layers	606
	18.4 Computation of Boundary Layers Using Integral Methods	609
	18.4.1 Direct Method	609
	18.4.2 Inverse Method	612
	18.5 Computation of Boundary Layers Using Field Methods	613
	18.5.1 Attached Boundary Layers (?w = 0)	613
	18.5.2 Boundary Layers with Separation	616
	18.5.3 Low–Reynolds–Number Turbulence Models	618
	18.5.4 Additional Effects	619
	18.6 Computation of Thermal Boundary Layers	622
	18.6.1 Fundamentals	622
	18.6.2 Computation of Thermal Boundary Layers Using Field Methods	624
	19. Turbulent Boundary Layers with Coupling of the Velocity Fieldto the Temperature Field	626
	19.1 Fundamental Equations	626
	19.1.1 Time Averaging for Variable Density	626
	19.1.2 Boundary–Layer Equations	628
	19.2 Compressible Turbulent Boundary Layers	632
	19.2.1 Temperature Field	632
	19.2.2 Overlap Law	634
	19.2.3 Skin–Friction Coefficient and Nusselt Number	636
	19.2.4 Integral Methods for Adiabatic Walls	638
	19.2.5 Field Methods	640
	19.2.6 Shock–Boundary–Layer Interaction	640
	19.3 Natural Convection	642
	20. Axisymmetric and Three–DimensionalTurbulent Boundary Layers	645
	20.1 Axisymmetric Boundary Layers	645
	20.1.1 Boundary–Layer Equations	645
	20.1.2 Boundary Layers without Body Rotation	646
	20.1.3 Boundary Layers with Body Rotation	649
	20.2 Three–Dimensional Boundary Layers	651
	20.2.1 Boundary–Layer Equations	651
	20.2.2 Computation Methods	655
	20.2.3 Examples	657
	21. Unsteady Turbulent Boundary Layers	658
	21.1 Averaging and Boundary–Layer Equations	658
	21.2 Computation Methods	661
	21.3 Examples	662
	22. Turbulent Free Shear Flows	665
	22.1 Remark	665
	22.2 Equations for Plane Free Shear Layers	667
	22.3 Plane Free Jet	671
	22.3.1 Global Balances	671
	22.3.2 Far Field	672
	22.3.3 Near Field	677
	22.3.4 Wall Effects	677
	22.4 Mixing Layer	679
	22.5 Plane Wake	681
	22.6 Axisymmetric Free Shear Flows	683
	22.6.1 Basic Equations	683
	22.6.2 Free Jet (U? = 0, = 8?(x ? x0))	684
	22.6.3 Wake (|UN| U?, = ?(x ? x0)1/3)	685
	22.7 Buoyant Jets	687
	22.7.1 Plane Buoyant Jet	687
	22.7.2 Axisymmetric Buoyant Jet	688
	22.8 Plane Wall Jet	689
	Part V Numerical Methods in Boundary–LayerTheory	693
	23. Numerical Integrationof the Boundary–Layer Equations	694
	23.1 Laminar Boundary Layers	694
	23.1.1 Remark	694
	23.1.2 Note on Boundary–Layer Transformations	695
	23.1.3 Explicit and Implicit Discretisation	696
	23.1.4 Solution of the Implicit Difference Equations	700
	23.1.5 Integration of the Continuity Equation	702
	23.1.6 Boundary–Layer Edge and Wall Shear Stress	702
	23.1.7 Integration of the Transformed Boundary–Layer Equations Using the Box Scheme	703
	23.2 Turbulent Boundary Layers	706
	23.2.1 Method of Wall Functions	706
	23.2.2 Low–Reynolds–Number Turbulence Models	711
	23.3 Unsteady Boundary Layers	712
	23.4 Steady Three–Dimensional Boundary Layers	714
	List of Frequently Used Symbols	719
	Indices	725
	Other Symbols	726
	References and Index of Authors	727
	Index	808