Notes on Rayleigh's hypothesis and the extended boundary condition method

Tom Rother*, Stuart C. Hawkins

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Regarding wave scattering on a three-dimensional nonspherical obstacle, the Rayleigh hypothesis states that the scattered field can be expanded everywhere outside the obstacle using only outgoing eigensolutions of the underlying Helmholtz equation. However, the correctness of this assumption has not yet been finally clarified, although it is important for the near-field analysis of scattering processes and for multiple scattering. To circumvent this uncertainty, Waterman introduced the extended boundary condition to develop his T-matrix method. This approach leads to the restriction that, when modeling multiple scattering processes using this T-matrix, the smallest circumscribing spheres of the individual obstacles must not overlap. The purpose of this paper is to provide a justification of the correctness of Rayleigh's hypothesis and clarify its implications for modeling multiple scattering. We show that Waterman's T-matrix can in fact be used inside the critical region between the surface of the obstacle and its smallest circumscribing sphere to represent the near-field and that one does not necessarily have to exclude an overlap of these spheres in the multiple scattering modeling. The theoretical considerations in the first part of this paper are supplemented by a numerical study of a benchmark configuration for multiple scattering in the last part.

    Original languageEnglish
    Pages (from-to)2179-2188
    Number of pages10
    JournalJournal of the Acoustical Society of America
    Volume149
    Issue number4
    DOIs
    Publication statusPublished - Apr 2021

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