Reciprocity and energy theorems for waves in a compressible inhomogeneous moving fluid

Wave Motion

Volumn 25, Issue 2, 1997, Pages 143-167

  Godin, Oleg A ^a,b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b SHIRSHOV INSTITUTE OF OCEANOLOGY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000402943     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0165-2125(96)00037-6     Document Type: Article

References (60)

1. L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics, Fluid Mechanics, Vol. 6, Pergamon Press, New York (1982).
2. L.M. Brekhovskikh and O.A. Godin, Acoustics of Layered Media. 2: Point Sources and Bounded Beams, Springer Serios in Wave Phenomena, Vol. 10, Springer, Berlin (1992).
3. A.D. Pierce, Acoustics: An Introduction to Its Physical Principles and Applications, McGraw-Hill, New York (1981).
4. L.M. Lyamshev, "A question in connection with the principle of reciprocity in acoustics", Doklady Akademii Nauk 125, 1231-1234 (1959) [English transl.: Sov. Phys. Dokl. 4, 405-409 (1959)].
5. L.M. Lyamshev, "A question in connection with the principle of reciprocity in acoustics", Doklady Akademii Nauk 125, 1231-1234 (1959) [English transl.: Sov. Phys. Dokl. 4, 405-409 (1959)].
6. Yu.I. Belousov and A.V. Rimskii-Korsakov, "The reciprocity principle in acoustics and its application to the calculation of sound fields of bodies", Akust, Zh. 21, 161-172 (1975) [English transl.: Sov. Phys. Acoust. 21, 103-109 (1975)].
7. Yu.I. Belousov and A.V. Rimskii-Korsakov, "The reciprocity principle in acoustics and its application to the calculation of sound fields of bodies", Akust, Zh. 21, 161-172 (1975) [English transl.: Sov. Phys. Acoust. 21, 103-109 (1975)].
8. L.M. Lyamshev, "On some integral relationships in acoustics of moving medium", Doklady Akademii Nauk 138, 575-578 (1961); L.M. Lyamshev, "Sound radiation from elastic shells excited by turbulent aerodynamic flow", Akust. Zh. 7, 59-66 (1961) [English transl.: Sov. Phys. Acoust. 7, 44-49 (1961)].
9. L.M. Lyamshev, "On some integral relationships in acoustics of moving medium", Doklady Akademii Nauk 138, 575-578 (1961); L.M. Lyamshev, "Sound radiation from elastic shells excited by turbulent aerodynamic flow", Akust. Zh. 7, 59-66 (1961) [English transl.: Sov. Phys. Acoust. 7, 44-49 (1961)].
10. L.M. Lyamshev, "On some integral relationships in acoustics of moving medium", Doklady Akademii Nauk 138, 575-578 (1961); L.M. Lyamshev, "Sound radiation from elastic shells excited by turbulent aerodynamic flow", Akust. Zh. 7, 59-66 (1961) [English transl.: Sov. Phys. Acoust. 7, 44-49 (1961)].
11. M.S. Howe, "The generation of sound by aerodynamic sources in an inhomogeneous steady flow", J. Fluid Mech. 67, 597-610 (1975).
12. M.S. Howe, "Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of flutte", J. Fluid Mech. 71, 625-673 (1975).
13. O.A. Godin, "Reciprocity relations for waves in a compressible fluid", Doklady Akademii Nauk 293, 322-325 (1987).
14. A.V. Generalov, "On some integral relationships for acoustic waves in inhomogeneous moving medium". Doklady Akademii Nauk 316, 1072-1076 (1991).
15. Nghiem-Phu Lan and F.D. Tappert, "Parabolic equaiton modeling of the effects of ocean currents on sound transmission and reciprocity in the time domain", J. Acoust. Soc. Am. 78, 642-648 (1985).
16. O.A. Godin and A.V. Mokhov, "Small-angle parabolic approximation for sound fields in a moving fluid", Akust. Zh. 38, 442-449 (1992) [English transl.: Sov. Phys. Acoust. 38, 243-246 (1992)].
17. O.A. Godin and A.V. Mokhov, "Small-angle parabolic approximation for sound fields in a moving fluid", Akust. Zh. 38, 442-449 (1992) [English transl.: Sov. Phys. Acoust. 38, 243-246 (1992)].
18. O.A. Godin and A.V. Mokhov, "Parabolic equation modeling of ocean currents influence on acoustic fields", in: Proc. European Conf. on Underwater Acoustics (Luxembourg, 14-18 September 1992) Elsevier, London, (1992) 280-283.
19. O.A. Godin, D.Yu. Mikhin and A.V. Mokhov, "A full field inversion method for acoustic tomography of ocean currents," in: Full Field Inversion Methods in Ocean and Seismo-Acoustics, O. Diachok, A. Caiti, P. Gerstoft and H. Schmidt eds., Kluwer Academic Publishers, Dordrecht (1995) 261-266.
20. R.H. Engler, D.W. Schmidt and W.J. Wagner, "Nondisturbing acoustical measurements of flow fields - New developments and applications", J. Acoust. Soc. Am. 85, 72-82 (1989).
21. W. Munk, P. Worcester and C. Wunsch, Ocean Acoustic Tomography, chapter 3, Cambridge University Press, Cambridge (1995).
22. L.A. Chernov, "On ray curvature and reciprocity principle in acoustics of moving medium", Tr. Komis. Akust. AN SSSR 6, 63-65 (1951).
23. W. Möhring, "Acoustic energy flux in inhomogeneous ducts", J. Acoust. Soc. Am. 64, 1186-1189 (1978).
24. O.A. Godin, "Reciprocity relations for acoustic fields in a moving fluid with three-dimensional inhomogeneities", Doklady Akademii Nauk 322, 79-85 (1992) [English transl.: Physics - Doklady 37, 44-47 (1992)].
25. O.A. Godin, "Reciprocity relations for acoustic fields in a moving fluid with three-dimensional inhomogeneities", Doklady Akademii Nauk 322, 79-85 (1992) [English transl.: Physics - Doklady 37, 44-47 (1992)].
26. L.M. Lyamshev, "Reciprocity principle and its applications in underwater acoustics", in: Proc. 14th Inte. Cong. on Acoustics (Beijing, China) Vol. 4, P5 (1992).
27. O.A. Godin, "Reciprocal relationships for acoustic disturbances in a stratified flow", Docklady Akademii Nauk 334, 37-40 (1994) [English transl.: Physics Doklady 39, 16-19 (1994)].
28. O.A. Godin, "Reciprocal relationships for acoustic disturbances in a stratified flow", Docklady Akademii Nauk 334, 37-40 (1994) [English transl.: Physics Doklady 39, 16-19 (1994)].
29. O.A. Godin, "Reciprocity relations for high-frequency sound fields in an inhomogeneous moving medium", Akust. Zh. 41, 581-586 (1995) [English transl.: Acoust. Physics 41, 510-514 (1995)].
30. O.A. Godin, "Reciprocity relations for high-frequency sound fields in an inhomogeneous moving medium", Akust. Zh. 41, 581-586 (1995) [English transl.: Acoust. Physics 41, 510-514 (1995)].
31. O.A. Godin, "A modification of the equation governing sound propagation in a layered medium", in: Acoustic Waves in the Ocean, I.B. Andreeva and L.M. Brekhovskikh, eds., Nauka, Moscow (1987) 34-40 (in Russian).
32. D.A. Chalyuk, "On the reciprocity relation in acoustics of moving media", Thesis, Moscow Institute of Physics and Technology, Moscow (1994) (in Russian).
33. O.A. Godin, "A new form of the wave equation for sound in a general layered fluid", in: Progress in Underwater Acoustics, H.M. Merklinger, ed., Plenum Press, New York 337-349 (1987).
34. S.S. Davis, "On an invariance property of acoustic waveguides", J. Acoust. Soc. Am. 59, 264-266 (1976).
35. O.A. Godin, "Parabolic approximation in acoustics of moving media", Akust. Zh. 37, 646-653 (1991) [English transl.: Sov. Phys. Acoust. 37, 335-338 (1991)].
36. O.A. Godin, "Parabolic approximation in acoustics of moving media", Akust. Zh. 37, 646-653 (1991) [English transl.: Sov. Phys. Acoust. 37, 335-338 (1991)].
37. L.D. Landau and E.M. Lifshitz, Course of Teheoretical Physics, Electrodynamics, of continuous Media, Vol. 8, 2nd ed., Pergamon Press, New York (1984).
38. C. Eckart, "Some transformations of the hydrodynamic equaitons", Phys. Fluids 6, 1037-1041 (1963).
39. E. Frieman and M. Rotenberg, "On hydrodynamic stability of stationary equilibria", Rev. Modern Phys. 32, 898-902 (1960).
40. W.D. Hayes, "Conservation of action and modal wave action", Proc. Roy. Soc. London A320, 187-208 (1970).
41. L.M. Brekhovskikh and O.A. Godin, Acoustics of Layered Media. I: Plane and Quasi-Plane Waves, Springer Series in Wave Phenomena, Vol. 5, Springer, Berlin (1990).
42. P.H. LeBlond and L.A. Mysak, Waves in the Ocean, Elsevier, Amsterdam (1978).
43. D.I. Blokhintsev, Acoustics of an Inhomogeneous Moving Medium, Brown University, Providence, RI (1956).
44. A.D. Pierce, "The Helmholtz-Kirchhoff integral relation as a framework for developing algorithms for sound propagation through inhomogeneous moving media", in: Computational Acoustics. Ocean-Acoustic Models and Supercomputing, D. Lee et al., eds., North-Holland, Amsterdam 53-66 (1990).
45. O.A. Godin, "A sound field in a vicinity of a caustic in a nonstationary moving fluid", Doklady Akademii Nauk 341, 185-189(1995) [English transl.: Physics Doklady 40, 102-106 (1995)].
46. O.A. Godin, "A sound field in a vicinity of a caustic in a nonstationary moving fluid", Doklady Akademii Nauk 341, 185-189(1995) [English transl.: Physics Doklady 40, 102-106 (1995)].
47. O.A. Godin, "An adiabatic invariant for acoustic waves in a nonuniform nonstationary flow", Doklady Akademii Nauk 342, 36-39 (1995) [English transl: Physics Doklady 40, 102-106 (1995)].
48. O.A. Godin, "An adiabatic invariant for acoustic waves in a nonuniform nonstationary flow", Doklady Akademii Nauk 342, 36-39 (1995) [English transl: Physics Doklady 40, 102-106 (1995)].
49. I. Tolstoy, "The theory of waves in stratified fluids including the effects of gravity and rotation". Rev. Modern Phys. 35, 207-230 (1963).
50. G.B. Whitham, "Non-linear dispersive waves", Proc. Roy. Soc. London A283, 238-261 (1965).
51. F.B. Bretherton and C.I.R. Garrett, "Wavetrains in inhomogeneous moving media", Proc. Roy. Soc. London A302, 529-554 (1968).
52. D.G. Andrews and M.E. McIntyre, "On wave action and its relatives", J. Fluid Mech. 89, 647-694 (1978).
53. M.K. Myers, "On the acoustic boundary condition in the presence of flow", J. Sound Vibr. 71, 429-434 (1980).
54. L.M. Brekhovskikh and V.V. Goncharov, Mechanics of Continua and Wave Dynamics, Springer Series in Wave Phenomena, Vol. 1, 2nd edn., Springer, Berlin (1994).
55. A.G. Voronovich, "Internal and surface gravity wave propagation in the geometric optics approximation", Izv. Akad. Nauk SSSR. Fiz. Atmos. Okeana 12, 850-857 (1976) [English transl.: Izv. Acad, Sci. USSR. Atoms. Oceanic Phys. 12, (8) (1976)].
56. A.G. Voronovich, "Internal and surface gravity wave propagation in the geometric optics approximation", Izv. Akad. Nauk SSSR. Fiz. Atmos. Okeana 12, 850-857 (1976) [English transl.: Izv. Acad, Sci. USSR. Atoms. Oceanic Phys. 12, (8) (1976)].
57. O.A. Godin, "An adiabatic invariant at guided sound propagation in a moving medium", Doklady Akademii Nauk 320, 204-208 (1991).
58. Yu. A. Stepanyants and A.L. Fabrikant, "Wave propagation in shear hydrodynamic flows", Uspekhi Fiz. Nauk 159, 83-123 (1989).
59. W. Möhring, "Energy flux in duct flow", J. Sound Vibr. 18, 101-109(1971).
60. W. Möhring, "Modelling low Mach number noise", in: Mechanics of Sound Generation in Flows, E.-A. Müller, ed., Springer, Berlin 85-96 (1979).