Quadratic cross-sections in the multiple scattering by a pair of liquid cylinders insonified by arbitrary-shaped acoustical sheets

Stemming from the law of energy conservation applied to scattering, generalized exact partialwave series expressions are derived for the extrinsic and intrinsic acoustic scattering, extinction and absorption cross-sections for a pair of fluid/liquid-like (viscous) cylinders of arbitrary radii. The incident insonifying field is of arbitrary shape such that any structured wavefront in two-dimensions is accomodated by this formalism, in contrast with the case of plane waves. The modal expansion method in combination with the translational addition theorem for cylindrical wave functions are used to derive the exact analytical expressions for the quadratic (nonlinear) cross-sections, and numerical computations for a non-paraxial focused Gaussian acoustical sheet chosen as an example illustrate the analysis. The results clearly show the difference between the behavior of the extrinsic and intrinsic cross-sections. The formalism presented here is generalized for any acoustical sheet such that Airy, Hermite-Gaussian and other wavefronts (in 2D) can be considered provided the appropriate beam-shape coefficients are used. The analogy with the optical counterpart is also noted.

Automated summary

This study derives exact expressions for the acoustic scattering, extinction, and absorption cross-sections of a pair of fluid/liquid cylinders, accommodating arbitrary incident insonifying field shapes and illustrating the differences between extrinsic and intrinsic cross-section behaviors. The formalism is generalized for any acoustical sheet with consideration for various wavefronts, and an analogy with optics is noted.