Shen N, Bourouiba L
The Fluid Dynamics of Disease Transmission Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
J Fluid Mech. 2023 Oct 25;973. doi: 10.1017/jfm.2023.722. Epub 2023 Oct 23.
Shear instabilities at the interface of two fluids, such as classical Kelvin-Helmholtz instability (KHI), is the precursor of interface destabilization, leading to fluid fragmentation critical in a wide range of applications. While many insights into such instabilities are derived for steady background forcing flow, unsteady impulse flows are ubiquitous in environmental and physiological processes. Yet, little is understood on how unsteadiness shapes the initial interface amplification necessary for the onset of its topological change enabling subsequent fragmentation. In this combined theoretical, numerical and experimental study, we focus on an air-on-liquid interface exposed to canonical unsteady shear flow profiles. Evolution of the perturbed interface is formulated theoretically as an impulse-driven initial value problem using both linearized potential flow and nonlinear boundary integral methods. We show that the unsteady airflow forcing can amplify the interface's inherent gravity-capillary wave, up to wave-breaking transition, even if the configuration is classically KH stable. For impulses much shorter than the gravity-capillary wave period, it is the cumulative action, akin to total energy, that determines amplification, independent of the details of the impulse profile. However, for longer impulses, the details of the impulse profile become important. In this limit, akin to a resonance, it is the entangled history of the interaction of the forcing, i.e. the impulse, that changes rapidly in amplitude, and the response of the oscillating interface that matters. The insights gained are discussed and experimentally illustrated in the context of interface distortion and destabilization relevant for upper respiratory mucosalivary fluid fragmentation in violent exhalations.
两种流体界面处的剪切不稳定性，如经典的开尔文 - 亥姆霍兹不稳定性（KHI），是界面失稳的先兆，会导致流体破碎，这在广泛的应用中至关重要。虽然对于这种不稳定性的许多见解是从稳定的背景强迫流中得出的，但非稳态脉冲流在环境和生理过程中普遍存在。然而，对于非稳态如何塑造初始界面放大，即其拓扑变化开始并导致后续破碎所必需的放大，人们了解甚少。在这项结合了理论、数值和实验的研究中，我们聚焦于暴露于典型非稳态剪切流剖面的气 - 液界面。使用线性化势流和非线性边界积分方法，将受扰界面的演化理论上表述为一个脉冲驱动的初值问题。我们表明，即使该构型在经典情况下是KH稳定的，非稳态气流强迫也能将界面固有的重力 - 毛细波放大至波破碎转变。对于比重力 - 毛细波周期短得多的脉冲，是类似于总能量的累积作用决定了放大，而与脉冲剖面的细节无关。然而，对于较长的脉冲，脉冲剖面的细节变得很重要。在这个极限情况下，类似于共振，重要的是强迫（即脉冲）与振荡界面响应之间相互作用的纠缠历史，其振幅变化很快。在剧烈呼气时上呼吸道黏膜唾液流体破碎相关的界面变形和失稳背景下，对所获得的见解进行了讨论并通过实验进行了说明。
