Abstract

Abstract 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.

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