Significance
Kelvin–Helmholtz instability (KHI) describes the growth of perturbations of the interface separating counterpropagating streams of Newtonian fluids with different velocities and densities with heavier fluid at the bottom. It is one of the most studied shear flow instabilities widespread in nature and industrial processes. The KHI mechanism is based on competition between destabilizing velocity difference and stabilizing stratification. We study KHI in channel shear flow of viscoelastic fluid, considered stable due to elastic stress generated by polymers stretched by shear strain. Contrary to generally accepted opinion, we discover the elastically driven KH-like instability with temporal dynamics similar to Newtonian KHI but driven by strikingly different elastically driven destabilizing mechanism of elastic wave interacting with wall-normal vorticity amplifying interface perturbations.
Abstract
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.
Data Availability
All study data are included in the article and/or supporting information.
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August 19, 2021 at 01:29AM
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Elastically driven Kelvin–Helmholtz-like instability in straight channel flow - pnas.org
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