Bubble Oscillations in the Vicinity of a Nearly Plane Free Surface

The linear oscillation frequency of a bubble in the vicinity of a distorted plane free surface is calculated by a perturbation method. The approximate expression found is compared with numerical results valid for surface deformations of arbitrary magnitude. It is found that the approximate analytical result is quite good, provided that the deformation is small compared with the depth of immersion of the bubble. It is also shown that, unless the deformation of the free surface extends to distances at least of the order of an acoustic wavelength, the ‘‘image’’ bubble has the same source strength of the real bubble so that a dipolar acoustic emission can be expected in spite of the deformation of the surface.