Differences between sound scattering by weakly scattering spheres and finite-length cylinders with applications to sound scattering by zooplankton

Abstract

A modeling study was conducted to determine the conditions under which fluidlike zooplankton of the same volume but different shapes (spherical/cylindrical) have similar or dramatically different scattering properties. Models of sound scattering by weakly scattering spheres and cylinders of finite length used in this analysis were either taken from other papers or derived and herein adapted for direct comparison over a range of conditions. The models were examined in the very low- (ka ≪ 1, kL ≪ 1), moderately low- (ka ≪ 1, kL ≳ 1), and high-frequency regions (ka ≫ 1, kL ≫ 1), where k is the acoustic wave number, a is the radius (spherical or cylindrical) of the body, and L is the length of the cylinders (for an elongated body with L/a = 10, "moderately low" corresponds to the range 0.1 ≲ ka ≲ 0.5). Straight and bent cylinder models were evaluated for broadside incidence, end-on incidence, and averages over various distributions of angle of orientation. The results show that for very low frequencies and for certain distributions of orientation angles at high frequencies, the averaged scattering by cylinders will be similar, if not identical, to the scattering by spheres of the same volume. Other orientation distributions of the cylinders at high frequencies produce markedly different results. Furthermore, over a wide range of orientation distributions the scattering by spheres is dramatically different from that of the cylinders in the moderately low-frequency region and in the Rayleigh/geometric transition region: (1) the Rayleigh to geometric scattering turning point occurs at different points for the two cases when the bodies are constrained to have the same volume and (2) the functional dependence of the scattering levels upon the volume of the bodies in the moderately low-frequency region is quite often different between the spheres and cylinders because of the fact that the scattering by the cylinders is still directional in this region. The study demonstrates that there are indeed conditions under which different shaped zooplankton of the same volume will yield similar (ensemble average) scattering levels, but generally the shape and orientation distribution of the elongated bodies must be taken into account for accurate predictions.