A two-dimensional bubble near a free surface

A boundary integral technique is used in conjunction with a conformal map to examine the motion of a two-dimensional bubble near a free surface. For small times, the results are shown to compare well with a first-order perturbation expansion for the problem of the response of a free surface to a deeply submerged dipole. For a large bubble, far from the free surface the bubble deformation is found to agree with previous theoretical and experimental results for a two-dimensional bubble in an infinite fluid.