Acoustic scattering by periodic arrays of air-bubbles
  This paper considers acoustic scattering by and propagation through line and plane arrays of air-bubbles in liquid media. The self-consistent method is used to derive the effective scattering function of a single bubble embedded in the arrays, incorporating all multiple scattering processes. For the line case, an exact result is derived. In the plane array situation, only an approximate analytic result is possible. Numerical computations have been carried out to show the multiple scattering effects on wave scattering. It is shown that depending on the distance between bubbles the resonance peak of a single bubble can either be broadened or narrowed due to multiple scattering and it shows an oscillatory behavior as the distance changes. Meanwhile, the peak scattering amplitude is also be either enhanced or reduced. The previously predicted strong enhancement, however, is not evident. For plane arrays, the usual resonant scattering of a single bubble in absence of other bubbles can be suppressed by multiple scattering when the distance between bubbles is sufficiently small. As the distance increases, the resonant scattering starts to appear, and the resonance peak position is alternately shifted towards higher and lower values. Moreover, it is predicted that wave propagation through a plane bubble array can be significantly inhibited in a range of frequencies slightly higher than the natural frequency of a single bubble, possibly a useful feature for noise screening. The ambiguities in the previous results are pointed out. 
Zhen Ye