Three-dimensional flow 24 26
Three-dimensional surface waves higher-order infinitesimal wave theory 662
Three-dimensional surface waves in a canal 551-553
Three-dimensional surface waves on the beach 545 547 551
Three-dimensional surface waves, diffraction 543 547
Tidal waves 466 668 669
Toepler’s schlieren method 38
Tomotika — Tamada fluid 77 145 147 150 152 172 173
Trailing edge of a profile 106
Trajectories of particles in surface waves 496-497 499 501 660 661 665
Transformations of Nekrasov and Rudzki 728 729
Translation 286
Transmission coefficient for surface wave, passing obstruction in canal 527 528
Transonic flow through a nozzle 147 149
Transonic flow, definition 130
Transonic flow, discovery of branch lines 87
Transonic region, extension of a solution into it 73
Transverse wave system 488
Trapping modes 551
Trefftz’ integral equation 431 434
Tricomi equation 81 131 133 150
Tricomi’s boundary value problem 137
Tsunami 617 619
Turbulence of viscous fluid surface waves 639
Two-dimensional compressible steady flow 249
Two-dimensional incompressible non-steady flow 294
Two-dimensional linearized supersonic flow 45 49
Two-dimensional steady flow, shallow-water first-order approximation 682 695
Two-dimensional surface waves on the beach 537 542
Two-dimensional surface waves, dock problem 527 536 537
Two-dimensional surface waves, integral equation methods 533 535 537
Two-dimensional surface waves, obstruction 526seq.
Two-dimensional surface waves, reflection coefficient 527 528
Two-dimensional surface waves, transmission coefficient 527 528
Underpressure wake 343
Uneven bottom 569 571
Uniform first-order approximation 251 280 282
Uniformly elliptic equation 118
Uniformly subsonic flow 98 104
Uniqueness of solution 14 40 102 104 106 113 131 132
Uniqueness theorems 227 231 234 255 266 275
Uniqueness theory for mixed differential equations 131 135seq.
Uniqueness theory in free boundary flow 406 415
Uniqueness theory of an inviscid gas 228seq. 283seq.
Uniqueness theory, shallow-water first-order approximation 677
Unstable see Stability of motion
Unsteady flow with free boundary 356
Unsteady two-dimensional incompressible flow 294
Ursell edge wave 551
Variation of constants 65
Variational equation 27 28
Variational methods in existence theory 394 403
Variational principles for free surface flow 387 391
Variational problem for two-dimensional subsonic flow with circulation 114 115
Variational problem for two-dimensional subsonic flow without circulation 92 107 111
Velocity ellipse in the hodograph plane 692
Velocity gradient 259
Velocity minimum of capillary-gravity waves 633
Velocity of a wave see Phase velocity and group velocity
Velocity of gravity waves 513-514
Velocity of gravity-capillary waves 514 614
Velocity of sound see Speed of sound.
Velocity plane see Hodograph method
Velocity plane, image of streamlines 24
Velocity potential 5 172 319 449 470
Velocity potential, asymptotic behavior 98 101 104
| Velocity potential, differential equation 6
Velocity potential, differential equation, three-dimensional explicit solutions 8 11
Velocity potential, Legendre transformation 56
Velocity potential, series expansion at infinity 104 106
Vena contracta 423 425 431 434
Vertical barrier in a canal 529
Vertical cylinder cutting water surface, diffraction 544
Vertical entry of a cone into water 361 362
Villlat’s integral equations 730 742
Virtual mass 362 387 403
viscosity 447
Viscosity, effect on gas dynamics 264 265 287
Viscosity, effect on stability 647-648
Viscosity, fictitious 479
Viscosity, neglected 225 263 448 462
Viscosity, neglected for cavitation 319
Viscous fluid, boundary conditions 451
Viscous fluid, surface waves in linear approximation 638 646
Viscous fluid, surface waves in second-order infinitesimal wave approximation 666
Viscous resistance, separation from wave resistance 581
Vortex flow in two dimensions 10
Vortex line 284
Vortex of pulsating strength in two dimensions 479 483
Vortex sheet 366
Vortex varying with time 495
Vorticity 3 4 284
Vorticity effect on shock formation 265
Vorticity of Gerstner’s waves 743
Wake 316
Wake in real fluid 311
Wake parameter 116 343
Wake pressure 316
Wake, infinite 321 325
Wall corrections in the windtunnel 297
Wall effects in water tunnel cavitation experiments 344
Water entry 312 360seq.
Water tunnel experiments on cavitation 312 314 344
Water waves, diffraction 543 545 560 566-567
Water-air interface, parameters 645 650
Wave crest 487 494
Wave crest form, Stokes’ theorem 731
Wave crest, average position 508-509
Wave crest, breaking 681
Wave equation 16 285
Wave front 234 23 5 243 260 262 267 272 276 278 281
Wave generation by oscillating bodies 553seq.
Wave generation by varying pressure distribution 592 603
Wave length of surface wave 487
Wave packet 509 518
Wave resistance 576seq.
Wave resistance of a ship 580 581
Wave velocity, definition 457
Wave-profile, second-order infinitesimal wave approximation 656 659
Wave-profile, third-order infinitesimal wave approximation 658 660
Waves at an interface of two fluids 502 506 634
Waves from a submerged oscillating body 554 563
Waves of infinitesimal amplitude see Infinitesimal waves
Waves on the beach 537 542 545 547 551
Weak discontinuities on characteristics 22
Wedge shaped surface wave system 488
Wedge, cavity formation behind it 330 331
Wedge, impact on a water surface 360 362
Wienef — Hopf integral equation 537 545
Wind generating water waves 650
Wind-tunnel wall corrections 297
Wing see Airfoil and Thin wing
Wing surface, boundary condition 288 291
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