Attenuation of underwater sound through stationary arrays of large tethered encapsulated bubbles

The ultimate goal of this work was to accurately predict attenuation from large tethered encapsulated bubbles used in an underwater noise abatement system. Measurements of underwater sound attenuation were obtained during a set of lake experiments, where a low-frequency sound source was surrounded by different arrays of encapsulated bubbles with various individual bubbles sizes and void fractions, and compared with an existing predictive model by Church [J. Acoust. Soc. Am. vol. 7, 1510-521 (1995)] for the dispersion relation in liquid containing encapsulated bubbles. Although Church's model was originally intended to describe ultrasound contrast agents, it was evaluated here for large bubbles (on the order of 10 cm) and fairly good quantitative agreement between the data and the model was observed. A modification of Church's model was made by combining it with Kargl's model [J. Acoust. Soc. Am. vol. 111, 168-173 (2002)], attempting to incorporate multiple scattering effects, which may be important at high void fractions. However, a comparison with the data indicates that the Church-Kargl hybrid as implemented here may overcompensate for these effects. These results indicate that Church's model is sufficient for use as a design tool for tethered encapsulated bubble screens with void fractions less than 2%.