Surface tension as the destabiliser of a vortical interface

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 similar to(kWe)(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.

Automated summary

The dynamics of an initially flat interface between two immiscible fluids with a vortex on it is studied. It is found that surface tension causes vorticity generation at a curved interface, resulting in a velocity jump and the Kelvin-Helmholtz instability. The instability is observed within the vortex core, destroying the flow structure, and is also influenced by the density difference between the fluids.