  The interaction of multiple bubbles is a complex physical problem. A
simplified case of multiple bubbles is studied theoretically with a bubble
located at the center of a circular bubble cluster. All bubbles in the cluster
are equally spaced and own the same initial conditions as the central bubble.
The unified theory for bubble dynamics (Zhang et al. arXiv:2301.13698) is
applied to model the interaction between the central bubble and the circular
bubble cluster. To account for the effect of the propagation time of pressure
waves, the emission source of the wave is obtained by interpolating the
physical information on the time axis. An underwater explosion experiment with
two bubbles of different scales is used to validate the theoretical model. The
effect of the bubble cluster with a variation in scale on the pulsation
characteristics of the central bubble is studied.
