DYNAMICS OF BUBBLE OSCILLATION AND PRESSURE PERTURBATION IN AN EXTERNAL MEAN FLOW

Abstract

The effects of the external mean flow on the bubble response to changes in the ambient pressure distribution are examined. The analysis of finite-amplitude shape oscillations of a constant-volume bubble in an arbitrary mean flow shows that a monopole pressure disturbance in the far-field can occur due only to the interaction between a disturbance flow associated with the shape oscillations and a special type of ambient flow. The result is independent of the degree of deformation and remains valid for any type of ambient pressure fluctuation that creates shape oscillations. Then, we specialize the problem to consider the nonlinear oscillation dynamics of a bubble in the presence of a uniaxial straining flow. In this case, the source of oscillations is a spatially inhomogeneous 'abrupt' change in the ambient pressure. The method of solution employed here is a domain perturbation in conjunction with a two timing analysis to examine small-amplitude oscillations of bubble shape relative to the non-spherical steady-state configuration in the ambient mean flow. The result shows that the ambient flow can interact directly with a mode of bubble deformation and produces a self-induced secularity that leads to a modification of the oscillation frequency. In addition, the disturbance pressure caused by shape oscillations exhibits at most a quadrupole character at large distances from the constant-volume bubble.