 function 289 599 602 637
A priori bounds of existence theory 401 415
Accelerated flow with cavity of constant shape 358 360
Accelerated fluid, stability problems 648 651 653
Acceleration of fluid 236 238
Acceleration of the piston 246 247
Acceleration potential 284 298
Accolade (shape of obstacle) 374 379 408
Added masses in ship theory 567
Adiabatic flow of an ideal gas 6 8 61-62
Affine transformation 30
Air-water interface, parameters 645 650
Airfoil nose-shock 244 271 274
Airfoil of delta shape 52 54
Airfoil, supersonic flow 244 253 274
Airfoil, thin, in linearized subsonic flow 32 33 34
Airfoil, thin, in linearized supersonic flow 43 45
Airfoil, thin-wing integral equation 584 590
Airy functions 487 511 600
Analytic continuation across a free streamline 348
Analytic continuation of solutions 65 73
Aperture of a surface wave system 488 489
Archimedes’ law 565
Asymmetric channel flow 413
Asymptotic behavior of free streamlines 375 378
Asymptotic behavior of the velocity potential 98 101
Asymptotic expansion for late times 472 510 512
Asymptotic shape of axially symmetric cavity 377
Asymptotic width zero of cavity 332 376
Average position of wave crest 508 509
Axially symmetric cavity flow, approximation 366 368
Axially symmetric cavity flow, existence theory 394 405
Axially symmetric cavity, asymptotic shape 377
Axially symmetric free surface flow 353
Axially symmetric jet flow 434
Axially symmetric potential flow 11 13 14 22 24
Axially symmetric Riabouchinsky cavity 337
Axially symmetric supersonic flow 274
Banach space 119 121 400
Barrier in a long canal 527 529
Basin of circular planform, shallow-water approximation 672
Basin of rectangular form, shallow-water approximation 671
Basin with elastic restoring forces 628
Basin with sloping side-walls, waves 624 627
Basins of different shape 623
Basins, infinitesimal waves 620 631
Beach, waves on it 537 542 545 547 551
Bergman’s series development of hodograph equation 67 73 77
Bernoulli’s equation 5 6 56 93 164 165 179 449 454
Bernoulli’s equation in the gravity field 320
Bernoulli’s equation, linearization 28
Bernoulli’s law for non-steady flow 285
Betz inversion formula 36
Bi-characteristic, definition 25
Blockage effect in water tunnels 344
Body of revolution, submerged 577
Borda mouthpiece 340 342 431
Bottom covered with dipole sources 571
Bottom, irregular 569 571
Boundaries of basins, special selection 622
Boundary conditions at a beach 537 548
Boundary conditions at a free surface 320 454
Boundary conditions at a rigid surface 454 455
Boundary conditions at an interface 451 455
Boundary conditions at infinity 471 472
Boundary conditions for capillary-gravity waves 631 632
Boundary conditions on wing surface 288 291
Boundary point lemma of elliptic equations 381
Boundary value problem of Frankl 137 253 261 267 269
Boundary value problem on characteristics 233 255 257 268
Branch-type singularity 236
Branching into two jets 342
Breaking of wave crest 681
Breakwaters 544 545
Brillouin conditions of cavity flow 322 373
Brouwer’s fixed point theorem 121
Canal theory of tides 669
Canal waves of long wavelength 669
Canal waves of long wavelength, bounded canal 670 681
Canal, wave resistance of a ship in it 581
Canonical form of a hyperbolic equation 691
Capillary waves, existence theorem 757
Capillary-gravity waves 511 614 631 638
Capillary-gravity waves of large amplitudes 746 749
Capillary-gravity waves, generated by a point sources 636 637
Capillary-gravity waves, initial-value problem 614 631 636
Capillary-gravity waves, orbits in second-order infinitesimal wave approach 661
Capillary-gravity waves, velocity 514 614
Carriage containing water, periodic motion 628
Cauchy initial value problem 232 2 4 257 268
Cauchy principal value of an integral 476
Cauchy — Poisson initial value problem 603 607 614
Cauchy — Poisson initial value problem for superposed fluids 614
Cauchy — Poisson initial value problem with surface tension 614 631
Cauchy — Riemann equations 12 470
Cauchy’s integral 534
Cavitating hydrofoil 586- 587-
Cavitation 312
Cavitation experiments in water tunnel 312 315 344
Cavitation number or cavitation parameter 312 323
Cavity 312
Cavity dimensions 314
Cavity flow 312
Cavity flow, plane, linearization 364 366
Cavity of asymptotic width zero 332 376
Cavity of constant shape in accelerated flow 358 360
Cavity pressure 312 316
Cavity shape 323
Cavity, finite 324
Cavity, infinite 322 328 331
Ch zy formula of hydraulics 697
Chaplygin — Molenbroek transformation 58 61
Chaplygin’s correspondence principle 346
Chaplygin’s equation 60
Chaplygin’s equation, solution by separation 62 65
Chaplygin’s equation, solution depending on an arbitrary analytic function 65 67
Characteristic boundary value problem 233 255 257 268
Characteristic diagram of Prandtl and Busemann 90
Characteristic invariants 234
Characteristic strip 15
Characteristic variable 1 7 246
Characteristics 16 22 229 254
Characteristics in shallow-water theory 676 677seq.
Characteristics, their role in linearized theory 226 252 279 281
Chord of a supersonic profile 48
Circular cylinder, horizontal reflection of surface waves 528
Circular cylinder, submerged 574 577
Circular cylinder, vertical, diffraction of surface waves 544
Circular orbits in ocean waves 499 501
Circular orbits of first-order infinitesimal wave theory 499 501
Circular orbits, modifications by second-order infinitesimal wave theory 660 665
Circular wing 297
Circular-cylinder basin, shallow-water approximation 672
Circular-cylinder basin, vertical motion 651 653
Circular-cylinder basin, waves 623
Circulation 4 71 101
Circulation theorem of Helmholtz and Kelvin 4
Cisotti’s differential-difference equation 611
Cnoidal wave 462 654 667 702 707
Cnoidal wave, existence theorems 751-753
Cnoidal wave, limiting height 712
Cnoidal wave, second approximation to its profile 709
Comer, supersonic flow around it 20 22
Comparison theorems 3 80-383 407
Complex variables fox infinitesimal surface waves 470-471
Complex velocity 35 471
Complex velocity potential 470 480 489 505
Complex velocity potential for finite depth 482 490 494 495
Composite wave, second-order infinitesimal wave theory 662
Compressibility law 173
| Compressible fluid jet 311
Computation of axially symmetric flows 421 438
Computation of plane flow past obstacles 416 420
Cone, impact on a water surface 361 362
Confluence of two jets 342
Confluent hypergeometric functions 613
Conical flow, shock waves 88 192
Conical supersonic flow 22 24 49 52
Conservation laws in subsonic flow 121-122
Continuity equation 2 228 249 283 448 450
Continuity method in uniqueness theory 409 413
Contraction coefficient 317 318 340 342 383 423
Control contour 129
Convolution theorem 492
Coordinate choice for surface waves 447 456 466 475 485
Correspondence principle of Chaplygin 346
Critical depth for capillary-gravity waves 633
Critical free stream Mach number 121 125
Critical frequencies of canal waves 502
Critical speed 7
Critical velocity for long waves 669 676 713
Crocco’s equation 4 250
Curvature by thin fluid layer covering surface 646
Curvature equation 400 401
Curvature of a free streamline at detachment 372
Curvature of a stream line 259
Curvature of free streamline 322
Curvature of waves in viscous fluids 639 646 651
Curved boundary, method of continuity 413
Curved shock 274
Cusped cavity 338 397
Cylinder see circular cylinder
Cylinders of any cross section, submerged 576
Cylindrical coordinates for surface waves 485
Dam breaking 681
Damping coefficients in ship theory 567
Delta wing 52 54
Dependence domain 40
Depth of water see also Finite depth
Depth of water, determination 673
Detachment of a free streamline 322 323 371 375
Differential equations of elliptic type 16 29 93 94 99 209 667 683
Differential equations of elliptic-hyperbolic type 93 101 135
Differential equations of hyperbolic type 16seq. 22 29 42 93 135 209 667 673 683 691
Differential equations of mixed type 93 101
Differential equations of the velocity potential 6
Differential equations of the velocity potential, its three-dimensional explicit solutions 8 11
Differential equations of the velocity potential, plane flow 11
Differential equations of Tricomi 81 431 133 150
Differential inequality for velocity fields 123
Differential-difference equation of Cisotti 611
Differential-difference equation of Levi — Civita 726-727-
Diffraction of water waves by a freely floating body 566 567
Diffraction of water waves by a horizontal cylinder 545
Diffraction of water waves by a vertical cylinder 544
Diffraction of water waves by a vertical half-plane 544 560
Diffraction of water waves, general obstruction 543
Dimensional analysis in initial value problems 610 611
Dimensional perturbation 421
Dipole approximating bow and stern of a ship 582
Dipole singularity 484 487 489 577
Dipole source covering bottom 571
Dirichlet integral 97
Dirichlet’s boundary problem 12 108
Discharge coefficient 317-318
Discharge rate 569
Discontinuities on characteristics 15 16 22
Discrete curvature equations 416 420
Dispersion law of capillary-gravity waves 614 633
Dispersion relations of surface waves 502 507 513 515 518 550
Dissipation of waves in viscous fluids 639
Dock problem 527 536 537 545
Domain of dependence 40
Domain of influence 19 40 233 256
Dominating function 74
Drag 34 48
Drag coefficient of the disk, computation 425 427
Drag coefficient, dependence on cavitation parameter 313
Drag in infinite cavity flow 329 331 376
Drag measurements, cavitation influence 312
Drag minimum from cavity formation 386
Drag of a flate plate 329 330 333
Drag of a hydrofoil 586
Drag of Riabouchinsky cavity 336 389
Droplet formation from a jet 326
d’Alembert solution of the wave equation 16 669
D’Alembert’s paradox 31
Edge wave of Stokes type 550
Edge wave of Ursell type 551
Efflux of a plane jet 341 (see also Discharge)
Eigenvalues of basin waves 623 627 630 652
Eigenvalues of modes in a bounded canal 670 671
Elastic medium and fluid, interface 455
Elastic restoring forces of a movable basin 628
Ellipsoid, submerged 577
Elliptic differential equation 16 29 93 94 99 209 667 683
Elliptic functions of Jacobi 706seq.
Elliptical orbits of first-order infinitesimal wave theory 500 501
Elliptical orbits, modifications by second-order infinitesimal wave theory 661
Energy flux in surface wave 519
Energy integral 135
Energy integral for free surface motion 718 721
Energy of surface waves 458 460
Energy propagation in surface waves 515 522
Energy propagation in surface waves, second-order infinitesimal wave theory 661
Enthalpy 3 250
Enthalpy of adiabatic ideal gas flow 6
entropy 3 167 193
Entropy of an in viscid gas 240 242 272 283
Entropy variation in gas flow 240 249 272 274
Envelope of characteristics see limit line
Epicycloids as principal curves 89
Epicycloids in hodograph plane 686 692 694 701
Equation of continuity 2 228 249 283 448 450
Equation of state 229 240 249 251 273 283 449
Equation of variations 414
Equations of motion 228 249 283 448 450
Escape velocity (into vacuum) 6
Estimates in subsonic flow 125 128
Eulerian derivative 2
Eulerian description 447
Evvard type equation 305 306
Exact solutions in surface wave theory 714 757
Existence of jet flow 392
Existence of solutions approached by infinitesimal waves 654
Existence proof for the cnoidal wave 462 668
Existence proof for the initial value problem 19
Existence proof for the solitary wave 462 668
Existence theorem for capillary waves 757
Existence theorems for subsonic flow 108 111 115 119
Existence theorems for surface waves 749 757
Existence theorems for transonic flow 138 145
Existence theory in free boundary flow 39 406
Expansion parameter of shallow-water theory 462 667 704
Experimental investigation of capillary dispersion 633 634
Explosion 211
Explosion under water 619
Fifth-order infinitesimal wave approach for progressive waves 663 665
Finite cavity 324
Finite cavity for the disk 427
Finite depth for progressive ocean waves 499
Finite depth for standing ocean waves 496 498
Finite depth, complex velocity potential 482 490 494 495
Finite depth, effect on wave profile 659 660
Finite difference approximation 43 5
Finite part of a divergent integral (Hadamard definition) 42 303
Finite-amplitude waves see also Solitary and Cnoidal waves
Finite-amplitude waves, limiting height 703 712
Finn — Gilbarg extension of the maximum-minimum principle 95 97 107
First-order shallow water approximation 467 469
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