Glory- and rainbow-enhanced acoustic backscattering from fluid spheres: Models for diffracted axial focusing

Transmitted-wave contributions to backscattering from large spheres are calculated. Amplitudes due to glory rays are enhanced, relative to those of axial reflections, because of focusing. The glory pressure amplitudes are proportional to a(ka)1/2, where a is the sphere’s radius and k is the wavenumber. The model, though similar in form to one for optical scattering from air bubbles [D. S. Langley and P. L. Marston, Phys. Rev. Lett. 47, 913–916 (1981)], contains new features to facilitate the summing of amplitudes in a range of angles. An additional enhancement due to rainbow focusing is modeled for certain sound velocity ratios M; for these M the backscattered amplitude is proportional to a(ka)2/3. Major features of the exact scattering are reproduced by these models when ka=1000 and (with defects) ka=100. The enhancements are not intrinsically due to resonance. Applications to the design of passive sonar targets are noted.