Energy transfer between the shape and volume modes of a nonspherical gas bubble

Anthony A. Harkin, Tasso J. Kaper, Ali Nadim
2013 Physics of Fluids  
A model for an axisymmetric, nonspherical gas bubble immersed in an incompressible and slightly viscous liquid is derived that explicitly allows oscillation energy to be transferred back and forth between the volume mode and a single shape mode. The bubble model, which is obtained from a Lagrangian, consists of the well-known equation for an n-th order shape mode along with the Rayleigh-Plesset equation that is augmented by second order shape mode terms. The parametric stability of the shape
more » ... ity of the shape mode is analyzed for a driven bubble. It is also demonstrated how a pure shape distortion can excite volume pulsations having a frequency component of twice the Lamb frequency, and an amplitude proportional to the square of the distortion amplitude.
doi:10.1063/1.4807392 fatcat:v4udlq6uyjbtvaqoco2r66a7fi