J.J. Stoker - Water waves. The mathematical theory with applications (796980), страница 101
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U.S.National Bureau of Standards, Gravity waves, N.B.S. Circular 521,1952, pp. 1-5.Trapping modes in the theory of surface leaves. Proceedings of the Cambridge Philosophical Society, Vol. 47, 1951.On the rolling motion of cylinders on the surface of a fluid. QuarterlyJournal of Mechanics and Applied Mathematics, Vol.
2, 1949.[U.10J On the heaving motion of a circular cylinder on the surface of a fluid.Quarterly Journal of Mechanics and Applied Mathematics, Vol. 2, 1949.[U.11J The long-wave paradox in the theory of gravity leaves. Proceedings of the[U.9]Cambridge Philosophical Society, Vol.[U.12J[U.13J49, 1953.See [B.4J.See [L.14].Unaki, G., and M. Nakano[U.14] On the Cauchy-Poisson waves caused by the eruption of a submarinevolcano, (I) and (II).
Oceanograph. Mag. 4,5; 1953.Vedernikov, V. V.[V. 1 ]Conditions at the front of a translation wave disturbing a steady motion of aDoklady (Comptes rendus) Akademiya Nauk SSSR, Vol. 48,1945.real fluid.WATER WAVES560[V.2]Characteristic features of a liquid flow in an open channel.(Comptes rendus), Vol. 52, 1946, pp. 207-210.DokladyVergne, Henri[V.3]Ondes liquides deHermanngravite*.ActualitesScientifiques etIndustrielles,et Cie., Paris, 1928.de Vries, G.See [K.15].[V.4]Wallet, A.See [R.12]Watson, G. N.[W.I]A Treatise on the Theory of Bessel Functions.
The UniversityPress,Cam-bridge, 1944.Wilkes, M. V.[W.2] Oscillations of the Earth's Atmosphere.1949.Weinblum, G. P.[W.3]Analysis of wave resistance. DavidD.C.),W.The University Press, Cambridge,Taylor Model Basin (Washington,Report 710, 1950.[W.4] See [S.I].Weinstein, A.[W.5] On surface waves.
Canadian Journal of Mathematics, Vol. 1, 1949,pp. 271-278.[W.6] Sur la vitesse de propagation de Vonde solitaire. Reale Acadcmia dciLincei, Rendiconti, Classe di scienze fisiche, matematiche, naturali,Ser. 6, Vol. 3, 1926, pp. 463.[W.7J Sur un probleme aux limites dans une bande inde'finie. Institut de France.Comptes Rendus de 1' Academic des Sciences.
Vol. 184, 1927, p. 497.Weitz, M., and J. B. Keller[W.8] Reflection of water waves from floating ice in water of finite depth. Com-munications on Pure and Applied Mathematics. Vol.305-318.3,1950, pp.Also see [K.9]Weliczker, L.[W.9] See [F.5].Wells, Leon W. (formerly L. Weliczker)[W.10] Some remarks on shallow water theory. New York University, Instituteof Mathematical Sciences, Report No. IMM-198, 1953.Westergaard, H. M.fW.ll] Water pressure on dams during earthquakes. Transactions of AmericanSociety of Civil Engineers, Vol. 93, 1933.Whitham, G. B.[W.12] Dynamicsof meteorological fronts.New YorkUniversity, Institute ofMathematical Sciences, Report No.
IMM-195, 1953.Wigley, W. C. S.[W.13] See [L.18].Author IndexAbdullah, A. J., 373, 388Arthur, R. S., 132, 133Freeman,408J. C., Jr. 375, 377, 384, 388,K. O., 27, 32, 73, 74, 75, 76,108, 293, 300, 343, 344, 345, 849, 371,Friedriclis,Baird, E. G., 412Bakhmeteff, B. A., 451Bateman, II., 117Bates, C. C., 138Biesel, F., 364, 305Birkhoff, G., 342Bjerknes, J., 376Boridi, H., 72Bouasse, H., 423Boussinesq, J., 342, 351, 451Broer, L. J. F., 53J. R.,Bruman,407, 470, 529Gerber, R., 522Gilcrest, B.
R., 451, 462, 482Goldstein, E., 447T., 359, 372Hanson, E. T., 72, 89Harleman, D. R. F., 412Haskind, M. D., 248, 259Haurwitz, B., 376Hamada,412Carr, J. H., 132, 445, 448Carson, R. L., XIVCauchy, A. L., 35, 154Charney, J. G., 375Chrystul, G., 424Cooper, R. I. B., 138Copson, E. T., 117, 181Cornish, V., 466Courant, R., 293, 300, 407, 470, 476, 477Crossley, H. E., 412Daily, J.
\V., 351Danel,P.,138Darby shire, J., 137Davies, T. V., 374, 522Deacon, G. E. R., 137, 171Deymie, P., 505Dressier, R. F., 466, 467, 468Dubreuil-Jaeotin, M. I,., 522Eekart,C., 73,Einstein,II.136A., 412Finkelstein, A., 153, 187Fjeldstad, J. E., 147Fleishman, B., 438Fleming, R. H., 133Forchheimer, P., 451Forel, F. A., 423Haveloek, T. II., 219, 242, 246, 248,253, 256Heins, A. E., 74, 108, 141Hinze, J. O., 160Hogner, E., 220, 242Hopf, E., 44Hyers, D. H., 32, 343, 345, 349, 371, 529Isaacs, J.
D., 133Isaaeson, E., 73, 74, 451, 476,Iversen,477H. W., 359Jeffreys, II., 352, 422John, F., 76, 113, 146, 175, 206, 249,431Johnson, J. W., 133Johnson, M. \V., 133Kampdde Feriet,von Kdrman,J.,T., 410,187482Karp, S. N., 117, 141Keldysh, M. V., 203Keller, J. B., 32, 141, 146, 343, 351, 371,447, 476, 481Kelvin, W. T., 163, 219Keulegan, G. H., 370Korteweg, D.
J., 342, 343Korvin-Krukovsky, B. V., 260Kotik, J., 153, 187Kotsehin, N. J., 61561WATEE WAVES562Kreisel, G., 146Re, R., 818Krylov, A. N., 248Rees, M., 476, 477Rellich, F., 113, 175Riabouchinsky, D., 25Laitone, E. V., 412, 418Lamb, H., 28, 27, 57, 58, 180, 421Lavrentieff, M., 344Lax, A., 368Lax, P., 476, 481Leray, J., 522Levi-Civita, T., 17, 21, 343, 345, 346, 347,374, 513, 522, 524Lewis, E. V., 260Lewy, H., 61, 72, 73, 74, 76, 79, 108, 537Lichtenstein, L., 515, 522, 529Littman, W., 522Longuet-Higgins, M. S., 137, 138Lowell, S. C., 136Lunde, J.
K., 246, 248, 257Macdonald, H. M., 117McNown, J. S., 426, 428Massau, J., 482Mason, M. A., 372Miche, A., 72, 137Michell, J. H., 248, 253, 256, 263, 285Munk, W. H., 69, 133, 352, 357, 369,870, 371Nekrassov, A. I., 522Nirenberg, L., 344, 522O'Brien, M. P., 133Roseau, M., 74, 75, 76, 78, 95, 146Rouse, H., 451, 462, 468, 482Rubin, H., 146Ruellan, F.. 41Russell, S., 342St.
Denis, M., 248, 261Schwinger, J. S., 117, 146H. R., 138Solberg, H., 376Sommerfeld, A., 52, 77, 116, 117Southwell, R., 426Sretenski, L. N., 234Stelzriede, M. E., 132Stoker, J. J., Ill, 451, 482Stokes, G. G., 96, 373Struik, D. J., 17, 21, 342, 343, 344, 347,Seiwell,522Suquet, F., 133Sverdrup, II. U., 133, 357, 369, 371Tepper, M., 375Thomas, II. A., 451, 462, 467, 468, 482Thompson, P. D., 375Thorade, H.
F., 368Thornhill, C. K., 513, 522Traylor, M. A., 133Troesch, B. A., 451, 487, 505Patterson, G. W., 370Penney, W. G., 513, 522Ursell, F., 96, 137, 146, 342,Peters, A. S., 74, 75, 76, 78, 95, 96, 98,102, 103, 111, 124, 224, 242, 245Pierson, W. J., Jr., 133, 138, 248Pohle, F. V., 513, 515de Vries, G., 342, 343Poincare, H., 181Poisson, S., 35, 154Preiswerk, E., 407, 411, 413, 482Putnam,J. A.,132W. J. M., 76Rayleigh, J. W., 49, 321, 342, 351Rankine,372Wallet, A., 41Weinblum, G.
P., 248, 261Weinstein, A., 40, 87, 208, ,342Weitz, M., 141Wells, L. W., 434, 444, 449Whitham, G. B., 368, 377, 378, 388,389, 395, 399, 404, 487, 505Wigley, W. C. S., 246, 257Wilkes, M. V., 147, 375Subject IndexAerodynamics, 411Characteristic^ ), curves, 294differential equations, 294Angle of trim, 286Archimedes' law, 254, 277envelope, 307, 314, 355intersection, 355Atmosphere, gravity waves, 374tidal oscillations, 374method, 293, 469waves on discontinuity surfaces, 375propagation of discontinuities along,473formula, 466ChezyBackwater curves, 4567Backwater effects in long rivers, 461 Circulation,Cliff, waves against a vertical, 84Beaches. (See also Sloping beaches.)Cnoidal waves, 342waves breaking on shallow, 352Cold front, 380Bernoulli's law, 9Comparison of predicted and observed43Bernstein, S., theorem,floods, 498Bifurcation conditions, 5293Compressibility,Bifurcation phenomenon, 343Contact discontinuity, 318board, as fixed breakwater, 432Continuity equation, 453as floating breakwater, 436Convolution theorem, 143Bore 307, 315, 326, 368Coriolis acceleration, 383351developmentforce, 381368Tsien-Tang River, 320,Crests, breaking of waves at, 36919Boundaryconditions, 10,dynamical, 55fixed boundary surface, 11free surface, 11kinematic, 16, 56small amplitude theory, 19tidal theory, 422Breaking of a dam, 313, 333, 513discharge rate, 338resulting bore, 334Breaking of waves, 69, 307, 315at crests, 369in shallow water, 351induced by wind action, 372on shallow beaches, 352Breakwaters, 429dispersion induced, 443fixed board, 432floating board, 436floating elastic beam, 438reflection of energy, 446Criticalspeed, inappropriatenesslinear theory at, 217, 344instability of steady flow with,Cyclone, 376, 399of344breaking, 313, 333, 513discharge rate on breaking, 338shock resulting from breaking, 334Diffraction around a vertical wedge, 109problem of Sommerfeld, 109theory, physical verification of, 132Dipoles, 13Discontinuities, propagated along char-Dam,acteristics,473Cauchy-Riemann equations, 345Discontinuity conditions, 314surfaces in the atmosphere, 375Dispersion, 51Divergence theorem, 6Diverging system of waves, 237Dock problem, 74two-dimensional, 108Domain of dependence, 298of determinancy, 299Cavitation, 310Dynamic boundary563condition, 16, 55WATER WAVES564Eigenvalue problems, 424Elastic beam, used as floating breakwater, 438Energy, 13average, 50balance across a shock, 318flux, 13rate of change, 13reflected by a breakwater, 446transmission by progressing waves, 15transmission by simple harmonicwaves, 47velocity of the flow of, 49exact, 11, 513linearized, 11, 12, 35Free surface elevation, 16Friction, 451Friction slope, 455Front, 378cold, 374, 380occluded, 381stationary, 378warm, 374, 380Front of shock, 320Gas dynamics analogy, 25Geometrical optics, 133Gravity waves in the atmosphere, 374Green's function, 280methodsinfloodwaveEngineeringtime-dependent, 187problems, 485Group of waves, 51Equation of continuity, 7, 453170Equations of flow in open channels, 452 Group velocity, 51,Equations of motion, 4Harbors, design of, 420Eulerian form, 6model studies, 4294Lagrangian form,oscillations, 414Equations of shallow water theory,Heave, 250, 255nonlinear, 24278Heaving,validity beyond the breaking point, HelmhoUVstheorem, 7362Higher-order approximations in shallowEuler variables, 5water theory, 28, 32Exact free surface condition, 513Hump, 35271wavetanks,Experimental,Hydraulic analogy, 412solitary wave, 351Hydraulic jumps, 307, 324, 407.
(See71waves onEnvelope of characteristics, 307, 314,355sloping beaches,Finite difference methods, 296, 424, 474convergence of, 477, 481Floating, bodies in shallow water, 431breakwaters, 414elasticbeam, 438rigid body, 245Flood prediction,482Flood routing, 461Flood waves, in the Mississippi andOhio Rivers, 458, 483, 494monoclinal, 462Flow, around bends, 405between two walls, 410in open channels, 451of energy, 13also Bore.)interaction of, 412Hydraulic radius, 454Hydraulics, mathematical, 451Hydrostatic pressure law, 24, 31in meteorology, 374, 382Influence point, 228Initial characteristic,302a wave, 357Instability of steady flow with criticalInitial steepness ofspeed, 344Interaction of two hydraulic jumps, 412Internal waves, 147Intersection of characteristics, 855Irrotational flow, 9Iteration process, 539over obstacles, 344through a sluice, 407Jump, hydraulic.
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