Fishline problem 637
Fixed point 117 119 121
Fixed-point method of Leray and Schauder 392 400 402
Flat plate, formation of cusped cavity behind it 338
Flat plate, infinite cavity formation behind it 328 330
Floating around an edge 85
Floating body 563seq.
Floating boundary 271 273
Floating of mixed type 226 256
Flow about submerged obstacles 571 573
Flow over an uneven bottom 569 571
Flow with circulation 71 83
Focusing equations 259 275
Force on a profile 130
Force on body entering into water 362
Force on obstacle 370
Forced standing waves in viscous fluids 643
Forces on a hydrofoil 586
Forces on a ship 567 580
Forces on a submerged body 573 574
Forces on a submerged cylinder 576
Formation of shock waves 253 265 268 279 280
Fourier analysis of initial surface profile 507
Fourier integral 507 523
Fourier series for surface waves 522seq.
Fourier transform 475
Fr chet differential 413
Frankl’s boundary value problem 137 139
Fredholm equation for surface waves 535 543
Free boundary 320
Free stream Mach number see Mach number.
Free streamline 63 320 322
Free streamline, analytic continuation across it 348
Free streamline, behavior at detachment 371 375
Free streamlines, asymptotic behavior 375-378
Free surface 320 446seq.
Free surface flow in the gravity field 350
Free surface with surface tension 352
Free surface, boundary conditions 454
Free surface, numerical methods 415 438
Freely floating body 563seq.
Freely floating body, diffraction of water waves 566 567
Freely floating body, initial displacement 619
Freely floating sphere 568
Fresnel integrals 545 613
Friedrichs’ shallow-water expansion see Shallow-water approximation
Froude number 581 675 676 695 699 701
Froude number for a cnoidal wave 2 713
Froude number for a solitary wave 713
Froude — Krylov hypothesis 566
Functional equations 395 400
Fundamental equation of potential flow 6
Fundamental equation of potential flow, linearization 26 29
Fundamental equation of potential flow, three-dimensional explicit solutions 8 11
Fundamental equation of potential plane flow 11
Fundamental equations for first-order shallow-water approximation 667 668
Garabedian’s iteration method 427 431
Gardner’s reduction method 304 305
Gas dynamics, connection with shallow-water theory 677 681
Gas dynamics, linearized 669
Gellerstedt’s differential equation 133 135
Generation of waves by oscillating bodies 553seq.
Geometrical boundary 459
Geometry of free boundary 378 380
Gerstner’s wave 742-744
Gerstner’s wave, uniqueness theorem 756
Glauert rule for airfoil theory 29 34
Gliding angle 48
Gliding on a water surface 343 344 587 592
Gravity effect upon a jet 326
Gravity field, free surface flow 350
Gravity wave 508 510
Gravity waves, velocity 513 514
Gravity-capillary wave 511 614 631 638
Gravity-capillary waves, velocity 514 614
Green’s function for surface waves 524 543 547 559 579 604seq. 614 616 621
Green’s function of second kind 291seq.
Green’s identity 40 41
Group velocity and energy propagation 519 520
Group velocity of surface waves 506 509 513 514 518
H lder continuity 99 104 400
H-function of Kochin 556 558 573 574
H-function of Kochin, time dependent motion 617
Hadamard’s finite part of an integral 42 303
Hadamard’s method 305
Hankel functions 296
Harmonic vibrations see also Oscillations
Harmonic vibrations in subsonic compressible flow 297 299
Harmonic vibrations in supersonic compressible flow 306
Havelock’s method for the investigation of wave crests 735-736
Heaslet — Lomax formula 304
Heat addition to subsonic flow 240 247
Heat conduction, effect on gas dynamics 264
Heat conduction, neglected 225 240 263
Heaving circular cylinder generating waves 563
Heaving hemisphere generating waves 562
Heaving motion of a floating body 562 619
Helmholtz — Kelvin circulation theorem 4
Helmholtz’s equation 284 291 298
Heterogeneous fluid 506
Heterogeneous fluids, theorems on wave motion 722 725
Hodograph differential equation 60 123 613 614
Hodograph method 27 56seq. 70 226 326seq. 345
Hodograph plane 59 123 683 684
Hodograph plane, logarithmic 71
Hodographic graphical construction 692
Homentropic motion 4 228 229 249 272
Hull shape, effect on wave resistance 580-581
Hydraulic analogy of shallow-water theory 668 673
Hydraulic friction 696-697
Hydraulic jump 685 689 692 696seq.
Hydraulic jump, oblique 700 701
Hydraulics 446
Hydraulics in open channels, steady one-dimensional case 695 701
Hydro dynamical derivative 2
Hydrofoil close to surface 586
Hydrofoil of finite span 586 590
Hydrofoil, thin body approximation 583 587
Hydrostatic approximation 468
Hyperbolic differential equation 16seq. 22 29 42 93 135 209 667 673 683
Hyperbolic differential equation, canonical form 691
Hypergeometric differential equation 63 69 150
Hypergeometric functions 240 612 672
Hypersonic flow 242
Ice sheet on water 455
Ideal fluid 448 450
Ideal gas, adiabatic flow 6 8 61 62 93
Ideal jet 271
Idealized fluid of Karman and Tsien 77 80 81 84 93
Idealized fluid of Tomotika and Tamada 77 145 147 150 172-173
Impact force 362
Impact of a body on a water surface 360 363
Incompressible flow 294
Induced mass of a fluid 362
Inequality for velocity fields 123
Infinite cavity 322 328 331
Infinite wake 321
Infinitely deep fluid 456
Infinitesimal uniqueness 410
Infinitesimal wave approximation 456 462 463 466 469seq.
Infinitesimal wave approximation for viscous fluids 638 646
Infinitesimal wave approximation, limits of application 522
Infinitesimal waves in irrotational flow 464
Infinitesimal waves, higher-order approximation 653 667
Inflection point on free boundary 379
Influence domain (or region) 19 40 233 256
Initial value problem for capillary-gravity waves 614 631 636
Initial value problem for the supersonic wing 43 45
Initial value problem of Cauchy 232 254-257 268
Initial value problem of Cauchy and Poisson 603 607 614 631
| Initial value problem of hyperbolic equations 16 20
Initial value problem of the wave equation 40 43
Initial value problem, method of images 610
Initial value problem, two-dimensional waves 610 614
Initial value problems for surface waves 603seq.
Initial-value method of Havelock 472 513 515
Integral equation method 271 299 306
Integral equation method for three-dimensional surface waves 545
Integral equation method for two-dimensional surface waves 533 535 537 543
Integral equation of Nekrasov 729 730
Integral equation of Trefftz 431 434
Integral equations of Villat 730 742
Integral operators of Bergman 67
Integro-differential equation 271
Interaction of pressure wave and shock wave 242 245 247
Interface, stress continuity 451
Interfaceof two immiscible fluids 451 455
Interfacial waves 502 506 634 635
Interfacial waves existence theorems 755
Interfacial waves, viscous fluids 644-646
Interior variations 405
Invariance of wave equation 286
Inverse method of boundary condition construction 736
Inverse methods 67
Inverse solution 350
Inviscid equations 225
Inviscid gas, entropy 240 242 272 283
Inviscid gas, steady flow in two dimensions 249seq
Inviscid gas, unsteady flow in one dimension 228seq.
Inviscid gas, unsteady flow in three dimensions 283seq. 297
Inviscid gas, unsteady incompressible flow in two dimensions 294
Ionized gas, shock propagation 220 221
Irrotational flow 4 449 462
Irrotational waves, existence theorems 749 755
Isentropic flow 3 164 174 197 686
Isothermal gas 62
Isovel 245
Iteration method of Garabedian 427-431
Iteration method of the discrete curvature equations 416 420
Jacobian elliptic functions 706seq.
Janzen — Rayleigh iteration 115 117
jet 64
Jet boundary 256 268
Jet flow 317 325 339 342
Jet of compressible fluid 311
Jet thrown out by a glider 588
Jet width 334
John’s inverse method 740 742
K rmn — Tsien fluid 77 80 81 84 93
Krmn’s method of singularity superposition 55
Kelvin — Helmholtz circulation theorem 4
Kinematic boundary condition 451 452 455
Kinematic viscosity 447
Kinematical theorems for free surface motion 715 716
Kirchhoff’s approach to beach waves 537 542 624 627
Kirchhoff’s Theorem 300 305
Kochin’s  -function 556 558 573 574
Kochin’s -function, time dependent motion 617
Kochin’s formulas for derivatives of Bessel functions 609
Kutta — joukowski condition 34 106 107 287 560 584 588
Kutta — Joukowski formula 34 130
Lagrangian description 447
Lam functions 297 299
Laplace equation 294 319 462 667
Laplace transform 483 491
Lattice-point method 691
Laval nozzle 8 695
Legendre polynomials 479 671
Legendre transformation for the velocity potential 56
Length parameters 259
Leray — Schauder fixed-point method 392 400-402
Levi — Civita’s differential-difference equation 726 727
Levi — Civita’s representation 369
Lift 34 36 47 130
Lift of a glider 592
Lift of a hydrofoil 586
Lighthill’s series development solution of hodograph equation 66 68 71
Limit Line 85 92 147 235 261 262 267 279 282
Limit point 243
Limit surface 9
Limit-type singularity 236
Limiting height of finite-amplitude waves 703 712seq.
Linearization for infinitesimal surface waves 463 469 554
Linearization of shallow-water approximation 668seq.
Linearization of the fundamental equation 26 29
Linearization parameter 463 466 526 554
Linearized Bernoulli equation 28
Linearized equations 285 286
Linearized gas dynamics 669
Linearized supersonic flow 38 40
Linearized supersonic flow, two-dimensional 45 49
Linearized theory of fluid dynamics, definition 28
Linearized theory of plane cavity flow 364 366
Linearized theory, role of characteristics 226 252 279 281
Liouville’s theorem 480 610
Liquid-gas interface, its stability 321
Loewner estimates 121 122
Logarithmic hodograph plane 71
Long wavelengths in canal 669
Lorentz transformation 286
Mach angle 39 179 250 692
Mach cone 38
Mach directions 88
Mach lines 16 20 22 45 61 130 138 229 241 245 250 273 275 687
Mach net of a flow 88 89
Mach number 6 7 167seq. 184 198 251
Mach number estimates 128
Mach number, critical 121
Mach quadrangle 232-233 255
Mass transport in free surface motion 716 718
Mass transport in second-order infinitesimal wave theory 661
Mass transport in viscous fluid 666
Massau semi-graphical procedure 20
Material derivative 451
Mathieu functions 298 652 653
Maximum amplitude waves 731 736 749
Maximum principle 380
Maximum-minimum principle for elliptic differential equations 94seq.
Membrane generating waves 558 559 616
Metacenter 565
Method of characteristics 254 255
Meyer’s type of transonic nozzle flow 147 148
Michell’s integral 580-581
Michell’s method for the investigation of wave crests 732-734
Milne — Thomson’s circle theorem 574
Minimal surface 81 93
Minimum cavity drag 386
Minimum of wave velocity for capillary-gravity waves 633
Minimum-maximum principle of free streamline 390
Mixed cavity problem 392 393
Mixed problem 226 256-257 270 272
Mixed type of differential equations 93 131
Modes of waves in a basin 623 627
Moment on a profile 128
Momentum integrals for free surface motion 718 721
Momentum of a surface wave 461
Monotonicity theorems 383 386
Movable basin, surface waves 627 631
Navier — Stokes equations 225 448
Negative cnoidal wave 714
Nekrasov — Yamada method for the investigation of wave crests 734 735
Nekrasov’s transformation and integral equation 728 730
Neumann’s boundary problem 12 622
Neumann’s function of a profil 116
Nose-shock of an airfoil 244 271 274
Nozzle design 685 693 695
Nozzle design for supersonic flow 264
Nozzle flow 147 149
Nozzle, simple waves in it 253
Numerical computation of free surface flow 415 438
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