Preface ........................................................ ix
Chapter 1. The Fluid Continuum ................................. 1
1.1 Eulerian and Lagrangian Descriptions ....................... 1
1.2 The Material Derivative .................................... 6
Problem Set 1 .................................................. 10
Chapter 2. Conservation of Mass and Momentum .................. 13
2.1 Conservation of Mass ...................................... 13
2.2 Conservation of Momentum in an Ideal Fluid ................ 16
2.3 Steady Flow of a Fluid of Constant Density ................ 18
2.4 Intrinsic Coordinates in Steady Flow ...................... 20
2.5 Potential Flows with Constant Density ..................... 21
2.6 Boundary Conditions on an Ideal Fluid ..................... 22
Problem Set 2 .................................................. 24
Chapter 3. Vorticity .......................................... 27
3.1 Local Analysis of the Velocity Field ...................... 27
3.2 Circulation ............................................... 29
3.3 Kelvin's Theorem for a Barotropic Fluid ................... 30
3.4 The Vorticity Equation .................................... 30
3.5 Helmholtz' Laws ........................................... 32
3.6 The Velocity Field Created by a Given Vorticity Field ..... 33
3.7 Some Examples of Vortical Flows ........................... 35
Problem Set 3 .................................................. 41
Chapter 4. Potential Flow ..................................... 45
4.1 Harmonic Flows ............................................ 45
4.2 Flows in Three Dimensions ................................. 51
4.3 Apparent Mass and the Dynamics of a Body in a Fluid ....... 57
4.4 Deformable Bodies and Their Locomotion .................... 62
4.5 Drift ..................................................... 65
Problem Set 4 .................................................. 70
Chapter 5. Lift and Drag in Ideal Fluids ...................... 73
5.1 Lift in Two Dimensions and the Kutta-Joukowski
Condition ................................................. 74
5.2 Smoothing the Leading Edge: Joukowski Airfoils ............ 77
5.3 Unsteady and Quasi-Steady Motion of an Airfoil ............ 79
5.4 Drag in Two-Dimensional Ideal Flow ........................ 81
5.5 The Three-Dimensional Wing: Prandtl's Lifting Line
Theory .................................................... 88
Problem Set 5 .................................................. 94
Chapter 6. Viscosity and the Navier-Stokes Equations .......... 97
6.1 The Newtonian Stress Tensor ............................... 97
6.2 Some Examples of Incompressible Viscous Flow ............. 101
6.3 Dynamical Similarity ..................................... 106
Problem Set 6 ................................................. 109
Chapter 7. Stokes Flow ....................................... 111
7.1 Solutions of the Stokes Equations ........................ 113
7.2 Uniqueness of Stokes Flows ............................... 114
7.3 The Stokes Solution for Uniform Flow Past a Sphere ....... 114
7.4 Two Dimensions: Stokes' Paradox .......................... 117
7.5 Time Reversibility in Stokes Flow ........................ 119
7.6 Stokesian Locomotion and the Scallop Theorem ............. 121
Problem Set 7 ................................................. 121
Chapter 8. The Boundary Layer ................................ 123
8.1 The Limit of Large Re .................................... 123
8.2 Blasius Solution for a Semi-Infinite Flat Plate .......... 125
8.3 Boundary Layer Analysis as a Matching Problem ............ 132
8.4 Separation ............................................... 133
8.5 Prandtl-Batchelor Theory ................................. 134
Problem Set 8 ................................................. 137
Chapter 9. Energy ............................................ 139
9.1 Mechanical Energy ........................................ 139
9.2 Elements of Classical Thermodynamics ..................... 141
9.3 The Energy Equation ...................................... 143
9.4 Some Basic Relations for the Nondissipative Case ......... 145
9.5 Kelvin's Theorem in a Compressible Medium ................ 146
Problem Set 9 ................................................. 149
Chapter 10. Sound ............................................ 151
10.1 One-Dimensional Waves ................................... 151
10.2 The Fundamental Solution in Three Dimensions ............ 152
10.3 Kirchhoff's Solution .................................... 153
10.4 Weakly Nonlinear Acoustics in One Dimension ............. 155
Problem Set 10 ................................................ 158
Chapter 11. Gas Dynamics ..................................... 161
11.1 Nonlinear Waves in One Dimension ........................ 161
11.2 Dynamics of a Polytropic Gas ............................ 162
11.3 Simple Waves ............................................ 163
11.4 Linearized Supersonic Flow .............................. 166
11.5 Alternative Formulation and Proof of the Drag Formula ... 171
11.6 Transonic Flow .......................................... 173
Problem Set 11 ................................................ 174
Chapter 12. Shock Waves ...................................... 175
12.1 Scalar Case ............................................. 175
12.2 Quasi-linear Supersonic Flow ............................ 177
12.3 The Stationary Normal Shock Wave ........................ 178
12.4 Riemann's Problem: The Shock Tube ....................... 183
Problem Set 12 ................................................ 186
Supplementary Notes ........................................... 189
Bibliography .................................................. 195
Index ......................................................... 197
| 
