An integrated wave-effects model for an underwater explosion bubble.

A model for a moderately deep underwater explosion bubble is developed that integrates the shock wave and oscillation phases of the motion. A hyperacoustic relationship is formulated that relates bubble volume acceleration to far-field pressure profile during the shock-wave phase, thereby providing initial conditions for the subsequent oscillation phase. For the latter, equations for bubble-surface response are derived that include wave effects in both the external liquid and the internal gas. The equations are then specialized to the case of a spherical bubble, and bubble-surface displacement histories are calculated for dilational and translational motion. Agreement between these histories and experimental data is found to be substantially better than that produced by previous models.