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arXiv · 1009.5642

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

Andrew N. Norris·Jean-Marc Conoir
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Abstract

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 ($n_0 $) of scatterers, in this paper the higher order dependence of the coherent wavenumber on $n_0$ 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 $n_0$, to higher orders. Explicit formulas are provided for corrections to the effective wavenumber up to O$(n_0^4)$. 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 some other approaches.

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Andrew N. Norris, Jean-Marc Conoir. 2010-09-28. Multiple scattering by cylinders immersed in fluid: high order approximations for the effective wavenumbers. https://doi.org/10.1121/1.3504711

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