The coherent dynamics of bubble clusters are of fundamental and industrial importance, and are elusive due to the complex interactions of disordered bubble oscillations. Here we introduce and demonstrate a method for decomposition of the Lagrangian time series of bubble dynamics data by combining theory and principal component analysis. The decomposition extracts coherent features of bubble oscillations based on their energy, in a way similar to proper orthogonal decomposition of Eulerian flow field data. This method is applied to a dataset of spherical clusters under harmonic excitation at different amplitudes, with various nuclei density and polydispersity parameters. Results indicate that the underlying correlated mode of oscillations is isolated in a single dominant feature in cavitating regimes, independent of the nuclei's parameters. A systematic data analysis procedure further suggests that this feature is globally controlled by the dynamic cloud interaction parameter of Maeda and Colonius (J. Fluid Mech., vol. 862, 2019, pp. 1105–1134) that quantifies the mean-field interactions, regardless of initial polydispersity or nonlinearity. The method provides a simplified and comprehensive representation of complex bubble dynamics as well as a new path to reduced-order modelling of cavitation and nucleation.

中文翻译：

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将气泡簇动力学回归为无序多体系统

气泡簇的相干动力学具有基础和工业重要性，并且由于无序气泡振荡的复杂相互作用而难以捉摸。在这里，我们介绍并演示了一种结合理论和主成分分析的气泡动力学数据拉格朗日时间序列分解方法。该分解根据气泡振荡的能量提取相干特征，其方式类似于欧拉流场数据的适当正交分解。该方法适用于不同振幅谐波激发下具有各种核密度和多分散性参数的球形团簇数据集。结果表明，潜在的相关振荡模式在空化状态中被隔离在单个主要特征中，与原子核的参数无关。系统的数据分析程序进一步表明，该特征是由 Maeda 和 Colonius 的动态云交互参数全局控制的（J.流体机械。，卷。 862, 2019, 第 1105–1134 页），无论初始多分散性或非线性如何，都可以量化平均场相互作用。该方法提供了复杂气泡动力学的简化和全面的表示，以及空化和成核降阶建模的新途径。