Scattering from superspheroidal acoustic objects

The extended boundary condition technique of Waterman [J. Acoust. Soc. Am. 45, 1417–1429 (1969)] has been used to study scattering from extended axisymmetric acoustic objects. These objects are formed using the mathematical function for a “super-ellipse” [i.e., (x/a)s + (z/b)s=1, where s=2n, n=1, 2, 3,…] 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 radius a and length 2b. The method allows the scattered field to be accurately determined for all azimuthal angles as a function of frequency. The method is applied to the case of 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 frequency increases with α, exactly as predicted using a geometrical method by Weston, and increases in a relatively minor way with $s$. In addition, the method shows that the monopole resonance, which leads to a spherically symmetric scattering distribution, continues to dominate low-frequency scattering even for cylindrically shaped, air-filled objects with an aspect ratio up to α=40 and s=32.