Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
Department of Applied Mechanics, Indian Institute of Technology, Delhi 110016, India.
Proc Natl Acad Sci U S A. 2021 Aug 24;118(34). doi: 10.1073/pnas.2105211118.
Originally, Kelvin-Helmholtz instability (KHI) describes the growth of perturbations at the interface separating counterpropagating streams of Newtonian fluids of different densities with heavier fluid at the bottom. Generalized KHI is also used to describe instability of free shear layers with continuous variations of velocity and density. KHI is one of the most studied shear flow instabilities. It is widespread in nature in laminar as well as turbulent flows and acts on different spatial scales from galactic down to Saturn's bands, oceanographic and meteorological flows, and down to laboratory and industrial scales. Here, we report the observation of elastically driven KH-like instability in straight viscoelastic channel flow, observed in elastic turbulence (ET). The present findings contradict the established opinion that interface perturbations are stable at negligible inertia. The flow reveals weakly unstable coherent structures (CSs) of velocity fluctuations, namely, streaks self-organized into a self-sustained cycling process of CSs, which is synchronized by accompanied elastic waves. During each cycle in ET, counter propagating streaks are destroyed by the elastic KH-like instability. Its dynamics remarkably recall Newtonian KHI, but despite the similarity, the instability mechanism is distinctly different. Velocity difference across the perturbed streak interface destabilizes the flow, and curvature at interface perturbation generates stabilizing hoop stress. The latter is the main stabilizing factor overcoming the destabilization by velocity difference. The suggested destabilizing mechanism is the interaction of elastic waves with wall-normal vorticity leading to interface perturbation amplification. Elastic wave energy is drawn from the main flow and pumped into wall-normal vorticity growth, which destroys the streaks.
最初，开尔文-亥姆霍兹不稳定性（KHI）描述了密度不同的牛顿流体反向流动界面处的扰动增长，较重的流体在底部。广义 KHI 也用于描述具有连续速度和密度变化的自由剪切层的不稳定性。KHI 是研究最多的剪切流不稳定性之一。它在自然界中广泛存在于层流和湍流中，并在从银河到土星带、海洋和气象流以及实验室和工业规模的不同空间尺度上起作用。在这里，我们报告了在直粘性弹性通道流中观察到的弹性驱动类 KHI 不稳定性的观察结果，该观察结果在弹性湍流（ET）中发现。目前的发现与公认的观点相矛盾，即界面扰动在可忽略的惯性下是稳定的。该流显示出弱不稳定的相干结构（CS）的速度波动，即条纹自组织成 CS 的自维持循环过程，由伴随的弹性波同步。在 ET 的每个循环中，反向传播的条纹都会被弹性类 KHI 不稳定性破坏。其动力学明显让人联想到牛顿 KHI，但尽管相似，不稳定性机制却明显不同。扰动条纹界面两侧的速度差使流动失稳，而界面扰动处的曲率产生稳定的环向应力。后者是克服速度差引起的失稳的主要稳定因素。建议的失稳机制是弹性波与壁面法向涡度的相互作用，导致界面扰动放大。弹性波能量来自主流，并被泵入壁面法向涡度的增长，从而破坏条纹。
