High-frequency acoustic scattering from prolate spheroids with high aspect ratio
The problems of high-frequency scattering by prolate soft and hard spheroids with high aspect ratio are studied. The asymptotics of the diffracted field and the far field amplitude are derived under the assumption that the spheroid is strongly elongated; that is, the ratio of its length measured in wavelengths to the square of its transverse wave size is on the order of unity. This ratio is presented as a parameter in all the asymptotic formulas, namely, in the asymptotics of the forward diffracted wave, the wave that is formed when forward wave "reflects" from the spheroid end, in the asymptotics of the far field amplitude, and effective cross-section. If this ratio tends to zero, the asymptotic formulas turn into classical. On the basis of the derived asymptotic formulas, the effects of the degree of elongation and the angle of incidence on the diffracted and scattered fields are analyzed. Comparison with some test examples allows one to expect good approximating properties of the presented asymptotic formulas.