Sound scattering by an air bubble near a plane sea surface

Abstract

This paper presents a study of low-frequency sound scattering by an air bubble near a flat pressure-release surface. Using a self-consistent approach to describe multiple-scattering interactions, and a monopole approximation for the individual scatterer, the complete scattering amplitude for a bubble near a surface is derived. Radiation, thermal, and viscous damping effects are incorporated. The method leads to simple theoretical expressions which show that the presence of the surface modifies the resonance frequency and damping of the bubble, and modulates the scattering amplitude. The analytic formula for the modified resonance frequency compares favorably with earlier theoretical results, and with experimental data reported by M. Strasberg [J. Acoust. Soc. Am. 25, 536–537 (1953)]. At off-resonance frequencies, when the bubble is close to the surface and thermal and viscous dampings are not included, the results obtained agree with those of the modal series solution presented by Gaunaurd and Huang [IEEE J. Ocean. Eng. 20, 285–295 (1995)]. The two methods disagree at resonance frequencies, however, since the present approach predicts that the value of the scattering amplitude should decrease as the bubble is moved closer to the surface. This feature remains even when thermal and viscous dampings are not included. When the bubble is moved further away from the surface, oscillations appear in the scattering amplitude, in full accordance with the Lloyd’s mirror effect.