Bubble oscillations of large amplitude

Abstract

A new equation is derived for large amplitude forced radial oscillations of a bubble in an incident sound field. It includes the effects of acoustic radiation, as in Keller and Kolodner’s equation, and the effects of viscosity and surface tension, as in the modified Rayleigh equation due to Plesset, Noltingk and Neppiras, and Poritsky. The free and forced periodic solutions are computed numerically. For large bubbles, such as underwater explosion bubbles, the free oscillations agree with those obtained by Keller and Kolodner. For small bubbles, such as cavitation bubbles, with small or intermediate forcing amplitudes, the results agree with those calculated by Lauterborn from the modified Rayleigh equation of Plesset et al. For large forcing amplitudes that equation yielded unsatisfactory results whereas the new equation yields quite satisfactory ones.