When excited at sufficiently high acoustic pressures, a wall-attached bubble may exhibit asymmetric nonspherical modes. These vibration modes can be decomposed over the set of spherical harmonics $Y_{nm}(\theta ,\varphi )$ for a degree $n$ and order $m$. We experimentally capture the time-resolved dynamics of asymmetric bubble oscillations in a top-view configuration. A spatiotemporal modal analysis is performed and allowed recovering the set of zonal ($m=0$), tesseral ($0<m<n$), and sectoral ($m=n$) spherical harmonics that develop at the bubble interface. The analysis of the surface instability thresholds reveals that the frequencies of asymmetric modes differ from the standard Lamb spectrum. In addition, the nondegeneracy of asymmetric modes for a given degree $n$ is evidenced by noncompletely overlapping resonance bands. Finally, the coexistence between zonal and sectoral modes is analyzed through their modal interaction, amplitude interplay and relation of phase, as well as their geometric compatibility.

中文翻译：

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系留气泡的非球模非简并性

当在足够高的声压下激发时，附壁的气泡可能会出现不对称的非球形模式。这些振动模式可以在一组球谐函数上分解${ÿ}_{ñ米}（\theta ，\varphi ）$ 一个学位 $ñ$ 和命令 $米$。我们通过实验捕获了顶视图配置中非对称气泡振荡的时间分辨动力学。进行时空模态分析并允许恢复带状（$米=0$），tesseral（$0<米<ñ$）和部门（$米=ñ$）在气泡界面处产生的球形谐波。表面不稳定性阈值的分析表明，不对称模式的频率与标准兰姆光谱不同。另外，给定程度的非对称模的非简并性$ñ$不完全重叠的共振带可以证明这一点。最后，通过区域模态和扇形模态之间的模态相互作用，振幅相互作用和相位关系，以及它们的几何相容性，分析了区域模态和扇形模态的共存。