# Observation of the resonance frequencies of a stable torus of fluid

## TL;DR

This study measures the resonance frequencies of a stable fluid torus in a Hele-Shaw cell, revealing azimuthal pattern formations and providing a model for understanding large-scale vortex structures.

## Contribution

First quantitative analysis of resonance frequencies in a stable fluid torus, extending the drop model to complex toroidal geometries.

## Key findings

- Resonance frequencies explained by adapted drop model.
- Observation of azimuthal patterns up to 25 lobes.
- Identification of instability 'tongues' in pattern formation.

## Abstract

We report the first quantitative measurements of the resonance frequencies of a torus of fluid confined in a horizontal Hele-Shaw cell. By using the unwetting property of a metal liquid, we are able to generate a stable torus of fluid with an arbitrary aspect ratio. When subjected to vibrations, the torus displays azimuthal patterns at its outer periphery. These lobes oscillate radially, and their number n depends on the forcing frequency. We report the instability ''tongues'' of the patterns up to n = 25. These resonance frequencies are well explained by adapting to a fluid torus the usual drop model of Lord Rayleigh. This approach could be applied to the modeling of large-scale structures arisen transiently in vortex rings in various domains.