Dynamical Equations for Oscillating Nonspherical Bubbles with Nonlinear Interactions
Dynamical Equations for Oscillating Nonspherical Bubbles with Nonlinear Interactions
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具有非线性相互作用的振荡非球形气泡的动力学方程
DOI：
10.1137/15m1048768
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
E. Kurihara
中科院分区：
文献类型：
--
作者：
Y. Kikuchi;N. Ohnishi;K. Ohtani;E. Kurihara
在这项研究中，相互作用的非球形气泡的动力学方程推导的框架内的拉格朗日形式主义与多极展开的气泡表面。这些边界扩展使用球谐函数来研究气泡的变形和平移。为了构成系统的拉格朗日量，选择相应的球谐振幅作为广义坐标。这项研究认为，第三（八极）模式，这是最低的振荡模式有助于不对称变形的气泡的球谐函数的订单。导出的方程表示相互作用的非球形气泡的运动，并同意定性与实验结果，包括发病的喷射。该方程揭示了形状振荡的起始机制，其精确到模式振幅的二次阶。
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.