Dynamics and acoustics of a spherical bubble rising under gravity in an inviscid liquid

The rising motion and the acoustic emission of a pulsating spherical gas/vapour bubble in an isochoric, inviscid liquid are investigated. The motion is driven by the uniform and constant force field due to the gravity. The liquid is assumed at rest at the initial time. Unlike previous work on this subject, the mass of the bubble is not neglected, so that the bubble motion is accurately simulated also in the presence of large volume variations. After developing the relationships between the bubble motion to the liquid flow, a system of two nonlinear ordinary differential equations (ODEs) for the radius and the position of the center of mass of the bubble is written. The near-field pressure disturbance produced in the liquid by the bubble motion is evaluated by means of elliptic integrals and an efficient approximation of it free from these special functions is also used. The numerical integration of the ODE system allows one to evaluate the acoustic signal. This is carried out with the above mentioned approximation, and several features of it are demonstrated through the study of a sample flow.