Surface tension as the destabiliser of a vortical interface. (10th April 2022)

• Record Type: Journal Article
• Authors: Ramadugu, Rashmi; Perlekar, Prasad; Govindarajan, Rama
• Is Part Of: Journal of fluid mechanics. Volume 936(2022)
• Publication Date: 2022-04-10
• Subjects: multiphase flow; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2022.97
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : We study the dynamics of an initially flat interface between two immiscible fluids, with a vortex situated on it. We show how surface tension causes vorticity generation at a general curved interface. This creates a velocity jump across the interface which increases quadratically in time, and causes the Kelvin–Helmholtz instability. Surface tension thus acts as a destabiliser by vorticity creation, winning over its own tendency to stabilise by smoothing out interfacial perturbations to reduce surface energy. We further show that this instability is manifested within the vortex core at times larger than ${\sim}(k We)^{1/4}$ for a Weber number $We$ and perturbation wavenumber $k$, destroying the flow structure. The vorticity peels off into small-scale structures away from the interface. Using energy balance we provide the growth of total interface length in time. A density difference between the fluids produces additional instabilities outside the vortex core due to centrifugal effects. We demonstrate the importance of this mechanism in two-dimensional turbulence simulations with a prescribed initial interface.