Vesipa Riccardo, Paissoni Eleonora, Manes Costantino, Ridolfi Luca
Department of Environment, Land and Infrastructure Engineering, Politecnico di Torino, C. so Duca degli Abruzzi 24, 10129 Torino, Italy.
Cranfield Water Science Institute, Cranfield University, Bedfordshire MK43 0AL, United Kingdom.
Phys Rev E. 2021 Feb;103(2-1):023108. doi: 10.1103/PhysRevE.103.023108.
Several studies have investigated the dynamics of a single spherical bubble at rest under a nonstationary pressure forcing. However, attention has almost always been focused on periodic pressure oscillations, neglecting the case of stochastic forcing. This fact is quite surprising, as random pressure fluctuations are widespread in many applications involving bubbles (e.g., hydrodynamic cavitation in turbulent flows or bubble dynamics in acoustic cavitation), and noise, in general, is known to induce a variety of counterintuitive phenomena in nonlinear dynamical systems such as bubble oscillators. To shed light on this unexplored topic, here we study bubble dynamics as described by the Keller-Miksis equation, under a pressure forcing described by a Gaussian colored noise modeled as an Ornstein-Uhlenbeck process. Results indicate that, depending on noise intensity, bubbles display two peculiar behaviors: when intensity is low, the fluctuating pressure forcing mainly excites the free oscillations of the bubble, and the bubble's radius undergoes small amplitude oscillations with a rather regular periodicity. Differently, high noise intensity induces chaotic bubble dynamics, whereby nonlinear effects are exacerbated and the bubble behaves as an amplifier of the external random forcing.
多项研究探讨了单个静止球形气泡在非平稳压力作用下的动力学特性。然而，几乎所有研究都聚焦于周期性压力振荡，而忽略了随机强迫的情况。这一事实颇为令人惊讶，因为随机压力波动在许多涉及气泡的应用中广泛存在（例如，湍流中的流体动力空化或声空化中的气泡动力学），而且一般来说，噪声已知会在诸如气泡振荡器等非线性动力系统中引发各种违反直觉的现象。为了阐明这一未被探索的主题，我们在此研究由凯勒 - 米克斯方程描述的气泡动力学，压力强迫由一个建模为奥恩斯坦 - 乌伦贝克过程的高斯色噪声描述。结果表明，根据噪声强度，气泡呈现出两种特殊行为：当强度较低时，波动的压力强迫主要激发气泡的自由振荡，气泡半径以相当规则的周期性进行小幅度振荡。不同的是，高噪声强度会引发混沌的气泡动力学，此时非线性效应加剧，气泡表现为外部随机强迫的放大器。
