Investigating the perturbed geometries of vortex rings in free fall through another liquid

TL;DR

This paper theoretically explores the origin of standing wave-like perturbations on vortex rings falling through another liquid, using simplified Navier-Stokes equations to identify steady-state velocity fields with wave-like features.

Contribution

It introduces a simplified theoretical model explaining the wave-like perturbations on vortex rings in a different liquid, based on observational evidence.

Findings

Existence of a steady-state velocity field with wave-like characteristics

Simplified Navier-Stokes equations can model observed perturbations

Visualizations support the theoretical findings

Abstract

The goal of this paper is to theoretically investigate the origin of the standing wave-like perturbation observed on the vortex rings falling through another liquid. We simplified the Navier-Stokes equation based on observational evidence from related research, and showed that there exists a steady-state velocity field with the required wave-like characteristics. For better visualisation we also plotted the velocity field.