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Updated: Oct 16, 2025

Preparation of Free-Surface Hyperbolic Water Vortices
Published on: July 28, 2023
Experimental Dispersion Relation of Surface Waves along a Torus of Fluid
Filip Novkoski1, Eric Falcon1, Chi-Tuong Pham2
1Université de Paris, MSC, UMR 7057 CNRS, F-75013 Paris, France.
Abstract:
We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its perimeter. Using a spatiotemporal optical measurement, we report the full dispersion relation of azimuthal waves propagating along the inner and outer torus borders, highlighting several branches modeled as varicose, sinuous, and sloshing modes. Standing azimuthal waves are also studied leading to polygonlike patterns arising on the two torus borders with a number of sides different when a tunable decoupling of the two interfaces occurs. The quantized nature of the dispersion relation is also evidenced.
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