Polygonal instabilities on interfacial vorticities

TL;DR

This paper theoretically investigates the stability of a toroidal vortex with an interface, identifying two distinct mechanisms—surface tension and fluid inertia—that can cause the vortex to transform into polygonal shapes, with relevance to several fluid phenomena.

Contribution

It introduces a theoretical framework revealing two separate instability mechanisms leading to polygonal shapes in interfacial vortices, connecting these findings to experimental observations.

Findings

Identified surface tension-driven instability mechanism.

Discovered inertia-driven instability mechanism.

Linked theoretical results to experimental phenomena like hydraulic jumps.

Abstract

We report the results of a theoretical investigation of the stability of a toroidal vortex bound by an interface. Two distinct instability mechanisms are identified that rely on, respectively, surface tension and fluid inertia, either of which may prompt the transformation from a circular to a polygonal torus. Our results are discussed in the context of three experiments, a toroidal vortex ring, the hydraulic jump, and the hydraulic bump.