Acoustic scattering by an air-bubble near the sea surface

If the air bubble is near, and strongly interacting, with the (flat) surface of a liquid half-space, then the scattering cross section (SCS) of the bubble differs substantially from its value far-away from the interface. We present the exact solution for this scattering problem which is valid for any incidence direction of the (plane) sound waves, and for any bubble depth, obtained by the general method of images. The bubble is described as a continuous, spatially extended body, having an infinity of modes and resonances. The interaction with the boundary, or the image, is treated by a general, extended continuum approach. This benchmark solution makes use of the addition theorems for the spherical wavefunctions. The resulting SCS contains contributions from the bubble, its image, the incident wave, and the reflected wave from the boundary. It is expressed in terms of coupling coefficients, b_mn, which contain products of Wigner-3j symbols. The formulation is illustrated with many computed plots for bubbles at various depths, and the results compare favorably with earlier experimental observations. The approach also serves to describe scattering by fish near the sea surface, in an exact fashion