Acoustic scattering by an air-bubble near the sea surfaceacoustic scattering by an air-bubble near the sea surface

Abstract

Sound scattering by and air bubble in a boundless fluid is an old classical problem (19). 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 no longer assumed to be a point simple, harmonic, radially pulsating oscillator, but is described as a continuous, spatially extended body, having an infinity of modes and resonances. The interaction with the boundary, or the image is not treated by means of the simple Lloy's mirror formula for point source ( or scatterers), but 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 invident wave, and the reflected wave from the boundary. It is expressed in terms of coupling coefficients, bmn, products of Wigner-3j simbols. The formulations in 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. Acoustic scattering by near-surface bubbles also has many other applications such as in the improvement of the performance of sensor that must operate through hubby media, and in the understanding of its connection with approaches to model oceanic fluxes.