Bubble pinch-off in turbulence
Bubble pinch-off in turbulence
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DOI：
10.1073/pnas.1909842116
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发表时间：
2019-11
影响因子：
11.1
通讯作者：
Daniel J. Ruth;W. Mostert;S. Perrard;L. Deike
中科院分区：
文献类型：
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作者：
Daniel J. Ruth;W. Mostert;S. Perrard;L. Deike
当泡沫破裂时，最后的挤压在奇点处达到高潮。我们研究了湍流中气泡的夹断，并证明了湍流流场在夹断过程中冻结，为接近于无扰动构型预测的自相似坍塌开辟了途径。因此，湍流流场的作用是设置复杂的初始条件，这些初始条件可能导致颈形在坍塌过程中振荡，并最终摆脱自相似性，出现扭结状界面结构。这项工作可以被视为理解现实多尺度系统中随机扰动存在的有限时间奇点路径的原型，具有基本和实际意义。虽然气泡掐断是动力系统向奇点演化的一个原型，但它一直是在理想化的理论和实验条件下描述的。在这里，我们结合实验室实验、数值模拟和理论建模，考虑了在强随机扰动存在的自然条件下紊流中的气泡夹断。我们发现湍流设定了掐断的初始条件，即初始气泡形状和流场，但在掐断开始后，颈部尺度上的湍流时间比掐断动力学慢得多：湍流冻结。我们证明平均颈尺寸d¯可以用d¯~ (t−t0)α来描述，其中t0是掐断或奇点时间，α≈0.5，与无初始流动的轴对称理论密切一致。在冻结状态下，湍流可以通过初始条件影响掐断。通过准二维（准二维）线性扰动模型可以观察到颈部的持续偏心率，这与气泡形状变形引起的复杂流场有关。当湍流应力无法被表面张力抵消时，在颈部形成一个三维（3D）扭结状结构，导致d¯逃避其自相似的减少。我们确定了控制这些扭结状界面结构外观的几何控制参数，这些结构驱动自相似路线的崩溃，控制逃离自相似过程的可能性以及发生的时间和长度尺度。
Significance As a bubble breaks apart, the final pinching culminates in a singularity. We investigate the pinch-off of a bubble in turbulence and demonstrate that the turbulent flow field freezes during the pinching process, opening the route for a self-similar collapse close to the one predicted for unperturbed configuration. The role of the turbulent flow field is, therefore, to set the complex initial conditions, which can lead to oscillations of the neck shape during the collapse and the eventual escape from self-similarity with the appearance of a kink-like interfacial structure. This work can be seen as a prototype for understanding the route to finite-time singularities in realistic multiscale systems where random perturbations are present, with both fundamental and practical implications. Although bubble pinch-off is an archetype of a dynamical system evolving toward a singularity, it has always been described in idealized theoretical and experimental conditions. Here, we consider bubble pinch-off in a turbulent flow representative of natural conditions in the presence of strong and random perturbations, combining laboratory experiments, numerical simulations, and theoretical modeling. We show that the turbulence sets the initial conditions for pinch-off, namely the initial bubble shape and flow field, but after the pinch-off starts, the turbulent time at the neck scale becomes much slower than the pinching dynamics: The turbulence freezes. We show that the average neck size, d¯, can be described by d¯∼(t−t0)α, where t0 is the pinch-off or singularity time and α≈0.5, in close agreement with the axisymmetric theory with no initial flow. While frozen, the turbulence can influence the pinch-off through the initial conditions. Neck shape oscillations described by a quasi–2-dimensional (quasi-2D) linear perturbation model are observed as are persistent eccentricities of the neck, which are related to the complex flow field induced by the deformed bubble shape. When turbulent stresses are less able to be counteracted by surface tension, a 3-dimensional (3D) kink-like structure develops in the neck, causing d¯ to escape its self-similar decrease. We identify the geometric controlling parameter that governs the appearance of these kink-like interfacial structures, which drive the collapse out of the self-similar route, governing both the likelihood of escaping the self-similar process and the time and length scale at which it occurs.