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Rough Surface Scattering and the Kirchhoff Approximation

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Abstract

Most approximate solutions to surface scattering begin with the Kirchhoff approximation to the unknown surface field. The validity of the Kirchhoff approximation is tested in this paper by the use of exact solutions for scattering from a pressure release sinusoid. Rough surfaces are expressed in a Fourier Series, and series solutions for small Rayleigh parameter are derived. The first order series term of Holford, Uretsky and Rayleigh are shown to be identical. Surface radiation patterns for shallow grazing angles are examined and conclusions are drawn on the region of validity of the Kirchhoff approximation.

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References

  1. W. C. Meecham, “On the Use of the Kirchhoff Approximation for the Solution of Reflection Problems,” J. Ration. Mech. Anal. 5, 323–333 (1956).

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  2. R. L. Holford, “Scattering of Sound Waves at a Periodic Pressure-Release Surface: An Exact Solution,” J. Acoust. Soc. Am. 70, 1116–1128 (1981).

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  3. Lord Rayleigh, Theory of Sound, Dover Publications, New York, 2, 89–96 (1945).

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  4. J. L. Uretsky, “The Scattering of Plane Waves From Periodic Surfaces,” Amn. Phys. 33, 400–427 (1965).

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  5. W. T. Pierson, “The Theory and applications of ocean wave measuring system at and below the sea surface, on the land, from aircraft and from spacecraft,” NASA Contract Rep CR-2646 NASA, Washington, DC, 305–308 (1976).

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Author information

Authors and Affiliations

  1. Applied Research Laboratory, The Pennsylvania State University, P.O. Box 30, State College, PA, 16804, USA

    Diana F. McCammon & Suzanne T. McDaniel

Authors
  1. Diana F. McCammon
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  2. Suzanne T. McDaniel
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Editor information

Editors and Affiliations

  1. Defence Research Establishment Atlantic, Dartmouth, Nova Scotia, Canada

    Harold M. Merklinger

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© 1987 Plenum Press, New York

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McCammon, D.F., McDaniel, S.T. (1987). Rough Surface Scattering and the Kirchhoff Approximation. In: Merklinger, H.M. (eds) Progress in Underwater Acoustics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1871-2_7

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  • DOI: https://doi.org/10.1007/978-1-4613-1871-2_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-9043-8

  • Online ISBN: 978-1-4613-1871-2

  • eBook Packages: Springer Book Archive

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