Using a partial-wave method for sound-mean-flow scattering problems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 3 2, 2003, Pages

  Berthet, R ^a   Coste, C ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b GPS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC FIELDS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; ELECTROMAGNETISM; FOURIER TRANSFORMS; ORDINARY DIFFERENTIAL EQUATIONS; QUANTUM THEORY; RAY TRACING; VORTEX FLOW; WAVE EQUATIONS; WAVEFRONTS;

BORN APPROXIMATION; PARTIAL-WAVE METHOD; SOUND-MEAN-FLOW INTERACTION; SOUND-VORTICAL-FLOW INTERACTION; VORTICAL FLOW; WAVE FRONT DISLOCATION;

ACOUSTIC WAVE SCATTERING;

EID: 42749106708     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (63)

1. I.G. Jonsson, in Wave-Current Interactions, edited by B. Le Mehaute and M. H. Hanes, Ocean Engineering Science, The Sea Vol. 9A (Wiley, New York, 1990), pp. 65-120.
2. L.M.B.C. Campos, Rev. Mod. Phys. 58, 117 (1986).
3. A.M. Obukhov, Waves Random Media 4, 9 (1994).
4. D. Sheres and K.E. Kenyon, Int. J. Remote Sens. 11, 27 (1990).
5. M. Karweit, P. Blanc-Benon, D. Juvé, and G. Comte-Bellot, J. Acoust. Soc. Am. 89, 52 (1991).
6. V.E. Ostashev, V. Mellert, R. Wandand, and F. Gerdes, J. Acoust. Soc. Am. 102, 2561 (1997).
7. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, New York, 1978).
8. V.A. Polyanskaya, Akust. Zh. 31, 698 (1985). [Sov. Phys. Acoust. 31, 376 (1985)].
9. D. Blokhintzev, J. Acoust. Soc. Am. 18, 322 (1946).
10. E.T. Kornhauser, J. Acoust. Soc. Am. 25, 945 (1953).
11. T.M. Georges, J. Acoust. Soc. Am. 51, 206 (1972).
12. E.G. Broadbent, J. Inst. Math. Appl. 19, 1 (1977).
13. J. Lighthill, ICASE Report No. 92-52, 1992 (unpublished).
14. D.S. Jones, Philos. Trans. R. Soc. London, Ser. A 255, 341 (1963).
15. T. Colonius, S.K. Lele, and P. Moin, J. Fluid Mech. 260, 271 (1994).
16. S.M. Candel, J. Fluid Mech. 83, 465 (1977).
17. M. Mathiesen, J. Geophys. Res. 92, 3905 (1987).
18. R.H. Kraichnan, J. Acoust. Soc. Am. 25, 1096 (1953).
19. A.L. Fabrikant, Akust. Zh. 29, 262 (1983) [Sov. Phys. Acoust. 29, 152 (1983)].
20. F. Lund and C. Rojas, Physica D 37, 508 (1989).
21. A.L. Fetter, Phys. Rev. 136, 1488 (1964).
22. J. Reinschke, W. Möhring, and F. Obermeier, J. Fluid Mech. 333, 273 (1997).
23. M. Umeki and F. Lund, Fluid Dyn. Res. 21, 201 (1997).
24. G.M. Golemshtok and A.L. Fabrikant, Akust. Zh. 26, 383 (1980) [Sov. Phys. Acoust. 26, 209 (1980)].
25. A.M. Obukhov, C. R. (Dokl.) Acad. Sci. URSS 30, 616 (1941).
26. M.J. Lightill, Proc. R. Soc. London, Ser. A 211, 564 (1952).
27. L. Landau and E. Lifchitz, Mécanique des Fluides, 2nd ed. Cours de Physique Thérique, Vol. 6 (Éditions Mir, Moscou, 1989), Sec. 12.
28. C. Coste, F. Lund, and M. Umeki, Phys. Rev. E 60, 4908 (1999).
29. J.D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
30. J.R. Taylor, Scattering Theory: The Quantum Theory on Non-relativistic Collisions (Wiley, New York, 1972).
31. P. Roux, J. de Rosny, M. Tanter, and M. Fink, Phys. Rev. Lett. 79, 3170 (1997).
32. R. Labbé and J.F. Pinton, Phys. Rev. Lett. 81, 1413 (1998).
33. S. Manneville, J.H. Robres, A. Maurel, P. Petitjeans, and M. Fink, Phys. Fluids 11, 3380 (1999).
34. M.V. Berry, R.G. Chambers, M.D. Large, C. Upstill, and J.C. Walmsley, Eur. J. Phys. 1, 154 (1980).
35. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
36. S. Olariu and I.I. Popescu, Rev. Mod. Phys. 57, 339 (1985).
37. F. Vivanco, F. Melo, C. Coste, and F. Lund, Phys. Rev. Lett. 10, 1966 (1999).
38. R. Berthet, S. Fauve, and R. Labbé, Eur. Phys. J. B. (to be published).
39. It should be noticed that this decomposition is not valid in a narrow cone around the forward direction [36].
40. P.M. Morse and K.U. Ingard, Theoretical Acoustics (Princeton University Press, Princeton, 1986).
41. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic Press, New York, 1994).
42. R.G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, New York, 1982).
43. L. Landau and E. Lifchitz, Mécanique Quantique, 3rd ed. Cours de Physique Théorique, Vol. 3 (Editions Mir, Moscow, 1988), Sec. 123.
44. D. Boyer, M. Baffico, and F. Lund, Phys. Fluids 11, 3819 (1999).
45. V.V. Klimov and V.L. Prozorovskii, Akust. Zh. 33, 128 (1987) [Sov. Phys. Acoust. 1, 79 (1987)].
46. R. Berthet and F. Lund, Phys. Fluids 7, 2522 (1995).
47. R. Bernal, C. Coste, F. Lund, and F. Melo, Phys. Rev. Lett. 89, 034501 (2002).
48. R. Berthet, Ph.D. thesis École Normale Supérieure de Lyon, France, 2001 (unpublished).
49. R. Berthet, D. Astruc, and S. Fauve (unpublished).
50. J.H. Ferziger, J. Acoust. Soc. Am. 56, 1705 (1974).
51. R. Ford and S.G. Llewellyn Smith, J. Fluid Mech. 386, 305 (1999).
52. A.K. Bose, Nuovo Cimento 32, 679 (1964).
53. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).
54. W.J. Wiscombe, Appl. Opt. 19, 1505 (1980).
55. P.R. Gromov, A.B. Ezerskii, and A.L. Fabrikant, Akust. Zh. 28, 763 (1982) [Sov. Phys. Acoust. 28, 452 (1982)].
56. C. Baudet, S. Ciliberto, and J.F. Pinton, Phys. Rev. Lett. 67, 193 (1991).
57. A.B. Ezerskii, P.L. Soustov, and V. V Chernov, Acoust. Phys. 46, 670 (2000).
58. R. Berthet, D. Astruc, and J.L. Estivalézes, in Proceedings of The Sixth AIAA/CEAS Aeroacoustics Conference, 2000 (unpublished).
59. R. Berthet and D. Astruc (unpublished). (Other details on the numerical simulation can be found in Ref. [48]).
60. inc includes the near-field interference pattern. it is an important advantage of the PW approach compared to usual Born approximation, and we hope that the reader will not be confused by this slight misuse of term.
61. Zhi-Yu Gu and Shang-Wu Qian, J. Phys. A 21, 2573 (1988).
62. B. Dernoncourt, J.-F. Pinton, and S. Fauve, Physica D 117, 181 (1998).
63. K. Oljaca, X. Gu, A. Glezer, M. Baffico, and F. Lund, Phys. Fluids 10, 886 (1998).