Stanton T K, Wiebe P H, Chu D
Department of Applied Ocean Physics and Engineering, Woods Hole Oceanographic Institution, Massachusetts 02543-1053, USA.
J Acoust Soc Am. 1998 Jan;103(1):254-64. doi: 10.1121/1.421135.
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 > or = 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 < or = ka < or = 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.
开展了一项建模研究，以确定相同体积但形状不同（球形/圆柱形）的类流体浮游动物具有相似或显著不同散射特性的条件。本分析中使用的有限长度弱散射球体和圆柱体的声散射模型，要么取自其他论文，要么进行了推导并在此处进行调整，以便在一系列条件下进行直接比较。在极低频率（ka << 1，kL << 1）、中等低频率（ka << 1，kL ≥ 1）和高频区域（ka >> 1，kL >> 1）对模型进行了研究，其中k是声波数，a是物体的半径（球形或圆柱形），L是圆柱体的长度（对于L/a = 10的细长物体，“中等低”对应于0.1 ≤ ka ≤ 0.5的范围）。对直圆柱体和弯圆柱体模型进行了评估，评估了其宽边入射、端入射以及各种取向角分布的平均值。结果表明，在极低频率下以及在高频时某些取向角分布情况下，圆柱体的平均散射即使不完全相同，也将与相同体积球体的散射相似。圆柱体在高频时的其他取向分布会产生明显不同的结果。此外，在广泛的取向分布范围内，球体的散射与圆柱体在中等低频率区域和瑞利/几何过渡区域的散射显著不同：（1）当物体被限制为具有相同体积时，两种情况下瑞利到几何散射的转折点出现在不同点；（2）由于在该区域圆柱体的散射仍然是有方向性的，所以在中等低频率区域，散射水平对物体体积的函数依赖性在球体和圆柱体之间通常是不同的。该研究表明，确实存在相同体积但形状不同的浮游动物产生相似（总体平均）散射水平的条件，但一般来说，为了进行准确预测，必须考虑细长物体的形状和取向分布。
