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Numerical solution of wave scattering problems in the parabolic approximation

Published online by Cambridge University Press:  19 April 2006

Sébastien M. Candel
Sébastien M. Candel
Affiliation:
Office National d'Etudes et de Recherches Aérospatiales (ONERA) and Université de Technologie de Compiègne, 92320 Châtillon, France
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Abstract

A numerical analysis of two-dimensional wave scattering problems is performed. The treatment relies on the parabolic approximation and provides the forward scattered wave field. Two problems are considered in particular: (i) the scattering of plane waves by a cylindrical inhomogeneity of uniform refraction index, (ii) the scattering of plane waves by a viscous core vortex. The structure of the scattered field is examined in detail and the numerical solutions of the two problems are compared to analytical results obtained in the Born approximation and interpreted according to the method of smooth perturbation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 3 , 13 February 1979 , pp. 465 - 507
Copyright
© 1979 Cambridge University Press

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References

Abramovitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Baerg, W. & Schwarz, W. H. 1966 Measurement of the scattering of sound from the turbulence. J. Acoust. Soc. Am. 39, 1125.Google Scholar
Barabanenkov, Yu. N., Kravtsov, Yu. A., Rytov, S. M. & Tatakski, V. I. 1971 Status of the theory of propagation of waves in a randomly inhomogeneous medium. Sov. Phys. 13, 551.Google Scholar
Brown, G. & Roshko, A. 1974 On density effect and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775.Google Scholar
Butler, G. F., Holbeche, T. A. & Fethney, P. 1973 Some experimental observations of the refraction of sound by a rotating flow. AGARD Conf. Proc. no. 131, p. 91.Google Scholar
Candel, S. M. 1976 Application of geometrical techniques to aeroacoustic problems. A.I.A.A. Paper no. 76–546.Google Scholar
Candel, S. M. 1977 Résolution numérique de problèmes de propagation et de rayonnement à l'aide de l'approximation parabolique. Univ. Tech. Compiègne Tech. Rep. no. 5–1978.Google Scholar
Candel, S. M., Guédel, A. & Julienne, A. 1975 Refraction and scattering in an open wind tunnel flow. Proc. 6th Int. Cong. Instrumentation in Aerospace Simulation Facilities, Ottawa, p. 288.
Candel, S. M., Guédel, A. & Julienne, A. 1976a Résultats préliminaires sur la diffusion d'une onde acoustique par un écoulement turbulent. Cong. Soc. FranÇaise Phys. Dijon 1975. J. de Physique 37, C1–153.Google Scholar
Candel, S. M., Guédel, A. & Julienne, A. 1976b Radiation refraction and scattering of acoustic waves in a free shear flow. A.I.A.A. Paper no. 76–544.Google Scholar
Candel, S. M., Guédel, A. & Julienne, A. 1977 Diffusion d'une onde monochromatique par un écoulement turbulent. Euromech 94: Propagation des Ondes dans les Milieux Inhomogènes, Marseille.Google Scholar
Candel, S. M., Julienne, A. & Julliand, M. 1976 Shielding and scattering by a jet flow. A.I.A.A. Paper no. 76–545.Google Scholar
Claerbout, J. F. 1976 Fundamentals of Geophysical Data Processing. McGraw-Hill.
Clifford, S. F. 1972 Propagation and scattering in random media. In Remote Sensing of the Troposphere (ed. V. E. Derr). University of Colorado, Boulder.
Clifford, S. F. & Brown, E. H. 1970 Propagation of sound in a turbulent atmosphere. J. Acoust. Soc. Am. 48, 1123.Google Scholar
De Santo, J. A., Perkins, J. S. & Baer, J. N. 1977 Corrections to the parabolic equation for sound propagation modelling. J. Acoust. Soc. Am. 61, S 12(A).Google Scholar
Dowdling, A. P. 1975 The refraction of sound by a shear layer made up of discrete vortices. Aero. Res. Counc. R. & M. no. 3770.Google Scholar
Ferziger, J. H. 1974 Low frequency acoustic scattering from a trailing vortex. J. Acoust. Soc. Am. 56, 1705.Google Scholar
Ffowcs Williams, J. E. & Howe, M. S. 1973 On the possibility of turbulent thickening of weak shock waves. J. Fluid Mech. 58, 461.Google Scholar
Frisch, U. 1968 Wave propagation in random media. In Probabilistic Methods in Applied Mathematics, vol. 1 (ed. A. T. Barucha Reid). Academic Press.
Gans, R. 1925 Ann. Phys. 76, 29.
Georges, T. M. 1972 Acoustic ray paths through a model vortex. J. Acoust. Soc. Am. 51, 206.Google Scholar
Hardin, R. H. & Tappert, F. D. 1973 Application of the split step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations. SIAM Rev. 15, 423.Google Scholar
Howe, M. S. 1973 Multiple scattering of sound by turbulence and other inhomogeneities. J. Sound Vib. 27, 455.Google Scholar
Huang, M. N. 1975 Sound scattering from atmospheric turbulence. A.I.A.A. Paper no. 75–544.Google Scholar
Ishimaru, A. 1977 Theory and application of wave propagation and scattering in random media. Proc. I.E.E.E. 65, 1030.Google Scholar
Jones, D. S. 1964 The Theory of Electromagnetism. Pergamon.
Kelley, P. L. 1965 Self focusing of optical beams. Phys. Rev. Lett. 15, 1005.Google Scholar
Lau, J. C. & Fisher, M. J. 1975 The vortex sheet structure of turbulent jets. Part 1. J. Fluid Mech. 67, 299.Google Scholar
Legendre, R. 1968 Interprétation des mesures de turbulence. ONERA Tech. Note no. 138.Google Scholar
Lighthill, M. J. 1953 On energy scattered from the interaction of turbulence with sound or shock waves. Proc. Camb. Phil. Soc. 49, 531.Google Scholar
Lilly, J. Q. & Miller, T. G. 1977 Target intensity enhancement for repetitively pulsed laser beams. A.I.A.A. J. 15, 434.Google Scholar
McDaniel, S. T. 1975 Propagation of normal mode in the parabolic approximation. J. Acoust. Soc. Am. 57, 307.Google Scholar
McDaniel, S. T. 1976 J. Acoust. Soc. Am. 58, 1178.
Monin, A. S. 1962 Characteristics of the scattering of sound in a turbulent atmosphere. Sov. Phys. Acoust. 7, 370.Google Scholar
Muller, E. A. & Matschat, K. R. 1959 The scattering of sound by a single vortex and by turbulence. Max-Planck-Institut für Strömungsforschung Technical Report, Göttingen.
O'Shea, S. 1975 Sound scattering by a potential vortex. J. Sound Vib. 43, 109.Google Scholar
Rayleigh, Lord 1881 Phil. Mag. 12, 81.
Roshiko, A. 1976 Structure of turbulent shear flows: a new look. A.I.A.A. J. 14, 1349.Google Scholar
Tatarski, V. I. 1961 Wave Propagation in a Turbulent Medium. Dover.
Tatarski, V. I. 1971 The Effects of the Turbulent Atmosphere on Wave Propagation. Israel Program of Scientific Translations, Jerusalem.
Ulrich, P. B. 1975 Numerical methods in high power laser propagation. In Optical Propagation in the Atmosphere. AGARD Conf. Proc. no. 183.
Wallace, J. & Lilly, J. Q. 1974 Thermal blooming of repetitively pulsed laser beams. J. Opt. Soc. Am. 64, 1651.Google Scholar
Watson, G. N. 1962 Theory of Bessel functions, 2nd edn. Cambridge University Press.
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing layer growth at moderate Reynolds numbers. J. Fluid Mech. 61, 237.Google Scholar
Woude, P. V. D. & Bremmer, H. 1975 Expansions applicable to a non-stationary scattering medium. Radio Sci. 10, 23.Google Scholar