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

Rother, Tom and Hawkins, Stuart C. (2021) Notes on Rayleigh's hypothesis and the extended boundary condition method. Journal of the Acoustical Society of America (149), pp. 2179-2188. Acoustical Society of America. doi: 10.1121/10.0003958. ISSN 0001-4966.

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Official URL: https://doi.org/10.1121/10.0003958


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.

Item URL in elib:https://elib.dlr.de/141692/
Document Type:Article
Title:Notes on Rayleigh's hypothesis and the extended boundary condition method
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Rother, TomTom.Rother (at) dlr.deUNSPECIFIED
Hawkins, Stuart C.Department of Mathematics and Statistics, Macquarie UniversityUNSPECIFIED
Date:April 2021
Journal or Publication Title:Journal of the Acoustical Society of America
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.1121/10.0003958
Page Range:pp. 2179-2188
Publisher:Acoustical Society of America
Keywords:Rayleigh hypothesis, extended boundary condition, T-matrix, scattering
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Earth Observation
DLR - Research area:Raumfahrt
DLR - Program:R EO - Earth Observation
DLR - Research theme (Project):R - Atmospheric and climate research
Location: Neustrelitz , Oberpfaffenhofen
Institutes and Institutions:Remote Sensing Technology Institute > Atmospheric Processors
Deposited By: Rother, Dr.rer.nat. Tom
Deposited On:08 Apr 2021 10:46
Last Modified:24 May 2022 23:47

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