Propagation of acoustic waves in disordered flows composed of many vortices. I. General aspects

Physics of Fluids

Volumn 11, Issue 12, 1999, Pages 3819-3828

  Boyer, Denis ^a   Baffico, Maurizio ^a   Lund, Fernando ^a  

^a DEPARTAMENTO DE FÍSICA   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038327484     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.870241     Document Type: Article

References (61)

1. E. Siggia, "Numerical study of small-scale intermittency in three-dimensional turbulence," J. Fluid Mech. 107, 375 (1981) Z. She, E. Jackson, and S. Orszag, "Intermittent vortex structures in homogeneous isotropic turbulence," Nature 344, 226 (1990); A. Vincent and M. Meneguzzi, "The spatial structure and statistical properties of homogeneous turbulence," J. Fluid Mech. 225, 1 (1991). S. Kida and K. Ohkitani, "Spatiotemporal intermittency and instability of a forced turbulence," Phys. Fluids A 4, 1018 (1992); M. Tanaka and S. Kida, "Characterization of vortex tubes and sheets," ibid. 5, 2079 (1993).
2. E. Siggia, "Numerical study of small-scale intermittency in three-dimensional turbulence," J. Fluid Mech. 107, 375 (1981) Z. She, E. Jackson, and S. Orszag, "Intermittent vortex structures in homogeneous isotropic turbulence," Nature 344, 226 (1990); A. Vincent and M. Meneguzzi, "The spatial structure and statistical properties of homogeneous turbulence," J. Fluid Mech. 225, 1 (1991). S. Kida and K. Ohkitani, "Spatiotemporal intermittency and instability of a forced turbulence," Phys. Fluids A 4, 1018 (1992); M. Tanaka and S. Kida, "Characterization of vortex tubes and sheets," ibid. 5, 2079 (1993).
3. E. Siggia, "Numerical study of small-scale intermittency in three-dimensional turbulence," J. Fluid Mech. 107, 375 (1981) Z. She, E. Jackson, and S. Orszag, "Intermittent vortex structures in homogeneous isotropic turbulence," Nature 344, 226 (1990); A. Vincent and M. Meneguzzi, "The spatial structure and statistical properties of homogeneous turbulence," J. Fluid Mech. 225, 1 (1991). S. Kida and K. Ohkitani, "Spatiotemporal intermittency and instability of a forced turbulence," Phys. Fluids A 4, 1018 (1992); M. Tanaka and S. Kida, "Characterization of vortex tubes and sheets," ibid. 5, 2079 (1993).
4. S. Kida and K. Ohkitani, "Spatiotemporal intermittency and instability of a forced turbulence," Phys. Fluids A 4, 1018 (1992);
5. S. Kida and K. Ohkitani, "Spatiotemporal intermittency and instability of a forced turbulence," Phys. Fluids A 4, 1018 (1992); M. Tanaka and S. Kida, "Characterization of vortex tubes and sheets," ibid. 5, 2079 (1993).
6. J. Jiménez, A. A. Wray, P. G. Saffman, and R. S. Rogallo, "The structure of intense vorticity in isotropic turbulence," J. Fluid Mech. 255, 65 (1993).
7. P. Abry, S. Fauve, P. Flandrin, and C. Laroche, "Analysis of pressure fluctuations in swirling turbulent flows," J. Phys. II 4, 725 (1994).
8. S. Douady, Y. Couder, and M. E. Brachet, "Direct observation of the intermittency of intense vorticity filaments in turbulence," Phys. Rev. Lett. 67, 983 (1991); O. Cadot, S. Douady, and Y. Couder, "Characterization of the low-pressure filaments in a three-dimensional turbulent shear flow," Phys. Fluids 7, 630 (1995).
9. S. Douady, Y. Couder, and M. E. Brachet, "Direct observation of the intermittency of intense vorticity filaments in turbulence," Phys. Rev. Lett. 67, 983 (1991); O. Cadot, S. Douady, and Y. Couder, "Characterization of the low-pressure filaments in a three-dimensional turbulent shear flow," Phys. Fluids 7, 630 (1995).
10. F. Belin, J. Maurer, P. Tabeling, and H. Willaime, "Observation of intense filaments in fully developed turbulence," J. Phys. II 6, 573 (1996).
11. A. N. Kolmogorov, "The local structure of turbulence in incompressible viscous fluids at very large Reynolds numbers," C. R. Acad. Sci. URSS 30, 301 (1941).
12. U. Frisch, Turbulence (Cambridge University Press, Cambridge, 1995), Chap. 8.
13. C. Baudet, S. Ciliberto, and J.-F. Pinton, "Spectral analysis of the von Karman flow using ultrasound scattering," Phys. Rev. Lett. 67, 193 (1991).
14. M. Oljaca, X. Gu, A. Glezer, M. Baffico, and F. Lund, "Ultrasound scattering by a swirling jet," Phys. Fluids 10, 886 (1998).
15. J.-F. Pinton, C. Baudet, C. Laroche, and S. Fauve, "Ultrasound scattering by buoyancy driven flows," J. Phys. II 3, 767 (1993).
16. B. Dernoncourt, J.-F. Pinton, and S. Fauve, "Study of vorticity filaments using ultrasound scattering," Physica D 117, 181 (1998).
17. A. Petrossian and J.-F. Pinton, "Sound scattering on a turbulent, weakly heated jet," J. Phys. II 7, 801 (1997).
18. S. Fauve (private communication).
19. D. O. Riese and G. H. Wedgam, "Sound propagation in suspensions of colloidal spheres with viscous coupling," Phys. Rev. Lett. 82, 1676 (1999).
20. A. M. Obukhov, "Uber die schallstreuung in der turbulenten strömung," Dokl. Akad. Nauk SSSR 30, 616 (1941).
21. M. J. Lighthill, "On the energy scattered from the interaction of turbulence with sound or shock waves," Proc. Cambridge Philos. Soc. 49, 531 (1953).
22. R. H. Kraichnan, "The scattering of sound in a turbulent medium," J. Acoust. Soc. Am. 25, 1096 (1953).
23. T. Kambe, "Scattering of sound by a vortex system," J. Jpn. Soc. Fluid Mech. 1, 149 (1982) (in Japanese).
24. M. S. Howe, "On the scattering of sound by a vortex ring," J. Sound Vib. 87, 567 (1983).
25. A. L. Fabrikant, "Sound scattering by vortex flows," Sov. Phys. Acoust. 29, 152 (1983).
26. F. Lund and C. Rojas, "Ultrasound as a probe of turbulence," Physica D 37, 508 (1989).
27. U. Frisch, "Wave propagation in random media," in Probabilistic Methods in Applied Mathematics, edited by A. T. Bharucha-Reid (Academic, New York, 1968), Vol. 1, pp. 76-198.
28. S. M. Rytov, Y. A. Kravtzov, and V. I. Tatarskii, Principles of Statistical Radio Physics. Part 4. Wave Propagation Through Random Media (Springer, Berlin, 1989).
29. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE/OUP, New York, 1997).
30. V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971).
31. V. E. Ostashev, Acoustics in Moving Inhomogeneous Media (E & FN SPON, London, 1997).
32. M. Karweit, Ph. Blanc-Benon, D. Juvé, and G. Comte-Bellot, "Simulation of the propagation of an acoustic wave through a turbulent velocity field: A study of phase invariance," J. Acoust. Soc. Am. 89, 52 (1991).
33. E. J. Kerschen, "Acoustics," in Research Trends in Fluids Dynamics, edited by J. L. Lumley, A. Acrivos, L. G. Leal, and S. Leibovich (AIP, New York, 1996), pp. 99-128.
34. S. M. Flatte, R. Dashen, W. H. Munk, K. M. Watson, and F. Zacharaisen, Sound Transmission Through a Fluctuating Ocean (CUP, New York, 1979).
35. M. Baffico, D. Boyer, and F. Lund, "Propagation of acoustic waves through a system of many vortex rings," Phys. Rev. Lett. 80, 2590 (1998).
36. D. Boyer and F. Lund, "Propagation of acoustic waves in disordered flows composed of many vortices. II. Examples," Phys. Fluds. (1999) following paper.
37. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis in Periodic Structures, (North-Holland, Amsterdam, 1978). For more recent developments, see G. Nguetseng, "A general convergence result for a functional related to the theory of homogenization," SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 608 (1989); G. Allaire, "Homogenization and two scale convergence," ibid. 23, 1482 (1992); F. Murat, "II-Convergence," in Topics in the Mathematical Modeling of Composite Materials, edited by R. Cohn (Birkhäuser, Boston, 1994); C. Conca, J. Planchard, and M. Vanninathan, Fluids and Periodic Structures (Wiley/ Masson, Paris, 1995).
38. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis in Periodic Structures, (North-Holland, Amsterdam, 1978). For more recent developments, see G. Nguetseng, "A general convergence result for a functional related to the theory of homogenization," SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 608 (1989); G. Allaire, "Homogenization and two scale convergence," ibid. 23, 1482 (1992); F. Murat, "II-Convergence," in Topics in the Mathematical Modeling of Composite Materials, edited by R. Cohn (Birkhäuser, Boston, 1994); C. Conca, J. Planchard, and M. Vanninathan, Fluids and Periodic Structures (Wiley/ Masson, Paris, 1995).
39. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis in Periodic Structures, (North-Holland, Amsterdam, 1978). For more recent developments, see G. Nguetseng, "A general convergence result for a functional related to the theory of homogenization," SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 608 (1989); G. Allaire, "Homogenization and two scale convergence," ibid. 23, 1482 (1992); F. Murat, "II-Convergence," in Topics in the Mathematical Modeling of Composite Materials, edited by R. Cohn (Birkhäuser, Boston, 1994); C. Conca, J. Planchard, and M. Vanninathan, Fluids and Periodic Structures (Wiley/ Masson, Paris, 1995).
40. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis in Periodic Structures, (North-Holland, Amsterdam, 1978). For more recent developments, see G. Nguetseng, "A general convergence result for a functional related to the theory of homogenization," SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 608 (1989); G. Allaire, "Homogenization and two scale convergence," ibid. 23, 1482 (1992); F. Murat, "II-Convergence," in Topics in the Mathematical Modeling of Composite Materials, edited by R. Cohn (Birkhäuser, Boston, 1994); C. Conca, J. Planchard, and M. Vanninathan, Fluids and Periodic Structures (Wiley/ Masson, Paris, 1995).
41. A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis in Periodic Structures, (North-Holland, Amsterdam, 1978). For more recent developments, see G. Nguetseng, "A general convergence result for a functional related to the theory of homogenization," SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 20, 608 (1989); G. Allaire, "Homogenization and two scale convergence," ibid. 23, 1482 (1992); F. Murat, "II-Convergence," in Topics in the Mathematical Modeling of Composite Materials, edited by R. Cohn (Birkhäuser, Boston, 1994); C. Conca, J. Planchard, and M. Vanninathan, Fluids and Periodic Structures (Wiley/ Masson, Paris, 1995).
42. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, 1975), Vol. 2.
43. T. Colonius, S. K. Lee, and P. Moin, "The scattering of sound waves by a vortex: Numerical simulations and analytical solutions," J. Fluid Mech. 260, 271 (1994).
44. J. Reinschke, W. Möhring, and F. Obermeier, "Scattering of sound waves by a cylindrical vortex: A semianalytical theory," J. Fluid Mech. 333, 273 (1997).
45. M. Lesieur, Turbulence in Fluids (Kluwer Academic, Dordrecht, 1990).
46. M. J. Lighthill, "On sound generated aerodynamically. I. General theory," Proc. R. Soc. London, Ser. A 221, 564 (1952).
47. S. C. Crow, "Aerodynamic sound emission as a singular perturbation problem," Stud. Appl. Math. 49, 21 (1970).
48. W. Mohring, "On vortex sound at low Mach number," J. Fluid Mech. 85, 685 (1978).
49. T. Kambe, "Acoustic emission by vortex motions," J. Fluid Mech. 173, 643 (1986).
50. J. H. Ferziger, "Low-frequency acoustic scattering from a trailing vortex," J. Acoust. Soc. Am. 56, 1705 (1974).
51. V. V. Klimov and V. L. Prozorovskii, "Scattering of acoustic waves by three-dimensional vortex," Sov. Phys. Acoust. 33, 79 (1987).
52. P. M. Morse and K. U. Ingard, Theoretical Acoustics (Princeton University Press, Princeton, 1986).
53. 0).
54. For a liquid, the result will depend on the equation of state. In the case of water, relation (2.16) remains valid, formally replacing γ∼7. This is obtained with the Tait equation of state. See, S. Ridah, "Shock waves in water," J. Appl. Phys. 64, 152 (1988), and references therein. We thank T. Kurz for useful correspondence concerning this point.
55. More precisely, truncating (2.19) to order M coincides with Eq. (2.75) of Ref. 27 and with Eq. (26.46) of Ref. 34 when the base flow is homogeneous and there is no external forcing.
56. F. K. Karal and J. B. Keller, "Elastic, electromagnetic, and other waves in a random medium," J. Math. Phys. 5, 537 (1964).
57. R. C. Bourret, "Fiction theory of dynamical systems with noisy parameters," Can. J. Phys. 43, 619 (1965).
58. L. L. Foldy, "The multiple scattering of waves," Phys. Rev. 67, 107 (1945).
59. M. Lax, "Multiple Scattering of waves," Rev. Mod. Phys. 23, 287-310 (1951); "Multiple scattering of waves. II. The effective field in dense systems," Phys. Rev. 85, 621 (1952)
60. M. Lax, "Multiple Scattering of waves," Rev. Mod. Phys. 23, 287-310 (1951); "Multiple scattering of waves. II. The effective field in dense systems," Phys. Rev. 85, 621 (1952)
61. C. A. Condat and T. R. Kirkpatrick, "Localization of acoustic waves," in Scattering and Localization of Classical Waves in Random Media, edited by P. Sheng (World Scientific, Singapore, 1990), pp. 423-540.