Oblique entry of a body into water 363
Obstructions in long canal 526seq.
Obstructions originating diffraction of surface waves 543 545
Ocean floor, waves from its sudden motion 617 619
Oceanography 446
Open-channel flow 466
Orbits see circular orbits elliptical particle trajectories
Orthogonality of elementary solutions 522 523
Oscillating basins, resonance waves 627 629
Oscillating basins, stability 651 653
Oscillating boundaries, wave formation 553-563
Oscillating submerged body generating waves 554 563
Oscillations of a freely floating body, oncoming waves 566 567
Oscillations of a freely floating body, steady case 563seq.
Oscillator in a wall generating waves 558 559 616
Oscillator without wall generating waves 560 562
Oscillatory motion 297 306 309
Parameter of linearization 463 466 526 554
Particle orbits in surface waves 496 497 499 501 660 661 665
Particle orbits, second-order infinitesimal wave approximation 660 661
Pendulum bob, containing fluid 631
Periodic wave of maximum height 732
Periodic waves in a basin 621 622
Permanent finite-amplitude wave forms 702 703
Perturbation method 27
Perturbation method for surface waves 462
Perturbation of pressure 28
Phase shift between pressure and displacement in viscous fluids 643
Phase velocity of an edge wave 550
Phase velocity of progressive ocean waves 499
Phase velocity of waves at an interface 503
Phase velocity of waves in a canal 502
Physical boundary 459
Piston acceleration 246 247
Piston generating a wave 230 236 243 245
Piston generating shock wave 196
Plane cavity flow theory, linearized 364 366
Plane jet 341
Plane potential flow 11 12
Planing on a water surface 343 344 587 592
Plemelj — Sokhotskii theorem 535 583 613
Poisson’s relation between pressure and density 6 61 93 284
Polar coordinates for surface waves 475 476
Polygonal boundary of a jet 409
Polytropic relation 345
Port basin waves 623
Possio’s equation 302
potential flow 448 450
Prandtl angle 250
Prandtl relation for shock waves 698
Prandtl — Busemann graphical procedure 90 91
Prandtl — Meyer expansion 20 254 263 693
Prandtl — Meyer function 688 690
Prandtl’s correspondence rules 29 31
Pressure at a free surface 454 460 472
Pressure at an interface 453
Pressure distribution along a glider 592
Pressure distribution, any dependence on time 614 615
Pressure distribution, moving with constant velocity 597 602 637
Pressure distribution, second-order infinitesimal wave theory 665 254 619
Pressure estimates 125 128
Pressure gradient 236 242 259 263 268 279 281 282
Pressure periodic in time, generating waves, three-dimensional case 593 595
Pressure periodic in time, generating waves, two-dimensional case 595 597
Pressure perturbation 28
Pressure point ( function) 599 602 637
Pressure-displacement phase shift in viscous fluids 643
Principal curves in the hodograph 89
Principal net of a flow (Mach net) 89
Principal value of an integral 476
Principle of linear superposition 55 57 63
Principle of minimum virtual mass 387 403
Problem of fixed detachment 323 373
Problem of smooth detachment 323 372 373 408
Progressive surface wave 456
Progressive wave, second-order infinitesimal wave approach 654 662
Progressive wave, third-order infinitesimal wave approach 657 658
Progressive waves in a canal 502
Progressive waves in an infinite ocean 498 501
Propagation of an initial elevation on a free surface 507-513
Propagation of energy in surface waves 515 522
Propagation of energy in surface waves, second-order infinitesimal wave theory 661
Propagation velocity of a solitary wave 710 711
Prow problem 323 373 392
Pseudo analytic function 04
Pseudo-exact solutions of Davies and Packham 736 744 746
Pulsating source in three dimensions 475
Pulsating source in two dimensions 479
Pulsating vortex in two dimensions 479 483
Quasi-linear partial differential equation 14
Radial flow 9 58
Radially symmetric potential flow 9 10
Radiation condition 298 471 475 493 595 616
Rayleigh’s higher-order infinitesimal wave approximations 663
Re-entrant jet 314-315 323 397
Re-entrant jet cavity 324 332 335
Reciprocity relations 307
Rectangular basin, waves 623
Rectangular canal, infinitesimal wave approximation 502
Rectangular canal, shallow-water approximation 670 671 696
Reduction method 525 545 546
Reflection coefficient of surface wave at obstruction in canal 527 528
Reflection from horizontal circular cylinder 528
Reflection method of Shiffman 347 349
Reflection of shock waves 182 204 211
Reflection of simple waves 693-694
Reflection of wave fronts 276
Region of influence 19 40 233 256
Relaxation method of approximation 255 434 436
Resonance waves for oscillating basins 627 629
Reynolds’ number 316
Riabouchinsky cavity 323 324 335 337 398 403
Riabouchinsky cavity, general case of axial symmetry 337
Riabouchinsky flow past a circular disk 427
Riccati equation 174 204
Riemann domains 65
Riemann function 239 240 269 272 277 354
Riemann invariant 677 679 687seq.
Rigid surface, boundary conditions 454 455
Ring vortex distribution 366
Ring-shaped basin, shallow-water approximation 672
Ring-shaped basin, waves 624
Ripples (capillary waves) 633
Rolling of a ship 555
Rotational waves, existence theorems 755 756
Rudzki’s inverse method 73 738
Rudzki’s transformation 727
Sauxreaux’ inverse method 736 737 742
Schlieren method 38
Schwarz — Christoffel transformation 326
Second order infinitesimal wave approach for progressive waves 654 662
Second-order shallow-water approximation 468 469
Sector-shaped basin, waves 624
Self-similar unsteady flow 360
Semi-infinite channel 559
Semi-inverse solution 350
Separation of variables for infinitesimal surface waves 472 475
Separation of variables in Chaplygin’s equation 62 65
Shallow-water approximation 456 462 466 469 667seq.
Shallow-water approximation, first-order fundamental equations 667 668
Shallow-water approximation, non-linear theory 676 701
Shallow-water approximations of higher order 701seq.
Shallow-water results, connection with infinitesimal wave approximation 673
Shallow-water second-order approximation 668 703 704
Shallow-water third order approximation 703 705 707
Shear flow 273 274
Shiffman’s theorem for subsonic flow 108 111
Ship floating on water 563seq.
Ship heading into waves 567
Ship rolling 555
| Ship waves 446
Ship, dipole approximation 582
Ship, forces on its body 567 580
Ship, forces on its body, transient problems 616-617
Shock equations 166 168 169
Shock expansion 245 247 274
Shock formation 253 265-268 279 280
Shock polar 701
Shock propagation in ionized gases 220 221
Shock wave 130 162 227 242
Shock wave detachment 174seq. 177
Shock wave in plane flow, seq 180 187
Shock wave in three-dimensional flow 188 195
Shock wave subsonic case 171
Shock wave, connection with shallow-water theory 681 693 693
Shock wave, formation 171seq. 203
Shock wave, reflection 182 204 211
Shock wave, spherical 211
Shock wave, supersonic case 171
Short-crested wave 545 547 549
Sigma-monogenic functions of Bers — Gelbart 67
Sign of cavitation number 323
Similarity principle of Bers 104
Simple backward-facing wave 679 680
Simple compression wave 689 694
Simple expansion wave 689 694
Simple forward-facing wave 679
Simple-wave 227 230 231 236 243 247 252 254 263 678
Simple-wave in shock waves 196-198
Simple-wave, Definition 22
Single intersection theorem 379
Singular line 261 267
Singular solutions in infinitesimal surface wave theory 475 478 479
Singular solutions including surface tension 635 638
Singularities in second-order infinitesimal wave approach 656 657
Singularities of constant strength in uniform motion 489
Singularities of higher order 481 484 495
Slender body 28 573 577 578 579
Slender body of revolution 54 56
Slender profile in shallow water 675
Solitary wave 462 654 667 702
Solitary wave, existence theorems 7 51-753
Solitary wave, limiting height 712
Solitary wave, propagation velocity 710 711
Solitary wave, second approximation to its profile 710 711
Sommerfeld’s radiation condition 298
Sound, velocity of, see Speed of sound.
Source distribution replacing ship’s hull 581
Source function see Green’s function
Source of constant strength in uniform motion 483
Source of position and strength varying with time 490 495
Source of pulsating strength in three dimensions 475
Source of pulsating strength in two dimensions 479
Source strength 101
Source type solutions including surface tension 635 638
Source-sink representation of cavity flow 314 430
Specific heat ratio 2 677 681
Spectrum 507
Speed of sound, local 5 7 209 228 231 235 250 285
Sphere floating freely 568
Sphere heaving on water surface 562
Sphere submerged 577
Spheroid, submerged 577 573
Spread of hump on a free surface 508
St. Venant — Wantzel formula 7
Stability of liquid-gas interface 321
Stability of motion, interface between moving fluids 648 650
Stability of motion, interface of stationary system 646-648
Stability of motion, interfacial waves 634 635
Stability of motion, moving basin 630-631
Stability of motion, second-order infinitesimal wave theory, r 663
Stability of motion, surface tension effects 647
Stability of motion, vertical oscillation of a basin 651 653
Stability of motion, viscosity effects 647 648
Stagnation point 107
Standing capillary-gravity waves 632 634
Standing surface wave 458
Standing waves in a canal 502
Standing waves in an infinite ocean 495 498
Standing waves in basins 622 627
Standing waves in viscous fluids 641 646
Steady state as asymptotic limit state 472 506seq.
Steady supercritical flow, shallow-water first- order approximation 682 695
Stokes’ edge waves 550
Stokes’ second method 654 726
Stokes’ theorem on wave crests 731
Stratified viscous fluids, interfacial waves 644 646
Stream direction 250
Stream function 12 319
Stream tube 8
Streamline curvature 259 322
Streamline of discontinuity 312 321
Streamline, free 63 320 322 3 75 3 78
Streamlines for standing ocean waves 496
Streamlines, Busemann image 24
Stress continuity at an interface 451
Stress tensor 452
Strip condition 14
Strong discontinuities in conical flow 23
Strongly elliptic mapping 124
Struve function 533
Sturm — Liouville problem 523
Subcritical flow in an open channel 673 675 676
Submarine explosion 617 619
Submarine, wave resistance 577
Submerged moving dipole 487 489
Subsonic compressible flow, harmonic vibrations 297 299
Subsonic compressible flow, solution by Green’s function 291seq.
Subsonic flow, definition 7
Subsonic infinite cavity flow, existence theory 394
Successive approximation of solution 19
Supercritical flow in an open channel 673 675 676 696
Supercritical steady flow, shallow-water first-order approximation 682 695
Superposition of singularities on the axis 55
Superposition principle 55 57 63
Supersonic compressible flow, harmonic vibrations 306
Supersonic conical flow 22 24 49 52
Supersonic flow around a corner 20 22
Supersonic flow past an airfoil 244 253 274
Supersonic flow, definition 7
Supersonic flow, linearized approximation 38 40
Supersonic flow, steady and axially symmetrical 274
Supersonic flow, tables 23
Supersonic linearized two-dimensional flow 45 49
Supersonic pockets in the flow around an edge 86
Supersonic profile 48
Surface impact 360 363
Surface normal 451
Surface tension 352 451 452 460 614 631 638
Surface tension in viscous fluids 633 641seq. 646
Surface tension, effect on cnoidal waves 714
Surface tension, effect on second-order infinitesimal wave approach 656seq.
Surface tension, effect on stability 647
Surface waves, dispersion relations 502 507 513-515 513 550
Surface waves, initial value problem 603seq
Surface, free 320
Symmetrization 404
System of fluids 506
System of two fluids see Interface
Taylor type of transonic nozzle flow 147 148 151
Taylor — Maccoll flow pattern 23
Thin airfoil in linearized subsonic flow 32 33 34
Thin body 28 46
Thin floating body, heaving motion 620
Thin hydrofoil 533-537
Thin ship approximation 572 579 583
Thin ship, transient problems 616 617
Thin supersonic wing 43 45
Thin wing approximation 32-34 43 45 572 584 590
Third-order infinitesimal wave approach, for progressive waves 657 658
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