Dynamical Equations for Oscillating Nonspherical Bubbles with Nonlinear Interactions

作者：Kurihara Eru^*

来源：SIAM Journal on Applied Dynamical Systems, 2017, 16(1): 139-158.

DOI：10.1137/15M1048768

• bubble dynamics
• Lagrangian formalism
• multipole expansion

In this study, dynamical equations for interacting nonspherical bubbles are derived in the framework of Lagrangian formalism with multipole expansion of bubble surfaces. These boundaries are expanded using spherical harmonics to study the deformation and translation of the bubbles. To compose the Lagrangian of the system, corresponding amplitudes of the spherical harmonics are chosen as generalized coordinates. This study considers orders of the spherical harmonics up to the third (octupole) mode, which is the lowest oscillation mode contributing to the asymmetrical deformation of a bubble. The derived equations represent the motion of interacting nonspherical bubbles and agree qualitatively well with experimental results, including the onset of jetting. The equations reveal the mechanism of initiation of shape oscillations which is accurate to the quadratic order in the mode amplitudes.

• 出版日期2017