| Preface | p. ix |
| Fundamental properties of vorticity | p. 1 |
| Relation between velocity and vorticity | p. 1 |
| Vorticity and rotation | p. 6 |
| Circulation | p. 8 |
| Vortex lines and tubes | p. 8 |
| The laws of vortex motion | p. 10 |
| Kelvin's circulation theorem | p. 14 |
| Cauchy's equations | p. 16 |
| Irrotational flow | p. 17 |
| Bernoulli's equation | p. 18 |
| Singular distributions of vorticity | p. 20 |
| Vortex jumps | p. 20 |
| Vortex sheets | p. 25 |
| Line vortices | p. 33 |
| Image vorticity | p. 39 |
| Vortex momentum | p. 46 |
| Vortex force and bound vorticity | p. 46 |
| Hydrodynamic impulse | p. 48 |
| Impulsive generation from rest | p. 51 |
| Effect of compressibility | p. 53 |
| Angular impulse | p. 55 |
| Effect of viscosity | p. 56 |
| Impulse of isolated vortices | p. 56 |
| Impulse of a line vortex | p. 60 |
| Vortex centroid | p. 61 |
| Impulse in two dimensions | p. 62 |
| Kinetic energy of vortices | p. 67 |
| Helicity | p. 69 |
| Axisymmetric motion with swirl | p. 71 |
| Motion with surfaces | p. 74 |
| Virtual momentum of a moving body | p. 74 |
| Virtual momentum and impulse | p. 76 |
| Virtual angular momentum | p. 78 |
| Two-dimensional motion with circulation | p. 79 |
| Some applications | p. 81 |
| Virtual mass | p. 81 |
| Attraction of vortices or bodies to walls | p. 84 |
| Force on a body in a non-uniform stream | p. 87 |
| Force on a body in an accelerated irrotational stream | p. 89 |
| Rotating bodies | p. 89 |
| Torque on a body in a non-uniform stream | p. 91 |
| Self-propulsion of a deformable body | p. 92 |
| Buoyant vortex rings | p. 93 |
| Creation of vorticity | p. 95 |
| Formation of a vortex sheet | p. 95 |
| Leading edge suction on the sheet | p. 97 |
| Approximate development of the sheet into a vortex pair | p. 99 |
| Formation of a vortex ring | p. 103 |
| Creation of circulation about a body | p. 105 |
| Generation of vorticity by flow separation | p. 107 |
| Accelerated flow past a wing | p. 109 |
| Dynamics of line vortices in two-dimensional flow | p. 116 |
| Stability of a polygonal array | p. 116 |
| Vortices near walls | p. 119 |
| Kirchhoff-Routh path function | p. 123 |
| Conformal mapping and the Kirchhoff-Routh path function | p. 126 |
| Stability of infinite periodic arrays | p. 130 |
| The Karman vortex street | p. 133 |
| Statistical mechanics of assemblies of line vortices | p. 138 |
| Vortex sheets in two dimensions | p. 141 |
| The Birkhoff-Rott equation | p. 141 |
| Kelvin-Helmholtz instability | p. 142 |
| The ill-posedness of vortex sheets | p. 145 |
| Roll-up of a semi-infinite vortex sheet: The Kaden spiral | p. 147 |
| General similarity solutions, single and multibranched spirals | p. 152 |
| Dynamics of two-dimensional vortex patches | p. 160 |
| Vortex sheets of finite thickness | p. 160 |
| Contour dynamics and Schwarz functions | p. 163 |
| The Kirchhoff vortex and elliptical patches in uniform strain | p. 167 |
| Equilibrium configurations for single patches | p. 171 |
| Filamentation | p. 175 |
| Vortex pairs | p. 179 |
| Arrays of vortex patches | p. 183 |
| Axisymmetric vortex rings | p. 192 |
| Formulation | p. 192 |
| Thin cored rings | p. 195 |
| Lamb's transformation and general core structure | p. 201 |
| Canonical co-ordinates for thin rings | p. 206 |
| Dynamics of vortex filaments | p. 209 |
| Local induction approximation | p. 209 |
| The cut-off method | p. 212 |
| Kelvin waves on a filament | p. 215 |
| Justification of the cut-off and higher-order approximations | p. 218 |
| Three-dimensional vortex instability | p. 230 |
| Oscillations of a vortex column | p. 230 |
| Long-wave co-operative instabilities | p. 235 |
| Short-wave co-operative instability | p. 241 |
| Ultra short-wave co-operative instability | p. 250 |
| Effects of viscosity | p. 253 |
| Viscous cores | p. 253 |
| Decay of trailing vortices | p. 257 |
| Burgers vortices | p. 264 |
| Miscellaneous topics | p. 271 |
| Minimum induced drag | p. 271 |
| Kelvin's variational principle | p. 273 |
| Hamiltonian dynamics of vortex patch moments | p. 278 |
| Vortex breakdown | p. 285 |
| Epilogue | p. 295 |
| References | p. 296 |
| Index | p. 309 |
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