- Access by Xinjiang University
On waves in gases. Part I: Acoustics of jets, turbulence, and ducts
Rev. Mod. Phys. 58, 117 – Published 1 January, 1986
DOI: https://doi.org/10.1103/RevModPhys.58.117
Abstract
This review on some aspects of waves in gases concentrates first (Part I) on modern research in the acoustics of fluids at rest or in steady or turbulent motion, in free space, in the presence of obstacles, or in ducts. The study of sound, for which the sole restoring force is pressure, will be extended in a later paper (Part II) to include the other three restoring forces, namely, gravity, electromagnetic, and Coriolis forces, leading to current research on internal, magnetic, and inertial waves and their couplings. The Introduction at the beginning of Part I, and the discussion at the end of Part II, concern all four types of waves in gases, and their relevance in physics and engineering. In Part I, the following areas of acoustics are addressed: the generation of noise by turbulence, inhomogeneities or bubbles, in natural and engineering flows, e.g., wind or jets; the scattering of sound by interfaces and diffraction by turbulence, and their effects on spectral and directional redistribution of energy; propagation in ducts, without or with mean flow, e.g., the horns of musical instruments and loudspeakers, and inlets and exhausts of engines; the effects of dissipation and nonlinearity on waves, e.g., in laboratory and engineering shock tubes, and in geophysical and astrophysical conditions. Underlying these topics is the interaction of acoustics with manking, ranging from the processes of human hearing and speech to the reproduction of desirable sounds (music) and reduction of undesirable sounds (noise).
References (637)
- Abramowitz, M., and I. Stegun, 1964, Handbook of Mathematical Functions (Dover, New York)
- Achenbach, J. D., 1973, Waves in Solids (North-Holland, Amsterdam)
- Acheson, D. J., and R. Hide, 1973, "Hydromagnetics of rotating fluids," Rep. Prog. Phys. 36, 159
- Adam, J. A., 1982, "Asymptotic solutions and spectral theory of linear wave equations," Phys. Rep. 86, 217
- Aggarwal, H. R., 1984, "The calculation of transonic rotor noise," Am. Inst. Aeron. Astron. J. 22, 996
- Ahmed, B. M., and I. A. Eltayeb, 1980, "On the propagation, reflexion, transmission and stability of atmospheric Rossby-gravity waves on a beta-plane in the presence of latitudinally sheared zonal flows," Philos. Trans. R. Soc. London, Ser. A 298, 6
- Akasofu, S. I., and S. Chapman, 1972, Solar-Terrestrial Physics (Oxford University, New York)
- d'Alembert, J. R., 1747, Opuscules Mathématiques (Gauthier-Villars, Paris), p. 1
- Alfvén, H., 1942, "The existence of electromagnetic hydrodynamic waves," Ark. Mat. Astron. Fys. B 29, 1
- Alfvén, H., 1948, Cosmical Electrodynamics (Oxford University, London)
- Alfvén, H., and C. G. Falthammar, 1962, Cosmical Electrodynamics (Oxford University, London)
- Aranha, J. A., D. K. Yue, and C. C. Mei, 1982, "Non-linear waves near a cut-off frequency in an acoustic duct—a numerical study," J. Fluid Mech. 121, 465
- Arbey, H., and J. Bataille, 1983, "Noise generated by airfoil profiles placed in an uniform laminar flow," J. Fluid Mech. 134, 33
- Athay, R. G., 1976, The Quiet Sun (Reidel, Dordrecht)
- Atvars, J., L. K. Schubert, and H. S. Ribner, 1964, "Refraction of sound from a point source placed in a jet," J. Acoust. Soc. Am. 37, 168
- Ballantine, S., 1927, "On the propagation of sound in the general Bessel horn of infinite length," J. Franklin Inst. 203, 85
- Balsa, T. F., 1976a, "The far-field of high-frequency convected singularities in sheared flows, with an application to jet noise prediction," J. Fluid Mech. 74, 193
- Balsa, T. F., 1976b, "Refraction and shielding of sound from a source in a jet," J. Fluid Mech. 76, 443
- Banos, A., 1955, "Magneto-hydrodynamic waves in uncompressible and compressible fluids," Proc. R. Soc. London, Ser. A 233, 350
- Barclay, D. W., T. B. Moodie, and J. B. Haddow, 1977, "Waves in thin-walled, non-uniform, perfectly elastic tubes containing an incompressible inviscid fluid," J. Acoust. Soc. Am. 62, 1
- Barraclough, D. R., J. M. Harwood, B. R. Leaton, and S. C. B. Malin, 1975, "A model of the geomagnetic fluid at epoch," Geophys. J. R. Astron. Soc. 43, 645
- Barrat, M. J., P. O. A. L. Davies, and M. J. Fisher, 1963, "The characteristics of turbulence in the mixing region of a round jet," J. Fluid Mech. 16, 337
- Barton, E. H., 1908, "On spherical radiation and vibration in conical pipes," Philos. Mag. 15, 69
- Basset, A. B., 1888, Treatise on Hydrodynamics, 2 vols. (Deighton and Bell, London; reprinted 1961 by Dover, New York)
- Batchelor, G. K., 1953, Theory of Homogeneous Turbulence (Cambridge University, Cambridge, England)
- Batchelor, G. K., 1967, Fluid Mechanics (Cambridge University, Cambridge, England)
- Bateman, H., 1915, Electrical and Optical Wave Motion (Cambridge University, Cambridge, England; reprinted 1954 by Dover, New York)
- Bateman, H., 1929, "Notes on a differential equation which occurs in the two-dimensional motion of a compressible fluid and the associated variational problems," Proc. R. Soc. London, Ser. A 125, 598
- Bateman, H., 1932, Partial Differential Equations of Mathematical Physics (Cambridge University, Cambridge, England)
- Bateman, H., F. P. Murnaghan, and H. L. Dryden, 1956, Hydrodynamics (Dover, New York)
- Baumeister, K. J., W. Eversman, R. J. Astley, and J. W. White, 1984, "Acoustics in a variable-area duct: Finite element and finite difference comparisons to experiment," Am. Inst. Aeron. Astron. J. 21, 193
- Baxter, S. M., 1984, "The first-order non-linear sound field of a two-frequency spherical source," J. Sound Vib. 94, 337
- Baxter, S. M., and C. L. Morfey, 1983, "Modal power distribution in ducts at high frequency," Am. Inst. Aeron. Astron. J. 21, 74
- Bechert, D. W., U. Michel, and E. Pfizenmaier, 1977, "Experiments on the transmission of sound through jets," Am. Inst. Aeron. Astron. Paper 79-575
- Bechert, D., and E. Pfizenmaier, 1975, "On the amplification of broadband jet noise by pure tone excitation," J. Sound Vib. 43, 581
- Beckmann, P., and A. Spizzichino, 1963, The Scattering of Electromagnetic Waves from Rough Surfaces (McGraw-Hill, New York)
- Beer, T., 1974, Atmospheric Waves (Wiley, New York)
- Bekesy, G., 1960, Experiments in Hearing (Delft University, Delft, Netherlands)
- Belcher, J. W., and L. Davis, 1971, "Large-amplitude Alfvén waves in the interplanetary medium," J. Geophys. Res. 76, 3534
- Benade, A. H., 1976, Fundamentals of Musical Instruments (Oxford University, New York)
- Benade, A. H., 1980, Horns, Strings and Harmony (Doubleday, New York)
- Benade, A. H., and E. V. Jansson, 1974, "On plane and spherical waves in horns with nonuniform flare. I: theory of radiation, resonance, frequencies and mode conversion," Acustica 31, 79
- Benjamin, T. B., 1967, "Internal waves of permanent form in fluids of great depth," J. Fluid Mech. 29, 559
- Beranek, L. L., 1954, Acoustics (McGraw-Hill, New York)
- Berg, R. E., and D. G. Storck, 1982, The Physics of Sound (Prentice-Hall, Englewood, Cliffs, New Jersey)
- Bergmann, P. G., 1946, "The wave equation in a medium with a variable index of refraction," J. Acoust. Soc. Am. 17, 329
- Bernoulli, D., 1767, "Mémoire sur les vibrations des cordes d'une épaisseur inégale, " Mem. Acad. Sci. Berlin 21, 281
- Berry, M. V., 1973, "The statistical properties of echoes refracted from rough surfaces," Philos. Trans. R. Soc. London, Ser. A 273, 611
- Beyer, R. T., 1972, "Nonlinear acoustics (experimental)," in American Institute of Physics Handbook (McGraw-Hill, New York), p. 3-206
- Beyer, R. T., 1974, Non-Linear Acoustics (Naval Sea Systems Command Report, Washington, D.C.)
- Beyer, R. T., and M. S. Korman, 1980, "The scattering of sound by turbulence in water," J. Acoust. Soc. Am. 67, 1980
- Bies, D. A., 1962, "Tapering bar of uniform stress in longitudinal oscillation," J. Acoust. Soc. Am. 34, 1567
- Bjørnø, L., 1974, Finite amplitude wave effects in fluids (I.P.C. Science and Technology Press, Guildford, England)
- Bjørnø, L., and P. N. Larsen, 1984, "Noise of air jets from rectangular slits," Acustica 54, 247
- Blackstock, D. T., 1964, "Thermoviscous attenuation of plane, periodic, finite-amplitude sound waves," J. Acoust. Soc. Am. 36, 534
- Blackstock, D. T., 1965, "Connection between the Fay and Fubini solutions for plane sound waves of finite amplitude," J. Acoust. Soc. Am. 39, 1019
- Blackstock, D. T., 1972, "Nonlinear acoustics (theoretical)," in American Institute of Physics Handbook (McGraw-Hill, New York), p. 3-183
- Blanc-Benon, P., and D. Juvé, 1981a, "Effet d'un jet turbulent sur le niveau d'onde cohérente et sur l'intensité d'un faisceau acoustique," C. R. Acad. Sci. Ser. II 292, 493
- Blanc-Benon, P., and D. Juvé, 1981b, "Élargissement d'un faisceau ultrasonore par transversée d'un champ turbulent," C. R. Acad. Sci. Ser. II 292, 551
- Blanc-Benon, P., and D. Juvé, 1982a, "Coherence spatialle d'un faisceau ultrasonare après transversée d'une turbulence cinématique," C. R. Acad. Sci. Ser. II 294, 1221
- Blanc-Benon, P., and D. Juvé, 1982b, "Corrélations spatiotemporelles d'un faisceau après transversée d'une turbulence cinématique," C. R. Acad. Sci. Ser. II 294, 1255
- Blevins, R. D., 1984, "Review of sound induced by vortex shedding from cylinders," J. Sound Vib. 92, 455
- Blokhintsev, D. I., 1946, "The propagation of sound in an inhomogeneous and moving medium," J. Acoust. Soc. Am. 18, 322
- Bolza, O., 1904, Lectures on the Calculus of Variations (University of Chicago, Chicago)
- Bolza, O.Bonnet, R. M., and K. Dupree, 1980, Eds., Solar Phenomena in Stars and Stellar Systems (Reidel, Dordrecht)
- Born, M., and E. Wolf, 1959, Principles of Optics (Pergamon, New York; 6th ed. 1975)
- Bostrom, A., 1983, "Acoustics waves in a duct with periodically varying cross section," Wave Motion 5, 59
- Boussinesq, J., 1871, "Théorie de l'intumescence liquide, appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire," C. R. Acad. Sci. 72, 755
- Bray, R. J., and R. E. Loughhead, 1974, The Solar Chromosphere (Chapman and Hall, London)
- Brekhovskikh, L. M., 1960, Waves in Layered Media (Academic, New York; 2nd ed. 1980)
- Brekhovskikh, L. M., and Y. P. Lysanov, 1982, Acoustic Propagation in the Ocean (Springer, Berlin)
- Bretherton, F. P., 1968, "Propagation in slowly varying waveguides," Proc. R. Soc. London, Ser. A 302, 555
- Bretherton, F. P., and C. J. R. Garrett, 1969, "Wavetrains in inhomogeneous moving media," Proc. R. Soc. London, Ser. A 302, 529
- Brillouin, L., 1926, "La mécanique ondulataire de Schrödinger: une méthode générale de solution par approximations successives," C. R. Acad. Sci. 183, 24
- Brindley, G. S., 1973, "Speed of sound in bent tubes and the design of wind instruments," Nature (London) 246, 479
- Broadbent, E. G., and D. W. Moore, 1979, "Acoustic destabilization of vortices," Philos. Trans. R. Soc. London 290, 353
- Brueckner, K. A., and S. Jorna, 1974, "Laser-driven fusion," Rev. Mod. Phys. 46, 325
- Bruzek, A., and C. J. Durrant, 1977, Glossary for Solar Physics (Reidel, Dordrecht)
- Bryan, G. H., 1918, "Compressible fluids," Aeron. J. 22, 255
- Bull, M. K., and M. P. Norton, 1980, "The proximity of coincidence and acoustic cut-off frequencies in relation to acoustic radiation from pipes with disturbed internal turbulent flow," J. Sound Vib. 69, 1
- Burgers, J. M., 1948, "A mathematical model illustrating the theory of turbulence," Adv. Appl. Math. 10, 171
- Burgers, J. M., 1974, The Non-Linear Diffusion Equation (Reidel, Dordrecht)
- Cabannes, H., 1970, Theoretical Magnetofluid-Dynamics (Academic, New York)
- Campos, L. M. B. C., 1977, "On the generation and radiation of magneto-acoustic waves," J. Fluid Mech. 81, 529
- Campos, L. M. B. C., 1978a, "On the emission of sound by an ionized inhomogeneity," Proc. R. Soc. London, Ser. A 359, 65
- Campos, L. M. B. C., 1978b, "The spectral broadening of sound by turbulent shear layers. Part I: Transmission of sound through turbulent shear layers," J. Fluid Mech. 89, 723
- Campos, L. M. B. C., 1978c, "The spectral broadening of sound by turbulent shear layers. Part II: Spectral broadening of sound and aircraft noise," J. Fluid Mech. 89, 751
- Campos, L. M. B. C., 1982, "On anisotropic, dispersive and dissipative wave equations," Portug. Math. 41, 13
- Campos, L. M. B. C., 1983a, "Modern trends in research on waves in fluids. Part I: Generation and scattering by turbulent and inhomogeneous flows," Portug. Phys. 11, 121
- Campos, L. M. B. C., 1983b, "On three-dimensional acoustic-gravity waves in model non-isothermal atmospheres," Wave Motion 5, 1
- Campos, L. M. B. C., 1983c, "On viscous and resistive dissipation of hydrodynamic and hydromagnetic waves in atmospheres," J. Méc. Théor. Appliq. 2, 861
- Campos, L. M. B. C., 1983d, "On the heating of the solar chromosphere by hydromagnetic waves with a five-minute period," Mem. Soc. Astrop. Ital. 55, 267
- Campos, L. M. B. C., 1983e, "On waves in non-isothermal, compressible, viscous and ionized atmospheres," Solar Phys. 82, 355
- Campos, L. M. B. C., 1983f, "On magnetoacoustic-gravity waves propagating or standing vertically in an atmosphere," J. Phys. A 16, 417
- Campos, L. M. B. C., 1983g, "Modern trends in research on waves in fluids. Part II. Propagation and dissipation in compressible and ionized atmospheres," Portug. Phys. 14, 145
- Campos, L. M. B. C., 1984a, "On some general properties of the exact acoustic fields in horns and baffles," J. Sound Vib. 95, 177
- Campos, L. M. B. C., 1984b, "On the propagation of sound in nozzles of strongly varying cross section containing a low-Mach-number mean flow," Z. Flugwiss. Weltraumf. 8, 97
- Campos, L. M. B. C., 1984c, "Sur la propagation du son dans les écoulements non-uniformes et non-stationaires," Rev. Acoust. 67, 217
- Campos, L. M. B. C., 1984d, "On a theory of solar spicules and the atmospheric mass balance," Mon. Not. R. Astron. Soc. 205, 547
- Campos, L. M. B. C., 1984e, "Mass and energy transfer by waves in atmosphere," in 25th Liège Astrophysics Symposium, edited by A. Noels and H. Gabriel (Liège University, Belgium), p. 393
- Campos, L. M. B. C., 1984f, "The effects of atmospheric disturbances on aircraft aerodynamics," J. R. Aeron. Soc. Paper 1085, June/July issue, p. 257
- Campos, L. M. B. C., 1984g, "On a concept of derivative of complex order with application to special functions," I.M.A. J. Appl. Math. 33, 109
- Campos, L. M. B. C., 1985a, "On the fundamental acoustic mode in variable-area, low-Mach-number nozzles," Prog. Aerosp. Sci. 22, 1
- Campos, L. M. B. C., 1985b, "On linear and non-linear wave equations for the acoustics of high-speed potential flows," J. Sound Vib. (to be published)
- Campos, L. M. B. C., 1985c, "On vertical hydromagnetic waves in a compressible atmosphere under an oblique magnetic field," J. Geophys. Astrophys. Fluid Dyn. 32, 217
- Campos, L. M. B. C., 1985d, "On longitudinal acoustic propagation in convergent and divergent nozzle flows," unpublished
- Campos, L. M. B. C., and J. F. P. G. Leitão, 1985, "On the computation of special functions with applications to waves in fluids," unpublished
- Candel, S. M., 1975, "Acoustic conservation principles and an application to plane and model propagation in nozzles and diffusers," J. Sound Vib. 41, 207
- Candel, S. M., 1983, "Sound source radiation in two-dimensional shear flow," Am. Inst. Aeron. Astron. J. 21, 221
- Candel, S. M., A. Guédel, and A. Julienne, 1976, "Refraction and scattering of sound in an open wind tunnel flow," in Proceedings of the 6th International Congress on Instrumentation in Aerospace Simulation Facilities, Ottawa; tiré à part 1975-79, Office National d'Études et de Recherches Aerospatiales (ONERA, Paris), p. 288
- Candel, S. M., A. Julienne, and M. Julliand, 1975, "Étude de l'effet de masque produit par un écran fluide," Société Nationale d' Étude et Construction de Moteurs d'Aviation (SNECMA), Villaroche, Paris, Fiche Tech. YKA-869
- Cantrell, R. H., and R. W. Hart, 1964, "Interaction between sound and flow in acoustic cavities: mass, momentum and energy considerations," J. Acoust. Soc. Am. 36, 697
- Carafoli, E., 1969, Wing Theory in Supersonic Flight (Pergamon, New York)
- Caratheodory, C., 1935, Calculus of Variations (Teubner, Leipzig; reprinted, Chelsea, New York, 1982)
- Caratheodory, C., 1950, Functions of a Complex Variable (Birkhauser, Basel; reprinted, Chelsea, New York, 1974)
- Cargill, A. M., 1982, "Low-frequency sound radiation and generation due to the interaction of unsteady flow with a jet pipe," J. Fluid Mech. 121, 59
- Carslaw, H. S., and J. C. Jaeger, 1946, Conduction of Heat in Solids (Oxford University, London; 2nd ed. 1959)
- Caussé, R., J. Kergomard, and X. Lurton, 1984, "Input impedance of brass musical instruments—comparison between experiment and numerical models," J. Acoust. Soc. Am. 75, 241
- Chandrasekhar, S., 1961, Hydrodynamic and Hydromagnetic Stability (Oxford University, London)
- Chandrasekhar, S., 1983, The Mathematical Theory of Black Holes (Oxford University, New York)
- Chandrasekhar, S., 1984, "On stars, their evolution and their stability," Rev. Mod. Phys. 56, 137
- Chang, P., W. K. Melville, and J. W. Miles, 1979, "On the evolution of a solitary wave in a gradually varying channel," J. Fluid Mech. 95, 401
- Chen, C. Y., 1977, "Predictions of aeroacoustic characteristics of coaxial jets," Am. Inst. Aeron. Astron. J. 15, 297
- Cheng, H., 1984, "An exact solvable non-linear partial differential equation with solitary-wave solutions," Stud. Appl. Math. 1, 183
- Chernov, L. A., 1967, Wave Propagation in a Random Medium (Dover, New York)
- Chester, W., and A. Moser, 1982, "On an equation which describes the resonant oscillations of a gas in an open-ended tube," Proc. R. Soc. London, Ser. A 380, 409
- Cho, Y. C., 1980, "Rigorous solution for sound radiation from circular ducts with hyperbolic horn or infinite plane baffle," J. Sound Vib. 69, 405
- Cho, Y. C., and K. Y. Ingard, 1983, "Mode propagation in non-uniform circular ducts with potential flow," Am. Inst. Aeron. Astron. J. 21, 970
- Clarke, R. H., 1973, "Theory of acoustic propagation in a variable ocean," Saclant A.S.W. Research Center, La Spezia, Italy, Memo SM-28
- Clebsch, A., 1857, "Über eine allgemeine transformation der hydrodynamischen Gleichungen," Crelle 64, 150
- Cole, J. D., 1950, "A quasilinear parabolic equation occurring in aerodynamics," Q. J. Appl. Math. 9, 225
- Cole, J. E., 1979, "Sound propagation in a duct with axial sound speed variation: an exact solution," J. Sound Vib. 63, 237
- Courant, R., and K. Friedrichs, 1948, Supersonic Flow and Shock Waves (Interscience, New York)
- Courant, R., and D. Hilbert, 1953, Methods of Mathematical Physics, 2 vols. (Academic, New York)
- Cowling, T. G., 1957, Magnetohydrodynamics (Interscience, New York; 2nd ed. 1980)
- Cowling, T. G., 1981, "Present status of dynamo theory," Annu. Rev. Astron. Astrophys. 19, 115
- Crandall, I. B., 1927, Theory of Vibrating Systems and Sound (MacMillan, London)
- Crighton, D. G., 1975, "Basic principles of aerodynamic noise generation," Prog. Aerosp. Sci. 16, 31
- Crighton, D. G., 1979, "Model equations for nonlinear acoustics," Annu. Rev. Fluid Mech. 11, 11
- Crighton, D. G., 1981, "Acoustics as a branch of fluid mechanics," J. Fluid Mech. 106, 261
- Crighton, D. G., 1984, "Transmission of energy down a periodically ribbed elastic structure under fluid loading," Proc. R. Soc. London, Ser. A 394, 405
- Crighton, D. G., and J. E. Ffowcs-Williams, 1969, "Sound generation by turbulent two-phase flow," J. Fluid Mech. 36, 585
- Crighton, D. G., and F. G. Leppington, 1973, "Singular perturbation methods in acoustics: diffraction by a plate of finite thickness," Proc. R. Soc. London, Ser. A 335, 313
- Crighton, D. G., and J. F. Scott, 1979, "Asymptotic solutions of model equations in non-linear acoustics," Philos. Trans. R. Soc. London, Ser. A 292, 101
- Crocco, L., and S. I. Cheng, 1967, Theory of Combustion Instability in Liquid Propellant Rocket Motors (Butterworths, London)
- Cummings, A., 1984, "Acoustic non-linearities and power losses at orfices," Am. Inst. Aeron. Astron. J. 22, 786
- Cummings, A., A. V. Parrett, and R. J. Astley, 1982, "A comparison of measured and computed sound pressure levels in a non-uniform acoustically lined duct," J. Sound Vib. 85, 407
- Curle, N., 1955, "The influence of solid boundaries upon aerodynamic sound," Proc. R. Soc. London, Ser. A 231, 505
- Curle, N., and H. J. Davies, 1968, Modern Fluid Mechanics (Van Nostrand, Princeton)
- Davies, P. O. A. L., 1981, "Flow-acoustic coupling in ducts," J. Sound Vib. 77, 191
- Davies, P. O. A. L., J. L. B. Coelho, and M. Bhattacharya, 1980, "Reflection coefficients for an unflanged pipe with flow," J. Sound Vib. 72, 543
- Deissler, R. G., 1984, "Turbulent solutions of the equations of fluid motion," Rev. Mod. Phys. 56, 223
- Deissler, R. G.Delloue, J., and P. Halley, 1972, Eds., Effects of Atmospheric Acoustic-Gravity Waves on Electromagnetic Wave Propagation, Advisory Group for Aerospace Research and Development, Paris, Conference Proceedings CP-115
- Denskat, K. U., and L. F. Burlaga, 1977, "Multi-spacecraft observations of microscale fluctuations in a solar wind," J. Geophys. Res. 82, 2693
- Dirac, P. A. M., 1927, Quantum Mechanics (Cambridge University, Cambridge, England; 4th ed. 1958)
- Disselhorst, J. H. M., and L. Van Wijngaarden, 1980, "Flow in the exit of open pipes during acoustic resonance," J. Fluid Mech. 99, 293
- Doppler, C., 1893, "Über das Farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels," Ostwarld Klass Exakt. Wiss. 161, 1
- Dowling, A. P., 1976, "Convective amplification of real simple sources," J. Fluid Mech. 74, 529
- Dowling, A. P., 1983, "Sound generation by turbulence near an elastic wall," J. Sound Vib. 90, 309
- Dowling, A. P., and J. E. Ffowcs-Williams, 1983, Sound and Sources of Sound (Harwood, London)
- Dowling, A. P., J. E. Ffowcs-Williams, and M. E. Goldstein, 1978, "Sound production in a moving stream," Philos. Trans. R. Soc. London, Ser. A 288, 321
- Drazin, P. G., 1984, Solitons (Cambridge University, Cambridge, England)
- Drazin, P. G., and W. H. Reid, 1981, Hydrodynamic Stability (Cambridge University, Cambridge, England)
- Duhamel, J. M. C., 1839, "Sur les vibrations des gas dans les tuyaux cylindriques, coniques, etc...." J. Math. Pures Appl. 14, 49
- Durbin, P. A., 1983a, "High-frequency Green's function for aerodynamic noise in moving media. Part I: General theory," J. Sound Vib. 91, 519
- Durbin, P. A., 1983b, "High-frequency Green's function for aerodynamic noise in moving media. Part II: Noise from a spreading jet," J. Sound Vib. 91, 527
- Eckart, C., 1960, Hydrodyanmics of Oceans and Atmospheres (Pegamon, London)
- Eddington, A. S., 1923, Mathematical Theory of Relativity (Cambridge University, Cambridge, England; 3rd ed. 1937; reprinted, Chelsea, New York, 1975)
- Eisenberg, N. A., and T. W. Kao, 1969, "Propagation of sound through a variable-area duct with a steady compressible flow," J. Acoust. Soc. Am. 49, 169
- Eisner, E., 1963, "Design of sonic amplitude transformers for high magnification," J. Acoust. Soc. Am. 35, 1367
- Eisner, E., 1964, "The design of resonant vibrators," in Physical Acoustics: Principle and Methods, 12 Vols., edited by W. P. Mason (Academic, New York), Vol. 1, p. 353
- Eisner, E., 1966, "Complete solutions of `Webster' horn equation," J. Acoust. Soc. Am. 41, 1126
- Eisner, E.Emmons, H. W., 1958, Ed., Fundamentals of Gas Dynamics, 8 vols. (Princeton University, Princeton, N.J.)
- Eisner, E.Erdelyi, A., 1953, Ed., Higher Transcendental Functions (McGraw-Hill, New York)
- Esclangon, E., 1917, "Réflexion et réfraction d'ondes acoustiques à la surface de séparation de deux fluides en repos ou en mouvement, dans l'acoustique des canons et des projectiles," C. R. Acad. Sci. 164, 99
- Esgolts, L., 1970, Differential Equations and the Calculus of Variations (Mir, Moscow)
- Essen, H. H., 1974, "Wave-facet interaction model applied to acoustic scattering by a rough sea surface," Acustica 31, 107
- Euler, L., 1759, "Supplément aux et continuation des recherches sur la propagation du son," Mem. Acad. Sci. Berlin 15 (1766), 210 (Opera Omnia, Teubner, Bern, Vol. 3, 1, p. 451)
- Euler, L., 1764, "De motu vibratorum cordarum inequaliter crassarum," Nov. Comm. Acad. Sci. Petr. 9, 246 (Opera Omnia, Vol. 2, 10, p. 293)
- Euler, L., 1766, "Recherches sur le mouvement des cordes inégalement grosses," Misc. Turnin. 3, 27 (Opera Omnia, Vol. 2, 10, p. 397)
- Euler, L., 1772, "De Motus Aeris tubis," Nov. Comm. Acad. Sci. Petr. 16, 281 (Opera Omnia, Vol. 2, 13b. p. 264)
- Euler, L., 1818, "Testamen novae theoricae musicae," Tip. Acad. Sci. Petr. (Opera Omnia, Vol. 3, 1, p. 197)
- Fabrikant, A. L., 1983, "Sound scattering by vortex flows," Akust. Zh. 29, 262
- Fanelli, M., A. Prosperetti, and M. Reali, 1984, "Shape oscillations of gas-vapour bubbles in liquids," Acustica 55, 213
- Ferraro, V. C. A., and C. Plumpton, 1958, "Hydromagnetic waves in an horizontally stratified atmosphere," Astrophys. J. 127, 149
- Ferraro, V. C. A., and C. Plumpton, 1963, An Introduction to Magneto-Fluid Dynamics (Oxford University, London; 2nd ed. 1966)
- Ffowcs-Williams, J. E., 1963, "The noise from turbulence convected at high speed," Philos. Trans. R. Soc. London, Ser. A 255, 471
- Ffowcs-Williams, J. E., 1964, "Sound production at the edge of a steady flow," J. Fluid Mech. 66, 791
- Ffowcs-Williams, J. E., 1969, "Hydrodynamic noise," Annu. Rev. Fluid Mech. 1, 197
- Ffowcs-Williams, J. E., 1984a, "The acoustic analogy thirty years on," I.M.A. J. Appl. Math. 32, 113
- Ffowcs-Williams, J. E., 1984b, "Anti-sound," Proc. R. Soc. London, Ser. A 395, 63
- Ffowcs-Williams, J. E., and D. L. Hawkins, 1968, "Sound generation by turbulence and surfaces in arbitrary motion," Philos. Trans. R. Soc. London, Ser. A 264, 321
- Ffowcs-Williams, J. E., and M. S. Howe, 1975, "The generation of sound by density inhomogeneities in low Mach number nozzle flows," J. Fluid Mech. 70, 605
- Ford, R. D., 1984, "Power requirement for active noise control in ducts," J. Sound Vib. 92, 411
- Fornberg, B., and G. B. Whitham, 1978, "A numerical and theoretical study of certain non-linear wave phenomena," Philos. Trans. R. Soc. London 289, 373
- Forsyth, A. R., 1885, Treatise on Differential Equations (MacMillan, London; 6th ed., 1929)
- Forsyth, A. R., 1926, Calculus of Variations (Cambridge University, Cambridge; reprinted, Dover, New York, 1960)
- Frank, N., and R. Von Mises, 1931, Differential- und Integral-gleichungen (Vieweg, Braunschweig; reprinted, Dover, New York, 1961)
- Franken, P. A., and U. Ingard, 1956, "Sound propagation in a moving medium," J. Acoust. Soc. Am. 27, 1044
- Francescutto, A., and R. Nabergoj, 1984, "A multiscale analysis of gas bubble oscillations: transient and steady-state solutions," Acustica 56, 12
- Freehafer, J. E., 1940, "Acoustical impedence of the infinite hyperbolic horn," J. Acoust. Soc. Am. 27, 1044
- Freeman, N. C., 1979, "A two-dimensional distributed soliton solution of the Korteweg-de Vries equation," Proc. R. Soc. London, Ser. A 366, 185
- Fuller, C. R., 1982, "Propagation and radiation of sound from flanged circular ducts with circumferentially-varying wall admittances," J. Sound Vib. 93, 341
- Fuller, C. R., and R. J. Silcox, 1984, "Experiments in sound radiation from a duct with a circumferentially varying liner," Am. Inst. Aeron. Astron. J. 22, 781
- Gabriel, A. H., 1976, "A magnetic model of the solar transition region," Philos. Trans. R. Soc. London, Ser. A 281, 339
- Gardner, C. S., J. M. Greene, M. D. Kruskal, and B. M. Miura, 1967, "Method for solving the Korteweg—de Vries equation," Phys. Rev. Lett. 19, 1095
- Gardner, C. S., J. M. Greene, M. D. Kruskal, and R. M. Miura, 1974, "Korteweg—de Vries equations and generalizations. VI: Methods for exact solution," Commun. Pure Appl. Math. 27, 97
- Garrett, C. J. R., 1967, "The adiabatic invariant for wave propagation in a non-uniform moving medium," Proc. R. Soc. London, Ser. A 299, 26
- Gazanhes, C., P. Arzeliés, and J. Léandre, 1984, "Propagation acoustique dans un milieu diphasique eau-bulles d'air; application à la caractérization d'un milieu diphasique par voie acoustique," Acustica 55, 113
- Gazanhes, C., and J. Léandre, 1974, "Propriétés statistiques d'une onde sonore diffusée par une surface aléatorie. Application à la réflexion sous-marine de surface," Acustica 30, 12
- Giovanelli, R. G., and J. M. Beckers, 1982, "Observations of Alfvén waves simultaneously in Hα and K," in Solar and Stellar Magnetic Fields: Origins and Coronal Effects, I.A.U. Symposium Number 102, edited by J. O. Stenflo (Reidel, Dordrecht), p. 407
- Glimm, J., G. Marshall, and B. Plohr, 1984, "A generalized Riemann problem for quasi-one-dimensional gas flows," Adv. Appl. Math. 5, 1
- Goldstein, M. E., 1976, Aeroacoustics (McGraw-Hill, New York)
- Goldstein, S., and N. W. McLachlan, 1935, "Sound waves of finite amplitude in the exponential horn," J. Acoust. Soc. Am. 6, 275
- Golub, L., R. Rosner, G. S. Vaiana, and N. O. Weiss, 1981, "Solar magnetic field: the generation of emerging flux," Astrophys. J. 243, 309
- Gossard, E. E., and W. Hooke, 1975, Waves in the Atmosphere (Elsevier, Amsterdam)
- Gottlieb, P., 1959, "Sound transmission through a fluid discontinuity," J. Acoust. Soc. Am. 31, 1036
- Green, G., 1837, "On the motion of waves in a variable canal of small depth and width," Proc. Cambridge Philos. Soc. 6, 457
- Greenspan, H. P., 1968, The Theory of Rotating Fluids (Cambrige University, Cambridge, England)
- Greenwood, J. A., 1984, "A unified theory of surface roughness," Proc. R. Soc. London, Ser. A 393, 133
- Grigoryan, F. E., 1984, "Theory of the circular waveguide with an abrupt change of cross section," Akust. Zh. 30, 39
- Grimshaw, R., 1981, "Slowly-varying solitary waves in deep fluids," Proc. R. Soc. London, Ser. A 376, 319
- Groen, P., 1948, "Contribution to the theory of internal waves," K. Ned. Akad. Met. Inst. 125b, 11
- Grosche, F. R., H. Stiewitt, and B. Binder, 1977, "Acoustic wind-tunnel measurements with a highly directional microphone," Am. Inst. Aeron. Astron. J. 15, 1590
- Guelfand, I. M., and G. Chilov, 1962-1970, Les Distributions, 5 vols. (Dunod, Paris)
- Haines, C. R., 1981, "A Wiener-Hopf approach to Kelvin wave generation by a semi-infinite barrier and depth discontinuity," Q. J. Mech. Appl. Math. 34, 139
- Hamilton, W. R., 1827-1832, "Theory of systems of rays" (with three supplements), Trans. R. Irish Acad. 15, 69 ibid.16, 1 ibid.17, 1
- Hanna, C. R., and J. Slepian, 1924, "The function and design of horns of loud-speakers," J. Acoust. Soc. Am. 6, 275
- Hansen, D. B., 1984, "Shielding of prop-pan cabin noise by the fuselage boundary layer," J. Sound Vib. 92, 591
- Hardin, J. C., and S. L. Lamkin, 1984, "Aeroacoustic computation of cylinder wake flow," Am. Inst. Aeron. Astron. J. 22, 51
- Hariharan, S. I., and H. C. Lester, 1984, "A finite difference solution for the propagation of sound in near-sonic flows," J. Acoust. Soc. Am. 75, 1052
- Hasan, M. A. Z., O. Islam, and A. K. M. F. Hussain, 1984, "Jet noise modification by the `Whistler nozzle,' " Am. Inst. Aeron. Astron. 22, 340
- Hasegawa, A., 1983, "Propagation of sound in acoustic slow waveguides," Acustica 52, 237
- Hayes, H., 1980, "Energy flux for trains of inhomogeneous plane waves," Proc. R. Soc. London, Ser. A 370, 417
- Hayes, W. D., 1958, "Gas dynamic discontinuities," in Fundamentals of Gas Dynamics, 8 vols., edited by H. W. Emmons (Princeton University, Princeton, N.J.), Sec. D., Vol. 3, p. 480
- Hayes, W. D., 1968, "Energy invariant for geometric acoustics in a moving medium," Phys. Fluids 11, 1654
- Hayes, W. D., 1973, "Sonic boom," Annu. Rev. Fluid Mech. 3, 269
- Heaviside, O., 1882, "Contributions to the theory of propagation of current in wires," Electrical Papers (MacMillan, London, 1892), Vol. 1, p. 141
- Heisenberg, W., 1924, "Über stabilitat und Turbulenz von Flussigkeitsstromen," Ann. Phys. Leipzig 74, 577 [National Advisory Committee on Aeronautics TM-1291 (1951)]
- Heisenberg, W., 1930, Physical Principles of Quantum Theory (University of Chicago, Chicago; reprinted, Dover, New York, 1949)
- Herlofson, N., 1950, "Waves in a compressible fluid conductor," Nature (London) 165, 1020
- Hermite, C., 1864, "Sur un nouveau développement en serie de fonctions," C.R. Acad. Sci. 53, 93, 266
- Heyvaerts, J., and E. R. Priest, 1983, "Coronal heating by phase-mixed Alfvén waves," Astron. Astrophys. 117, 220
- Hines, C. O., 1974, The Upper Atmosphere in Motion (American Geophysical Union, Washington, D.C.)
- Hinze, J. O., 1975, Turbulence (McGraw-Hill, New York)
- Ho, C. M., and L. S. G. Kovasznay, 1976a, "Propagation of a coherent acoustic wave through a turbulent shear flow," J. Acoust. Soc. Am. 60, 40
- Ho, C. M., and L. S. G. Kovasznay, 1976b, "Acoustical shadowgraph," Phys. Fluids 19, 1118
- Hoersch, V. A., 1925, "Non-radial harmonic vibrations within a conical horn," Phys. Rev. 25, 218
- Hollweg, J. V., 1972, "Supergranulation-driven Alfvén waves in the solar chromosphere and related phenomena," Cosmic Electrodyn. 2, 423
- Hoop, A. T., and J. H. M. T. Hijden, 1984, "Generation of acoustic waves by an impulsive point source in a fluid/solid configuration with a plane boundary," Am. Inst. Aeron. Astron. J. 75, 1709
- Hopf, E., 1951, "The partial differential equation ," Commun. Pure Appl. Math. 3, 201
- Howarth, L., 1953, Modern Developments in Fluid Mechanics: High-speed Flow (Oxford University, Oxford; 2nd ed., 1964)
- Howe, M. S., 1970, "Transmission of an acoustic pulse through a plane vortex sheet," J. Fluid Mech. 43, 353
- Howe, M. S., 1973a, "Kinetic theory of wave propagation in random media," Philos. Trans. R. Soc. London, Ser. A 274, 523
- Howe, M. S., 1973b, "Multiple scattering of sound by turbulence and other inhomogeneities," J. Sound Vib. 27, 455
- Howe, M. S., 1975a, "Contributions to the theory of aerodynamic sound, with applications to excess jet noise and the theory of the flute," J. Fluid Mech. 71, 625
- Howe, M. S., 1975b, "The generation of sound by aerodynamic sources in an inhomogeneous steady flow," J. Fluid Mech. 67, 597
- Howe, M. S., 1975c, "Application of energy conservation to the solution of radiation problems involving uniformly convected source distributions," J. Sound Vib. 43, 77
- Howe, M. S., 1976a, "The influence of vortex shedding on the generation of sound by convected turbulence," J. Fluid Mech. 76, 711
- Howe, M. S., 1976b, "The attenuation of sound by a randomly irregular impedance layer," Proc. R. Soc. London, Ser. A 347, 513
- Howe, M. S., 1978, "A review of trailing edge noise," J. Sound Vib. 61, 437
- Howe, M. S., 1979a, "The attenuation of sound by a low Mach number nozzle flow," J. Fluid Mech. 91, 209
- Howe, M. S., 1979b, "On the added mass of a perforated shell, with application to the generation of aerodynamic sound by a perforated trailing edge," Proc. R. Soc. London, Ser. A 365, 209
- Howe, M. S., 1979c, "A note on the interaction of unsteady flow with an acoustic liner," J. Sound Vib. 63, 429
- Howe, M. S., 1979d, "On the theory of unsteady high-Reynolds-number flow through a circular aperture," Proc. R. Soc. London, Ser. A 366, 205
- Howe, M. S., 1980, "On the diffraction of sound by a screen with circular apertures in the presence of a low Mach number grazing flow," Proc. R. Soc. London, Ser. A 370, 523
- Howe, M. S., 1981, "The role of displacement thickness fluctuations in hydroacoustics, and the jet-drive mechanism of the flue organ pipe," Proc. R. Soc. London, Ser. A 374, 543
- Howe, M. S., 1983a, "On the scattering of sound by a vortex ring," J. Sound Vib. 43, 77
- Howe, M. S., 1983b, "The attenuation of sound in a randomly lined duct," J. Sound Vib. 87, 83
- Howe, M. S., 1984a, "On the generation of sound by turbulent boundary layer over a rough wall," Proc. R. Soc. London, Ser. A 395, 247
- Howe, M. S., 1984b, "On the absorption of sound by turbulence and other hydrodynamic flows," I.M.A. J. Appl. Math. 32, 187
- Howe, M. S., and J. E. Ffowcs-Williams, 1978, "On the noise generated by an imperfectly expanded supersonic jet," Philos. Trans. R. Soc. London, Ser. A 289, 271
- Hudde, H., 1983, "Estimation of the area function of the human ear canals by sound pressure measurements," J. Acoust. Soc. Am. 73, 24
- Hudson, J. D., 1978, The Generation and Propagation of Waves in Elastic Solids (Cambridge University, Cambridge, England)
- Huerre, P., and K. Karamcheti, 1973, "Propagation of sound through a fluid moving in a duct of varying area," in University Research on Transportation Noise (Interagency Symposium, Stanford University), Vol. 2, p. 397
- Hunt, J. C. R., and J. A. Shercliff, 1971, "Magnetohydrodynamics at high Hartmann number," Annu. Rev. Fluid Mech. 3, 37
- Hurle, I. R., R. B. Price, T. M. Sugden, and H. Thomas, 1968, "Sound emission from open turbulent premixed flames," Proc. R. Soc. London, Ser. A 303, 409
- Ince, E. L., 1926, Ordinary Differential Equations (Longmans, Green, New York; reprinted, Dover, New York, 1956)
- Ingard, K. U., 1959, "Influence of fluid motion past a plane boundary on sound reflection, absorption and transmission," J. Acoust. Soc. Am. 31, 1035
- Ingard, K. U., 1983, "Acoustics in physics and engineering," Acustica 50, 127
- Ishimaru, A., 1978, Wave Propagation and Scattering in Random Media (Academic, New York)
- Ishizaka, K., M. Matsudaira, and T. Kaneko, 1976, "Input acoustic impedance measurement of the sub-glottal system," J. Acoust. Soc. Am. 60, 190
- Jackson, A. C., J. P. Butler, and R. W. Pyle, 1978, "Acoustic input impedance of excised dog lungs," J. Acoust. Soc. Am. 64, 1020
- Jacques, J. R., 1975, "The acoustic response of a nozzle flow to an externally applied low-frequency pressure field," J. Sound Vib. 41, 13
- Jansson, E. V., and A. H. Benade, 1974, "On plane and spherical waves in horns with non-uniform flare. II: Predictions and measurements of resonance frequencies and radiation losses," Acustica 31, 185
- Jeans, J., 1908, The Theory of Electricity and Magnetism (Cambridge University, Cambridge, England; 5th ed. 1932)
- Jeans, J., 1937, Science and Music (Cambridge University, Cambridge, England; reprinted, Dover, New York, 1968)
- Jeffrey, A., and T. Taniuti, 1964, Non-Linear Wave Propagation (Academic, New York)
- Jeffrey, A., and T. Taniuti, 1966, Magnetohydrodynamic Stability and Thermonuclear Containment (Academic, New York)
- Jeffreys, H., 1924, "On certain approximation solutions of linear differential equations of the second order," Proc. London Math. Soc. 23, 428
- Jeffreys, H., and B. S. Jeffreys, 1946, Methods of Mathematical Physics (Cambridge University, Cambridge, England; 3rd ed. 1956)
- Johnson, C. O., and R. I. Loehrke, 1984, "An experimental investigation of wake edge tones," Am. Inst. Aeron. Astron. J. 22, 1249
- Jones, D. S., 1966, Generalized Functions (McGraw-Hill, New York)
- Jones, D. S., 1968, Electromagnetic Theory (Pergamon, New York)
- Jones, D. S., 1973, "Diffraction by a thick semi-infinite plate," Proc. R. Soc. London, Ser. A 217, 153
- Jones, D. S., 1977, "The scattering of sound by a simple shear layer," Philos. Trans. R. Soc. London 284, 287
- Jones, D. S., and J. D. Morgan, 1972, "The instability of a vortex sheet on a subsonic stream under acoustic radiation," Proc. Cambridge Philos. Soc. 72, 465
- Jones, D. S., and J. D. Morgan, 1974, "A linear model of a finite amplitude Helmholtz instability," Proc. R. Soc. London, Ser. A 338, 17
- Jones, H., 1979, "The generation of sound by flames," Proc. R. Soc. London, Ser. A 367, 291
- Jordan, E. J., 1963, Loudspeakers (Focal Press, London)
- Kaiser, J. E., and A. H. Nayfeh, 1977, "A wave-envelope technique for wave propagation in non-uniform ducts," Am. Inst. Aeron. Astron. J. 15, 533
- Kamke, E., 1944, Differentialgleichungen (Teubner, Leipzig; reprinted, Chelsea, New York, 1971)
- Katz, J., and D. Lynden-Bell, 1982, "A Lagrangian for Eulerian fluid mechanics," Proc. R. Soc. London, Ser. A 381, 267
- Keefe, D. H., 1984, "Acoustical wave propagation in cylindrical ducts: transmission line parameter approximations for isothermal and non-isothermal boundary conditions," J. Acoust. Soc. Am. 75, 58
- Keller, J. B., 1955, "Reflection and transmission of sound by a moving medium," J. Acoust. Soc. Am. 27, 1044
- Keller, J. J., 1984, "Non-linear self-excited acoustic oscillations in cavities," J. Sound Vib. 94, 397
- Kelly, J. J., A. H. Nayfeh, and L. T. Watson, 1982, "Acoustic propagation in partially-choked converging-diverging ducts," J. Sound Vib. 81, 519
- Kelvin, Lord, 1880, "Vibrations of a columnar vortex," Philos. Mag. 10, 155
- Kempton, A. J., 1976, "The ambiguity of acoustic sources—a possibility for active control," J. Sound Vib. 48, 475
- Kergomard, J., 1981, "Ondes quasi-stationnaires dans les pavillons avec pertes visco-thermiques aux parois," Acustica 48, 31
- Kergomard, J., 1982, "Propagation des ondes dans les lignes finies: discussion des notions d'onde évanescente et de fréquence de coupure," Rev. Phys. Appl. 17, 307
- Khinchin, S. I., 1948, Mathematical Foundations of Statistical Mechanics (Dover, New York)
- Kinsler, L. E., and A. R. Frey, 1950, Fundamentals of Acoustics (Wiley, New York; 3rd ed. 1982)
- Klein, F., 1933, Vorlesungen über die hypergeometrische funktion (Teubner, Leipzig)
- Koch, W., and W. Möhring, 1983, "Eigensolutions for liners in uniform mean flow ducts," Am. Inst. Aeron. Astron. J. 21 200
- Kolmogorov, A. N., 1933, Foundations of the Theory of Probability (Springer, Berlin; reprinted, Chelsea, New York, 1950)
- Korteweg, D. J., and G. de Vries, 1895, "On the change of form of long waves advancing in a rectangular canal, and a new type of long stationary waves," Philos. Mag. 39, 422
- Kramers, H. A., 1926, "Wellenmechanik und halbzahlige Quantisierung," Z. Phys. 39, 828
- Krasnov, N. F., 1971, Aerodynamika (Vishaia Shkola, Moscow) (NASA technical translation F-265, Washington, 1978)
- Kraus, E. B., 1977, The Upper Layers of the Ocean (Oxford University, New York)
- Labonte, B. J., and R. Howard, 1982, "Torsional waves on the sun and the activity cycle," Solar Phys. 75, 161
- Lagrange, J. L., 1760, "Nouvelles recherches sur la nature et la propagation du son," Misc. Turin. 2, 11 (Oeuvres, Gauthier-Villars, Paris, Vol. 1, p. 151)
- Lamb, H., 1879, Hydrodynamics (Cambridge University, Cambridge, England, 6th ed., 1932)
- Lamb, H., 1910, "On the theory of waves propagated vertically in the atmosphere," Proc. London Math. Soc. 7, 122
- Lambert, R. F., 1954, "Acoustical studies of the tractrix horn," J. Acoust. Soc. Am. 26, 1024
- Landau, L. D., and E. F. Lifshitz, 1949, Mechanics (Pergamon, London)
- Landau, L. D., and E. F. Lifshitz, 1953, Fluid Mechanics (Pergamon, London)
- Landau, L. D., and E. F. Lifshitz, 1956, Electrodynamics of Continuous Media (Pergamon, London)
- Landau, L. D., and E. F. Lifshitz, 1966, Quantum Mechanics (Pergamon, New York)
- Landau, L. D., and E. F. Lifshitz, 1967a, Theory of Elasticity (Pergamon, New York)
- Landau, L. D., and E. F. Lifshitz, 1967b, Statistical Physics (Pergamon, New York)
- Laufer, J. and T. Yen, 1983, "Noise generation by a low Mach number jet," J. Fluid Mech. 134, 1
- Lavoie, J. L., T. J. Osler, and R. Tremblay, 1976, "Fractional derivatives and special functions," SIAM Rev. 18, 240
- Lehnert, B., 1954, "Magnetohydrodynamic waves under the action of the Coriolis force. I," Astrophys. J. 119, 647
- Lehnert, B., 1955, "Magnetohydrodynamic waves under the action of the Coriolis force. II," Astrophys. J. 120, 481
- Leppington, F. G., 1972, "Scattering of quadrupole sources near the end of a rigid semi-infinite circular pipe," Aeron. Res. Council CP-1195, Chap. 5
- Leppington, F. G., E. G. Broadbent, and K. H. Heron, 1984, "Acoustic radiation from rectangular panels with constrained edges," Proc. R. Soc. London, Ser. A 393, 67
- Leppington, F. G., and H. Levine, 1980, "Acoustics of a blocked duct with flow," J. Sound. Vib. 72, 303
- Leroy, B., 1980, "Propagation of waves in an atmosphere in the presence of a magnetic field: II. The reflection of Alfvén waves," Astron. Astrophys. 91, 136
- Leroy, B., 1982, "Propagation of waves in an atmosphere in the presence of a magnetic field: III. Alfvén waves in the solar atmosphere," Astron. Astrophys. 97, 245
- Lesser, M. B., and D. G. Crighton, 1975, "Physical acoustics and the method of matched asymptotic expansions," in Physical Acoustics: Principles and Methods, edited by W. P. Mason (Academic, New York), Vol. 11, p. 1
- Levine, A. H., 1975, "Acoustical diffraction radiation," Philips Res. Rep. 30, 240, 276
- Levine, A. H., 1978, Unidirectional Wave Motions (North-Holland, Amsterdam)
- Lighthill, M. J., 1952, "On sound generated aerodynamically: I. General theory," Proc. R. Soc. London, Ser. A 211, 564
- Lighthill, M. J., 1953, "On the energy scattered from the interaction of turbulence with sound and shock waves," Proc. Cambridge Philos. Soc. 44, 531
- Lighthill, M. J., 1954, "On sound generated aerodynamically. II: Turbulence as a source of sound," Proc. R. Soc. London, Ser. A 222, 1
- Lighthill, M. J., 1956, "Viscosity effects in sound waves of finite amplitude," in Surveys in Mechanics, edited by G. K. Batchelor and R. M. Davies (Cambridge University, Cambridge, England), p. 250
- Lighthill, M. J., 1958, Fourier Series and Generalized Functions (Cambridge University, Cambridge, England)
- Lighthill, M. J., 1960, "Studies in magnetohydrodynamic waves and other anisotropic wave motions," Philos. Trans. R. Soc. London, Ser. A 252, 397
- Lighthill, M. J., 1961, "Bakerian lecture: sound generated aerodynamically," Proc. R. Soc. London 267, 147
- Lighthill, M. J., 1963, "Jet noise," Am. Inst. Aeron. Astron. J. 1, 1587
- Lighthill, M. J., 1964, "Group velocity," J. Inst. Math. Appl. 1, 1
- Lighthill, M. J., 1969, "Dynamic response of the Indian ocean to the onset of the southwest monsoon," Philos. Trans. R. Soc. London, Ser. A 265, 45
- Lighthill, M. J., 1972, "Fourth annual Fairey lecture: the propagation of sound through moving fluids," J. Sound Vib. 24, 471
- Lighthill, M. J., 1975, Mathematical Biofluidmechanics (Society for Industrial and Applied Mathematics, Philadelphia)
- Lighthill, M. J., 1978a, Waves in Fluids (Cambridge University, Cambridge, England)
- Lighthill, M. J., 1978b, "Acoustic Streaming," J. Sound Vib. 61, 391
- Lighthill, M. J., 1981, "Energy flow in the cochlea," J. Fluid Mech. 106, 149
- Lilley, G. M., 1973, "On the noise from jets," AGARD Conference Proceedings CP-131, 13.1
- Lin, C. C., 1955, Theory of Hydrodynamic Stability (Cambridge University, Cambridge, England)
- Lindeberg, J. W., 1922, "Eine neue Erleitung der Exponential Gezetses in der Wahrscheinlichtkeitrechnung," Math. Z. 15, 211
- Lindzen, R. S., 1970, "Internal gravity waves in atmospheres with realistic dissipation and temperature," Geophys. Fluid Mech. 1, 303
- Liu, C. H., and L. Maestrello, 1975, "Propagation of sound through a real jet flowfield," Am. Inst. Aeron. Astron. J. 13, 66
- Long, D. F., and R. E. A. Arndt, 1984, "Jet noise at low Reynolds number," Am. Inst. Aeron. Astron. J. 22, 187
- Longuet-Higgins, M. S., 1964, "Planetary waves on a rotating sphere," Proc. R. Soc. London, Ser. A 279, 446
- Longuet-Higgins, M. S., 1968, "On the trapping of waves along a discontinuity of depth in a rotating ocean," J. Fluid Mech. 31, 417
- Love, A. E. H., 1927, Theory of Elasticity, 4th ed. (Cambridge University, Cambridge; reprinted, Dover, New York, 1944)
- Lumsdaine, E., and S. Ragab, 1977, "Effect of flow on quasi-one-dimensional acoustic wave propagation in a variable duct of finite length," J. Sound Vib. 53, 47
- Lundquist, S., 1949, "Experimental investigation of magnetohydrodynamic waves," Phys. Rev. 76, 1805
- Lynden-Bell, D., and J. Katz, 1981, "Isocirculational flows and their Lagrangian and energy principles," Proc. R. Soc. London, Ser. A 378, 179
- Lyons, P., and M. Yanowitch, 1974, "Vertical oscillations in a viscous and thermally conducting isothermal atmosphere," J. Fluid Mech. 66, 273
- Macaskill, C. C., and B. J. Uscinski, 1981, "Propagation in waveguides containing random irregularities: second moment equation," Proc. R. Soc. London, Ser. A 377, 73
- MacGregor, G. R., H. S. Ribner, and H. Lam, 1973, "Basic jet noise patterns after deletion of convection and rarefaction effects: experiment vs theory," J. Sound Vib. 27, 437
- Mach, E., 1926, The Principles of Physical Optics (Methuen, London; reprinted, Dover, New York, 1953)
- Mani, R., 1976a, "The influence of jet flow on jet noise. Part 1. The noise of unheated jets," J. Fluid Mech. 80, 321
- Mani, R., 1976b, "The influence of jet flow on jet noise. Part 2. The noise of heated jets," J. Fluid Mech. 73, 779
- Mani, R., 1980, "Sound propagation in parallel sheared flows in ducts: the mode estimation problem," Proc. R. Soc. London, Ser. A 371, 393
- Mani, R., 1981, "Low-frequency sound propagation in quasione-dimensional flow," J. Fluid Mech. 104, 81
- Marble, F. E., and S. M. Candel, 1977, "Acoustic disturbance from gas nonuniformities convected through a nozzle," J. Sound Vib. 55, 225
- Marble, F. E.S. M. CandelMason, W. P., 1964-1973, Ed., Physical Acoustics: Principles and Methods, 12 vols. (Academic, New York)
- Marble, F. E.S. M. CandelMassey, H., 1980, Ed., "The middle atmosphere as observed from balloons, rockets and satellites," Philos. Trans. R. Soc. London, Ser. A 296, 1
- Mawardi, O. K., 1949, "Generalized solutions of Webster horn theory," J. Acoust. Soc. Am. 57, 1030
- Maxwell, J. C., 1873, Treatise on Electricity and Magnetism, 2 vols. (Clarendon, Oxford; 3rd ed. 1891; reprinted, Dover, New York, 1954)
- McGowan, R. S., and R. S. Larson, 1984, "Relationship between static, flight and simulated flight jet noise measurements," Am. Inst. Aeron. Astron. J. 22, 460
- McIntyre, M. E., and T. N. Palmer, 1983, "Breaking planetary waves in the stratosphere," Nature (London) 305, 593
- McLachlan, N. W., 1934a, Bessel Functions for Engineers (Oxford University, London; 2nd ed. 1955)
- McLachlan, N. W., 1934b, Loudspeakers: Theory, Performance, Testing and Design (Oxford University, London)
- McLachlan, N. W., 1935, Elements of Loudspeakers Practice (Oxford University, London)
- McLachlan, N. W., 1936, The New Acoustics (Oxford University, London)
- McLachlan, N. W., and T. M. McKay, 1936, "Transient oscillations in a loud-speaker horn," Proc. Cambridge Philos. Soc. 32, 265
- Meecham, W. C., 1983, "Aerosound from corner flow and flap flow," Am. Inst. Aeron. Astron. J. 21, 228
- Melville, W. K., 1980, "On the Mach reflexion of a solitary wave," J. Fluid Mech. 98, 285
- Merkulov, L. G., 1957, "Design ultrasonic concentrators," Akust. Zh. 3, 230
- Merkulov, L. G., and A. V. Kharitonov, 1959, "Theory and analysis of sectional concentrators," Akust. Zh. 5, 183 (1959)
- Mermelstein, P., 1966, "Determination of the vocal tract shape from measured formant frequencies," J. Acoust. Soc. Am. 40, 1283
- Michalke, A., and U. Michel, 1979, "Prediction of jet noise in flight from static tests," J. Sound Vib. 67, 341
- Mihalas, D., and B. W. Mihalas, 1983, "On the propagation of acoustic waves in a radiating fluid," Astrophys. J. 273, 355
- Miles, J. H., 1981, "Acoustic transmission matrix of a variablearea duct or nozzle carrying a compressible mean flow," J. Acoust. Soc. Am. 64, 1186
- Miles, J. W., 1954, "Reflection of sound due to a change in cross section of a tube," J. Sound Vib. 26, 14
- Miles, J. W., 1957, "On the reflection of sound at an interface of relative motion," J. Acoust. Soc. Am. 29, 226
- Miles, J. W., 1958, "On the disturbed motion of a vortex sheet," J. Fluid Mech. 4, 538
- Miles, J. W., 1959, The Potential Theory of Unsteady Supersonic Flow (Cambridge University, Cambridge, England)
- Miles, J. W., 1972, "Kelvin waves on oceanic boundaries," J. Fluid Mech. 55, 113
- Miles, J. W., 1981, "The Korteweg—de Vries equation: a historical essay," J. Fluid Mech. 106, 131
- Milne-Thomson, L. M., 1938, Theoretical Hydrodynamics (Mac-Millan, London; 5th ed. 1968)
- Milne-Thomson, L. M., 1958, Theoretical Aerodynamics (Mac-Millan, London; reprinted, Dover, New York, 1966)
- Misner, C. W., K. S. Thorne, and J. A. Wheeler, 1973, Gravitation (Freeman, San Francisco)
- Mobbs, S. D., 1982, "Variational principles for perfect and dissipative fluid systems," Proc. R. Soc. London, Ser. A 381, 457
- Moffat, H. K., 1976, "Generation of magnetic fields by fluid motion," Adv. Appl. Mech. 16, 119
- Moffatt, H. K., 1978, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University, Cambridge, England)
- Moffatt, H. K.Moffatt, H. K., and M. R. E. Proctor, 1982, Eds., Metallurgical Applications of Magnetohydrodynamics, proceedings of the International Union of Theoretical and Applied Mechanics Symposium, Cambridge (Metals Society, London, 1984)
- Möhring, W., 1971, "Energy flux in duct flow," J. Sound Vib. 18, 101
- Möhring, W., 1978a, "On vortex sound at low Mach number," J. Fluid Mech. 85, 685
- Möhring, W., 1978b, "Acoustic energy flux in non-homogeneous ducts," J. Acoust. Soc. Am. 64, 1186
- Möhring, W., 1980, "Acoustic momentum and energy theorems for piecewise uniform ducts," J. Acoust. Soc. Am. 67, 1463
- Möhring, W., E. A. Müller, and F. Obermeier, 1983, "Problems in flow acoustics," Rev. Mod. Phys. 55, 707
- Möhring, W., and S. Rahman, 1976, "The influence of perturbations of the velocity and speed of sound on the propagation of sound waves in ducts," Am. Inst. Aeron. Astron. Paper 76-493
- Moir, J., 1961, High-Quality Sound Reproduction (Chapman and Hall, London)
- Møller, C., 1952, The Theory of Relativity (Oxford University, London; 2nd ed. 1972)
- Molloy, C., 1975, "-parameter ducts," J. Acoust. Soc. Am. 57, 1030
- Moore, C. J., 1979, "The role of shear-instability waves in jet exhaust noise," J. Fluid Mech. 80, 321
- Moore, D. W., and E. A. Spiegel, 1964, "The generation and propagation of waves in a compressible atmosphere," Astrophys. J. 139, 48
- Moorhem, W. K., and G. K. Landheim, 1984, "Propagation of plane waves in a thermally stratified atmosphere," J. Acoust. Soc. Am. 76, 867
- Morfey, C. L., 1971, "Sound transmission and generation in ducts with flow," J. Sound Vib. 14, 37
- Morfey, C. L., 1973, "Amplification of aerodynamic noise by convected flow inhomogeneities," J. Sound Vib. 31, 391
- Morse, P. M., and H. Feshbach, 1953, Methods of Theoretical Physics (McGraw-Hill, New York)
- Morse, P. M., and K. U. Ingard, 1968, Theoretical Acoustics (McGraw-Hill, New York)
- Mortell, M. P., and B. R. Seymour, 1979, "Non-linear forced oscillations in a closed tube: continuous solutions of a functional equation," Proc. R. Soc. London, Ser. A 367, 253
- Mowbray, D. E., and B. S. H. Rarity, 1967, "A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified fluid," J. Fluid Mech. 28, 1
- Mungur, P., and H. E. Plumblee, 1969, "Propagation and attenuation of sound in a soft-walled annular duct containing a sheared flow," NASA SP-207, p. 305
- Munt, R. M., 1977, "The interaction of sound with a subsonic jet issuing from a semi-infinite pipe," J. Fluid Mech. 83, 609
- Myers, M. K., 1980, "On the acoustic boundary condition in the presence of flow," J. Sound Vib. 71, 429
- Myers, M. K., and A. J. Callegari, 1972, "On the singular behavior of linear acoustic theory in near-sonic flows," J. Sound Vib. 51, 517
- Myers, M. K., and S. L. Chuang, 1984, "Uniform asymptotic expansions for duct acoustic modes in a thin boundary-layer flow," Am. Inst. Aeron. Astron. J. 22, 1234
- Nagarkar, B. N., and R. D. Finch, 1971, "Sinusoidal horns," J. Acoust. Soc. Am. 50, 23
- Nagel, R. T., J. W. Denham, and A. G. Papathanasiou, 1983 "Supersonic jet screech tone cancellation," Am. Inst. Aeron. Astron. J. 21, 1541
- Namba, M., and K. Fukushige, 1980, "The application of the equivalent source method to the acoustics of duct systems with non-uniform wall impedance," J. Sound Vib. 73, 125
- Namba, M., T. Notomi, and T. Fujimoto, 1984, "Analysis of sound attenuation in a duct with a solid or porous splitter," J. Sound Vib. 92, 47
- Nayfeh, A. H., 1973, Perturbation Methods (Wiley, New York; 2nd ed. 1982)
- Nayfeh, A. H., 1975a, "Acoustic waves in a duct with sinusoidally perturbed walls and mean flow," J. Acoust. Soc. Am. 57, 1036
- Nayfeh, A. H., 1975b, "Finite-amplitude plane waves in ducts with varying properties," J. Acoust. Soc. Am. 57, 1413
- Nayfeh, A. H., J. E. Kaiser, R. L. Marshall, and C. J. Hurst, 1980, "A comparison of experiment and theory for sound propagation in variable-area ducts," J. Sound Vib. 71, 241
- Nayfeh, A. H., J. E. Kaiser, and D. P. Telionis, 1975a, "Acoustics of aircraft engine-duct systems," Am. Inst. Aeron. Astron. J. 13, 130
- Nayfeh, A. H., J. E. Kaiser, and D. P. Telionis, 1975b, "Transmission of sound through annular ducts of varying cross sections," Am. Inst. Aeron. Astron. J. 13, 60
- Nayfeh, A. H., J. J. Kelly, and L. T. Watson, 1982, "Propagation of spinning acoustic modes in partially-chocked converging ducts," J. Acoust. Soc. Am. 71, 796
- Nayfeh, A. H., B. S. Shaker, and J. E. Kaiser, 1980, "Transmission of sound through non-uniform circular ducts with compressible mean flows," Am. Inst. Aeron. Astron. J. 18, 515
- Newton, I., 1686, Principia (Pepys, London; reprinted, Dover, New York, 1934), 2 vols
- Noble, B., 1958, The Wiener-Hopf Technique (Oxford University, London)
- Norum, T. D., 1984, "Screech suppression in supersonic jets," Am. Inst. Aeron. Astron. J. 21, 235
- Ockendon, H., and D. A. Spence, 1969, "Non-linear wave propagation in a relaxing gas," J. Fluid Mech. 39, 329
- Oldham, K. B., and J. Spanier, 1974, The Fractional Calculus (Academic, New York)
- Olson, H. F., 1938, "A horn consisting of manifold exponential sections," J. Soc. Motion Pict. Eng. 30, 511
- Olson, H. F., 1940, Elements of Acoustic Engineering (Van Nostrand, Princeton)
- Olson, H. F., 1952, Music, Physics and Engineering (Dover, New York; 2nd ed. 1967)
- Olson, H. F., 1972, Modern Sound Production (Van Nostrand, Princeton)
- Olson, H. F., and I. Wolff, 1930, "A sound concentrator for microphones," J. Acoust. Soc. Am. 1, 410
- Olson, H. F., and F. Massa, 1934, Applied Acoustics (Blakiston, Philadelphia)
- Ono, H., 1975, "Algebraic solitary waves in stratified fluids," J. Phys. Soc. Jpn. 39, 1082
- Orr, W. M., 1907, "The stability or instability of steady motions of a perfect liquid and a viscous liquid," Proc. R. Irish Acad., Sec. A 27, 9
- Osborne, A. R., and T. L. Burch, 1980, "Internal solitons in the Andaman sea," Science 208, 451
- Page, N. W., and D. J. Mee, 1984, "Wall effects on sound propagation in tubes," J. Sound Vib. 93, 473
- Page, N. W.D. J. MeePao, Y. H., and A. Goldburg, 1969, Eds., Clear Air Turbulence and its Detection (Plenum, New York)
- Parker, E. N., 1979, Cosmical Magnetic Fields (Clarendon, London)
- Parodi, M., 1945, "Propagation sur une ligne électrique sans pertes, dont les paramètres lineiques sont des fonctions exponentielles du carré de l'espace," J. Phys. (Paris) 6, 331
- Pars, L. A., 1960, Calculus of Variations (Heinemann, London)
- Pauling, L., and E. B. Wilson, 1935, Introduction to Quantum Mechanics (McGraw-Hill, New York)
- Paynter, H. M., and F. D. Ezekiel, 1958, "Water hammer in non-uniform pipes as an example of wave propagation in gradually varying media," Trans. Am. Soc. Mech. Eng. 80, 1585
- Péclet, E., 1843, Traité de la Chaleur Considerée dans ses Applications, 3 vols. (Hachette, Paris)
- Pedley, T. J., 1980, The Fluid Mechanics of Large Blood Vessels (Cambridge University, Cambridge, England)
- Pedlosky, J., 1960, Geophysical Fluid Dynamics (Springer, Berlin; 2nd ed. 1979)
- Peixoto, J. P., and A. H. Oort, 1984, "Physics of climate," Rev. Mod. Phys. 56, 365
- Peregrine, D. H., and R. Smith, 1979, "Non-linear effects of waves near caustics," Philos. Trans. R. Soc. London, Ser. A 292, 341
- Perulli, M., 1979, "Propagation acoustique dans les conduits," AGARD Report 686, Chap. 6
- Peube, T. L., and J. Chasseriaux, 1973, "Non-linear acoustics in ducts with varying cross section," J. Sound Vib. 27, 533
- Philips, O. M., 1960a, The Dynamics of the Upper Ocean (Cambridge University, Cambridge, England; 2nd ed. 1976)
- Philips, O. M., 1960b, "On the generation of sound by supersonic turbulent shear layers," J. Fluid Mech. 9, 1
- Pickering, W. M., and C. Sozou, 1982, "The axisymmetric flow field induced by a point force in the presence of a plane wall," Proc. R. Soc. London, Ser. A 380, 349
- Pierce, A. D., 1981, Acoustics (McGraw-Hill, New York)
- Pinker, R. A., and W. D. Bryce, 1976, "The radiation of plane wave duct noise from jet exhausts, statically and in flight," Am. Inst. Aeron. Astron. Paper 76-581
- Plumblee, H. E., and P. D. Dean, 1983, "Sound measurements within and in the radiated field of an annular duct with flow," J. Sound Vib. 28, 715
- Plumblee, H. E., P. D. Dean, G. A. Wynne, and R. H. Burrin, 1973, "Sound propagation in and radiation from acoustically-lined flow ducts: a comparison of experiment and theory," NASA CR-2306
- Pochhammer, L., 1876, "Über die Fortplanzungsgeschwindigkeiten der Schwingungen in einem unbegrentzen isotropen Kreiscylinder," Crelle 81, 324
- Poirée, B., 1982, "Équations de perturbations et équations de passage associés: application au dioptre acoustique," thèse doctorale (Université de Paris VI), p. 113
- Poisson, S. D., 1807, "Mémoire sur la theorie du son," J. E. Polytech. 7, 367
- Poisson, S. D., 1817, "Sur les mouvements des fluides élastiques dans les tuyaux cylindriques, et sur la théorie des instruments à vent," Mem. Acad. Sci. 2, 305
- Poole, E. G. C., 1936, Linear Differential Equations (Oxford University, Oxford; reprinted, Dover, New York, 1960)
- Powell, A., 1959, "Propagation of a pressure pulse in a compressible flow," J. Acoust. Soc. Am. 31, 1527
- Powell, A., 1960, "Theory of sound propagation through ducts carrying high-speed flows," J. Acoust. Soc. Am. 32, 1640
- Powell, A., 1961, "Vortex sound," University of California, Los Angeles, Department of Engineering Report 61-70
- Powell, A., 1964, "Theory of vortex sound," J. Acoust. Soc. Am. 36, 177
- Prandtl, L., and O. G. Tietjens, 1934, Applied Hydro- and Aeromechanics, 2 vols. (McGraw-Hill, New York; reprinted, Dover, New York, 1957)
- Prasad, M. G., and M. J. Crocker, 1984, "A note on the propagation of acoustic plane waves in a uniform pipe with mean flow," J. Sound Vib. 92, 284
- Prasad, P., 1973, "Non-linear wave propagation on an arbitrary steady transonic flow," J. Fluid Mech. 57, 721
- Priest, E. R., 1982, Solar Magnetohydrodynamics (Reidel, Dordrecht)
- Pridmore-Brown, D. C., 1959, "Sound propagation in a fluid flowing through an attenuating duct," J. Fluid Mech. 4, 393
- Pyle, R. W., 1965, "Duality principle for horns," J. Acoust. Soc. Am. 37, 1187A
- Pyle, R. W., 1967, "Solid torsional horns," J. Acoust. Soc. Am. 41, 1147
- Quinn, M. C., and M. S. Howe, 1984, "The influence of mean flow on the acoustic properties of a tube bank," Proc. R. Soc. London, Ser. A 396, 383
- Quinn, T. J., A. R. Collough, and T. R. D. Chandler, 1976, "A new determination of the gas constant by an acoustical method," Philos. Trans. R. Soc. London, Ser. A 283, 367
- Rabinovich, M. I., V. P. Reutov, and G. V. Rybushkina, 1984, "Dipole acoustic radiation from a turbulent boundary layer on a rigid surface with a geometrical irregularity," Akust. Zh. 30, 105
- Rae, I. C., and B. Roberts, 1983, "MHD wave motion in magnetically structured atmospheres," Solar Phys. 84, 99
- Raiser, Y. P., and Y. B. Zel'dovich, 1966-1967, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, 2 vols. (Academic, New York)
- Ramachandra, M. K., and W. C. Strahle, 1983, "Acoustic signature from flames as a combustion diagnostic tool," Am. Inst. Aeron. Astron. J. 21, 1107 [Rayleigh Papers, 6 vols. (Cambridge University, Cambridge, 1899-1920; reprinted, Dover, New York, 1964, 3 vols.), Vol. 1, p. 33]
- Rayleigh, J. W. S., 1868, "On the theory of resonance," Philos. Trans. R. Soc. London 159, 77
- Rayleigh, J. W. S., 1873, "Note on a natural limit to the sharpness of spectral lines," Nature 8, 474 (Papers, Vol. 1, p. 83)
- Rayleigh, J. W. S., 1876, "On waves," Philos. Mag. 1, 257 (Papers, Vol. 1, p. 251)
- Rayleigh, J. W. S., 1879, The Theory of Sound, 2 vols. (MacMillan, London; reprinted, Dover, New York, 1945)
- Rayleigh, J. W. S., 1880, "On the stability or instability, of certain fluid motions," Proc. London Math. Soc. 11, 57 (Papers, Vol. 1, p. 474)
- Rayleigh, J. W. S, 1887, "On the instability of jets II," Proc. London Math. Soc. 19, 67 (Papers, Vol. 3, p. 17)
- Rayleigh, J. W. S., 1889, "On the limit to interference when light is emitted from moving molecules," Philos. Mag. 27, 298 (Papers, Vol. 3, p. 258)
- Rayleigh, J. W. S., 1890, "On the vibrations of an atmosphere," Philos. Mag. 29, 173 (Papers, Vol. 3, p. 335)
- Rayleigh, J. W. S., 1915, "On the widening of spectral lines," Philos. Mag. 29, 274 (Papers, Vol. 6, p. 291)
- Rayleigh, J. W. S., 1916, "On the propagation of sound in narrow tubes of variable section," Philos. Mag. 31, 89 (Papers, Vol. 6, p. 376)
- Reitz, J. R., and F. J. Milford, 1967, Foundations of Electromagnetic Theory (Addison-Wesley, Reading, Mass.)
- Reynolds, O., 1883, "An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels," Philos. Trans. R. Soc. London 156, 935
- Ribe, F. L., 1975, "Fusion reactor systems," Rev. Mod. Phys. 46, 325
- Ribner, H. S., 1957, "Reflection, transmission and amplification of sound by a moving medium," J. Acoust. Soc. Am. 29, 435
- Riemann, B., 1860, "Uber die Fortpflanzung Evener Luftwellen von Endlicher Schwingunsweite," Ges. Werke, p. 156
- Rienstra, S. W., 1981, "Sound diffraction at a trailing edge," J. Fluid Mech. 108, 443
- Rienstra, S. W., 1984, "Acoustic radiation from a semi-infinite duct," J. Sound Vib. 94, 267
- Roberts, B., and A. Mangeney, 1982, "Solitons in a magnetic flux tube," Mon. Not. R. Astron. Soc. 198, 7p
- Roberts, P. H., 1971, "Dynamo theory," in Mathematical Problems in the Geophysical Sciences, edited by W. H. Reid (American Mathematical Society, Providence, Rhode Island), p. 126
- Roberts, P. H.Ross, B., 1975, Ed., Fractional Calculus and its Applications, Proceedings of the New International Conference, New Haven, June, 1974 (Springer, Berlin), Lecture Notes in Mathematics, Vol. 457
- Ross, B., 1981, "Spectral broadening effects in open wind tunnels in relation to noise assessment," Am. Inst. Aeron. Astron. J. 19, 567
- Rossby, C. G., 1939, "Relation between variations in the intensity of zonal circulation of the atmosphere and the displacement of semi-permanent centers of action," J. Mar. Res. 2, 38
- Rossby, C. G.R. T. BeyerRudenko, O. V., and S. I. Soluyan, 1975, Eds., Theoretical Foundations of Nonlinear Acoustics (Nauka, Moscow) [translation by , Plenum, New York (1977)]
- Rudnick, I., 1946, "Acoustic transmission through a fluid lamina," J. Acoust., Soc. Am. 17, 245
- Russel, J. S., 1845, "Reports on waves," British Assoc. Rep. 13, 311
- Salikuddin, M., and P. Mungur, 1983, "Acoustic radiation impedance of a duct-nozzle system," J. Sound Vib. 86, 497
- Salmon, V., 1946a, "A new family of horns," J. Acoust. Soc. Am. 17, 212
- Salmon, V., 1946b, "Generalized plane wave horn theory," J. Acoust. Soc. Am. 17, 199
- Schiff, L. I., 1949, Quantum Mechanics (McGraw-Hill, New York; 3rd ed. 1968)
- Schlichting, H., 1933, "Zur entstehung der Turbulenz bei der platten-stromung," Nachr. Ges. Wiss. Goettingen Math. Phys. K1. 181
- Schlichting, H., G. Breun1951, Boundary Layer Theory (G. Braunsche, Karlsruhe) [translation of 7th ed. by , McGraw-Hill, New York (1970)]
- Schlichting, H., and E. Truckenbrodt, 1979, Aerodynamics of the Airplane (McGraw-Hill, New York)
- Schmidt, D. W., and P. M. Tillmann, 1970, "Experimental study of sound phase fluctuations caused by turbulent wakes," J. Acoust. Soc. Am. 47, 1310
- Schroeder, M. R., 1967, "Determination of the shape of the human vocal tract by acoustic measurements," J. Acoust. Soc. Am. 41, 1002
- Schulten, J. B. H. M., 1984, "Vane stagger angle and camber effects in fan noise generation," Am. Inst. Aeron. Astron. J. 22, 1071
- Schwarzschild, M., 1958, Structure and Evolution of Stars (Princeton University, Princeton, N.J.; reprinted, Dover, New York, 1965)
- Schwartz, L., 1949, Théorie des Distributions (Hermann, Paris)
- Schwartz, R. F., 1974, "Transformations in the analysis of non-uniform transmission lines," J. Franklin Inst. 278, 163
- Scott, J. F., 1981, "Uniform asymptotics for spherical and cylindrical nonlinear acoustic waves generated by a sinusoidal source," Proc. R. Soc. London, Ser. A 375, 211
- Scott, J. F., 1982, "The non-linear propagation of acoustic noise," Proc. R. Soc. London, Ser. A 383, 55
- Seeliger, R. L., and G. B. Whitham, 1968, "Variational principles in continuum mechanics," Proc. R. Soc. London, Ser. A 305, 1
- Seiner, J. M., and J. C. Yu, 1984, "Acoustic near-field properties associated with broadband shock noise," Am. Inst. Aeron. Astron. J. 22, 1207
- Seymour, B. R., and M. P. Mortell, 1980, "A finite-rate theory of resonance in a closed tube: discontinuous solutions of a functional equation," J. Fluid Mech. 99, 365
- Shapiro, A. H., 1954, The Dynamics and Thermodynamics of Compressible Fluid Flow, 2 vols. (Ronald, New York)
- Shaw, E. A. G., 1970, "Acoustic horns with spatially varying density or elasticity," J. Acoust. Soc. Am. 50, 830
- Shercliff, J. A., 1965, Textbook of Magnetohydrodynamics (Pergamon, London)
- Shermann, A., and G. W. Sutton, 1965, Engineering Magnetohydrodynamics (McGraw-Hill, New York)
- Sholnik, M. I., 1962, Introduction to Radar Systems (McGraw-Hill, New York)
- Silcox, R. J., 1984, "Geometry and static flow effects on acoustic radiation from ducts," Am. Inst. Aeron. Astron. J. 22, 1087
- Silcox, R. J., and H. C. Lester, 1982, "Sound propagation through a variable-area duct: experiment and theory," Am. Inst. Aeron. Astron. J. 20, 1377
- Sinai, Y. L., 1981, "Two-dimensional acoustic wave propagation in elastic ducts," J. Sound Vib. 74, 519
- Sneddon, I. N., 1972, The Use of Integral Transforms (McGraw-Hill, New York)
- Sobolev, A. F., 1982, "Sound radiation from a cylindrical duct with impedance walls," Sov. Phys. Acoust. 29, 310
- Sommerfeld, A., 1896, "Mathematical theorie der Diffraction," Math. Ann. 67, 317
- Sommerfeld, A., 1908, "Eine Beitrag zur hydrodynamischen Erklaerung der turbulenten Fluessigkeits bewegungen," in Atti del IV Congresso Internazionali dei Matematici, edited by G. Castelnuovo (Tipografia della Reale Academia dei Lincei, Roma, 1909), Vol. 3, p. 116
- Sornette, D., and M. Lagier, 1984, "Nature monopolaire du rayonnement acoustique engendré par les écoulements instables," Acustica 55, 255
- Spitzer, L., 1956, Physics of Fully Ionized Gases (Interscience, New York)
- Spruit, H. C., and B. Roberts, 1984, "Magnetic flux tubes on the sun," Nature 304, 401
- Stein, R. F., 1967, "The generation of acoustic and acoustic-gravity waves by turbulence in an isothermal stratified atmosphere," Solar Phys. 2, 385
- Stein, R. F.Stenflo, J. O., 1982, Ed., Solar and Stellar Magnetic Fields: Origins and Coronal Effects (Reidel, Dordrecht)
- Stevenson, A. F., 1951a, "General theory of electromagnetic horns," J. Appl. Phys. 22, 1447
- Stevenson, A. F., 1951b, "Exact and approximate solutions for wave propagation in acoustic horns," J. Appl. Phys. 21, 1461
- Stevin, G. O., 1984, "A computational model of the ear reflex," Acustica 55, 277
- Stewart, G. W., 1920, "The performance of conical horns," Phys. Rev. 16, 313
- Stix, T. H., 1962, The Theory of Plasma Waves (McGraw-Hill, New York)
- Stoker, J. J. 1953, Water Waves (Interscience, New York)
- Stollery, J. L., A. G. Gaydon, and P. R. Owen, 1971, Shock Tube Research (Chapman and Hall, London)
- Stone, J. R., D. E. Groesbeck, and C. L. Zola, 1983, "Conventional profile coaxial jet noise prediction," Am. Inst. Aeron. Astron. J. 21, 336
- Stratton, J. A., 1941, Electromagnetic Theory (McGraw-Hill, New York)
- Strouhal, V., 1878, "Reibungstöne," Ann. Phys. Chem. (Wied. Ann.) 5, 216
- Sunyach, M., D. Juvé, and G. Comte-Bellot, 1982, "Acoustics of turbulent flows: a report on Euromech 142," J. Fluid Mech. 122, 511
- Swinbanks, M. A., 1973, "The active control of sound propagation in long ducts," J. Sound Vib. 27, 441
- Swinbanks, M. A., 1975, "Sound field generated by a source distribution in a long duct carrying sheared flow," J. Sound Vib. 40, 51
- Synge, J. L., 1960, Relativity: The General Theory (North-Holland, Amsterdam)
- Tatarski, V. I., 1971, Wave Propagation in a Turbulent Medium (Dover, New York)
- Taylor, G. I., 1910, "The conditions necessary for discontinuous motions in gases," Proc. R. Soc. London, Ser. A 84, 371
- Taylor, K., 1978, "A transformation of the acoustic equation with implications for wind-tunnel and low-speed flight tests," Proc. R. Soc. London, Ser. A 363, 271
- Tester, B. J., 1973a, "The optimization for modal sound attenuation in ducts, in the absence of mean flow," J. Sound Vib. 27, 477
- Tester, B. J., 1973b, "Ray models for sound propagation and attenuation in ducts, in the absence of mean flow," J. Sound. Vib. 27, 515
- Tester, B. J., and R. H. Burrin, 1974, "On sound radiation from sources in parallel sheared jet flows," Air Force Aero Propulsion Lab. Technical Report No. TR-74-24, p. 59
- Thiessen, G. J., 1950, "Resonance characteristics of a finite sinusoidal horn," J. Acoust. Soc. Am. 75, 346
- Thomas, J. H., 1983, "Magneto-atmospheric waves," Annu. Rev. Fluid Mech. 15, 321
- Thomson, C., 1984, "Linear inviscid wave propagation in a waveguide having a single boundary discontinuity," J. Acoust. Soc. Am. 75, 346
- Thorpe, S. A., 1968, "On the shape of progressive internal waves," Philos. Trans. R. Soc. London, Ser. A 263, 563
- Titchmarsch, E. C., 1937, Theory of Fourier Integrals (Clarendon, London; 2nd ed. 1948)
- Tollmien, W., 1929, "Uber die Entstehung der Turbulenz," Nachr. Ges. Wiss. Goettingen Math. Phys. K1. 21, 44 [N.A.C.A. TM-609 (1931)]
- Tolman, R. C., 1934, Relativity, Thermodynamics and Cosmology (Clarendon, London)
- Tolstoy, I., 1963, "The theory of waves in stratified fluids including the effects of gravity and rotation," Rev. Mod. Phys. 35, 207
- Townsend, A. A., 1956, Structure of Turbulent Shear Flow (Cambridge University, Cambridge, England)
- Trevena, D. H., 1984, "Cavitation and the generation of tension in liquids," J. Phys. D 17, 2139
- Truesdell, C. A., 1955, "Theory of aerial sound 1687-1788," in Euleri Opera Omnia (O. Füssli, Lausanne), Vol. 3, 13b, p. 19
- Truesdell, C. A., 1960, "The rational mechanics of flexible or elastic bodies 1638-1788," in Euleri Opera Omnia (O. Füssli, Turin), Vol. 2, 116, p. 15
- Tsien, H. S., 1952, "The transfer functions of rocket nozzles," J. Am. Rocket Soc. 22, 139
- Tsien, H. S., 1958, "The equations of gas dynamics," in Fundamentals of gas dynamics, 8 vols., edited by H. W. Emmons (Princeton University, Princeton), Vol. 3, p. 3
- Turner, J. S., 1973, Buoyancy Effects in Fluids (Cambridge University, Cambridge, England)
- Uenishi, K., and M. K. Myers, 1984, "Two-dimensional acoustic field in a non-uniform duct carrying compressible flow," Am. Inst. Aeron. Astron. J. 22, 1242
- Uscinski, B. J., 1977, Elements of Wave Propagation in Random Media (McGraw-Hill, New York)
- Uscinski, B. J., 1980, "Parabolic moment equations and acoustic propagation through internal waves," Proc. R. Soc. London, Ser. A 372, 117
- Vaidya, P. G., 1984, "Multiple pure tone generation in aeroengine fans at subsonic and supersonic relative tip speeds," Am. Inst. Aeron. Astron. J. 22, 1366
- Van Dyke, 1964, Perturbation Methods in Fluid Mechanics (Academic, New York)
- Van Dyke, M., 1972, An Album of Fluid Motion (Parabolic, Stanford)
- Varley, E., and E. Cumberbatch, 1970, "Large-amplitude waves in stratified media: acoustic pulses," J. Fluid Mech. 43, 513
- Varley, E., J. Y. Kazakya, and P. A. Blythe, 1977, "The interactions of large-amplitude barotropic waves with ambient shear flow: critical flows," Philos. Trans. R. Soc. London, Ser. A 287, 24
- Viergeuer, M., 1980, Mechanics of the Inner Ear (Delft University, Delft, Netherlands)
- Von Mises, R., 1958, Mathematical Theory of Compressible Fluid Flow (Academic, New York)
- Von Mises, R., 1964, Mathematical Theory of Probability and Statistics (Academic, New York)
- Wang, K. S., and T. G. Tszeng, 1984, "Propagation and radiation of sound in a finite length duct," J. Sound Vib. 93, 71
- Waterhouse, R. V., and R. D. Berendt, 1958, "Reverberation chamber study of sound power output from subsonic air jets," J. Aeron. Sci. 30, 114
- Watson, G. N., 1944, Bessel Functions (Cambridge University, Cambridge, England)
- Watson, J. G., and J. B. Keller, 1984, "Rough surface scattering via the smoothing method," J. Acoust. Soc. Am. 75, 1705
- Watson, W. B., 1984, "An acoustic evaluation of circumferentially segmented duct liners," Am. Inst. Aeron. Astron. J. 22, 1229
- Webster, A. G., 1919, "Acoustical impedance and the theory of horns and the phonograph," Proc. Natl. Acad. Sci. U.S.A. 5, 275
- Weibel, E. S., 1955, "On Webster's horn equation," J. Acoust. Soc. Am. 75, 1705
- Welsh, M. C., A. N. Stokes, and R. Parker, 1984, "Flow-resonant interaction in a duct containing a plate," J. Sound Vib. 95, 395
- Wentzel, A. R., 1980, "Spectral broadening of waves propagating in a random medium," J. Math. Phys. 21, 2131
- Wentzel, G., 1926, "Eine Varallgemeinerung der Qiarterbedomgiger für die Zwecke der Wellenmechanik," Z. Phys. 38, 518
- Westervelt, P. J., 1963, "A parametric acoustic array," J. Acoust. Soc. Am. 25, 60
- Wever, E. G., and M. Lawrence, 1954, Physiological Acoustics (Princeton University, Princeton, N.J.)
- Whitfield, O. J., and M. S. Howe, 1976, "The generation of sound by two-phase nozzle flows and its relevance to excess jet noise of jet engines," J. Fluid Mech. 75, 353
- Whitham, G. B., 1974, Linear and Non-Linear Waves (Wiley, New York)
- Whittaker, E. T., 1904, Analytical Dynamics of Particles and Rigid Bodies (Cambridge University, Cambridge, England; 4th ed. 1937)
- Whittaker, K. W., and G. L. Morrison, 1984, "Acoustic measurements of high-speed subsonic jets," Inst. Aeron. Astron. J. 22, 756
- Wiener, N., 1933, The Fourier Integral and Certain of its Applications (Cambridge University, Cambridge; reprinted, Dover, New York, 1958)
- Woods, A., 1944, The Physics of Music (Chapman and Hall, London, 7th ed. 1975)
- Yanowitch, M., 1967a, "Effect of viscosity on the vertical oscillations of an isothermal atmosphere," Can. J. Phys. 45, 2003
- Yanowitch, M., 1967b, "Effect of viscosity on gravity waves and the upper boundary condition," J. Fluid Mech. 29, 209
- Yanowitch, M., 1969, "A numerical study of vertically propagating waves in a viscous, isothermal atmosphere," J. Comput. Phys. 4, 531
- Yeh, K. C., and C. H. Liu, 1974, "Acoustic-gravity waves in the upper atmosphere," Rev. Geophys. Space Sci. 12, 193
- Yeow, K. W., 1974, "Webster wave equation in two dimensions," J. Acoust. Soc. Am. 56, 19
- Yeow, K. W., 1984, "Variation with distance of aircraft noise impact parameters," J. Sound Vib. 95, 127
- Yih, C. S., 1965, Dynamics of Non-Homogeneous Fluids (MacMillan, London)
- Yoshida, H., 1981, "Sound wave propagation in ducts whose walls are lined with a porous layer backed by cellular cavities," J. Sound Vib. 74, 519
- Zamorski, T., and R. Wyrzykowski, 1981, "Approximate methods for the solution of the equation of acoustic wave propagation in horns," Arch. Acoust. 6, 237
- Zhugzhda, Y. D., and N. S. Dzhalilov, 1981, "Conversion of magnetogravitational waves in the solar atmosphere," Astron. Zh. 58, 838