Experimental nonlinear waves along a torus of fluid*

Curved interfaces such as toroidal drops are ubiquitous in nature, but are unstable, making them difficult to study. Using an original technique we create a stable torus of liquid on a superhydrophobic substrate allowing a systematic study of waves along its inner and outer border under curved and periodic conditions [1,2]. By exciting the torus, we recover the displacements of the borders and study the dispersion relation of the torus, yielding a rich spectral structure: gravity-capillary waves, sloshing modes and a center-of-mass mode [1]. We will show that nonlinear waves in form of solitons can propagate along the torus. We stress the observation of subsonic elevation solitons due to a strong influence of periodic boundary conditions in the Korteweg-de Vries equation, giving a non-trivial dependence of the soliton velocity on its amplitude. Finally, a triadic resonance instability is observed between sloshing and gravity-capillary modes, potentially allowing wave turbulence.

1. F. Novkoski, E. Falcon and C.-T. Pham, Experimental Dispersion Relation of Surface Waves along a Torus of Fluid, Phys. Rev. Lett., 127, 144504 (2021).

2. F. Novkoski, C.-T. Pham and E. Falcon, Experimental Periodic Korteweg-de Vries solitons along a torus of fluid, submitted to Europhys. Lett., (2022).