Multiple scattering by cylinders immersed in fluid: high order approximations for the effective wavenumbers

Acoustic wave propagation in a fluid with a random assortment of identical cylindrical scatterers is considered. While the leading order correction to the effective wavenumber of the coherent wave is well established at dilute areal density (n0) of scatterers, in this paper the higher order dependen...

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Bibliographic Details
Published inThe Journal of the Acoustical Society of America Vol. 129; no. 1; p. 104
Main Authors Norris, Andrew N, Conoir, Jean-Marc
Format Journal Article
LanguageEnglish
Published United States 01.01.2011
Subjects
Acoustics
Models, Theoretical
Motion
Solutions
Sound
Time Factors
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Summary:Acoustic wave propagation in a fluid with a random assortment of identical cylindrical scatterers is considered. While the leading order correction to the effective wavenumber of the coherent wave is well established at dilute areal density (n0) of scatterers, in this paper the higher order dependence of the coherent wavenumber on n0 is developed in several directions. Starting from the quasi-crystalline approximation (QCA) a consistent method is described for continuing the Linton and Martin formula, which is second order in n0, to higher orders. Explicit formulas are provided for corrections to the effective wavenumber up to O (n0(4)). Then, using the QCA theory as a basis, generalized self-consistent schemes are developed and compared with self-consistent schemes using other dynamic effective medium theories. It is shown that the Linton and Martin formula provides a closed self-consistent scheme, unlike other approaches.
ISSN:1520-8524
DOI:10.1121/1.3504711