Coupled Oscillations of Spherical Gas Bubbles

The dynamics of several (two, three and four) interacting spherical gas bubbles are investigated using the method of multiple scale. Numerical solutions for the steady-state amplitudes and phases of systems of two and four bubbles are presented. An interesting phenomenon observed is that of nonlinear localization, wherein vibrational energy becomes spatially localized to a single bubble (strong localization) or to a subset of bubbles (weak localization). Moreover, it is shown that the spatially extended motion (wherein all bubbles oscillate with identical amplitudes and phases, which one would obtain based upon a linearized analysis) is unstable, and thus not physically realizable, for certain separation distances.