Superspheroidal modeling of resonance scattering from elongated air bubbles and fish swim bladders

The extended boundary condition technique of Waterman [J. Acoust. Soc. Am. 45, 1417-1429 (1969)] has been used to make accurate studies of the frequency and azimuthal scattering distributions from extended axisymmetric acoustic objects. These objects are formed using the mathematical function for a "superellipse" [i.e., (x/a)(s) + z/b)(s) = 1, where s = 2n, n = 1,2,[ellipsis (horizontal)]], and revolving around the z-axis. For s = 2, the object is a spheroid with aspect ratio α = b/a. As s increases, the shape of the object approaches a right circular cylinder of diameter 2a and length 2b. The method is applied to the case of prolate (i.e., α > 1) air-filled objects in water, which has importance for the interpretation of acoustic scattering from oceanic objects such as air-bubbles, the swim bladders of some fish, and zooplankton. It is found that the resonance frequency increases with α, essentially as predicted using a different method by Weston, and increases in a relatively minor way with s. The resonance peak amplitude, and Q, are also more sensitive to changes in α, than s. The method shows that the monopole resonance continues to dominate low frequency scattering, leading to an almost spherically symmetric azimuthal scattering distribution, even for elongated, cylindrical, air-filled, objects with an aspect ratio up to α = 20, and s = 32.