Filip Novkoski (Université Paris Cité, MSC, CNRS) will speak at the Courant PIs Workshop on Tuesday, November 29th at 3:30pm
“Nonlinear Waves along a Torus of Fluid”
Curved interfaces such as toroidal drops are ubiquitous in nature, but are unstable, making them difficult to control and study. Using an original technique we create a stable and stationary torus of liquid, deposited on a superhydrophobic substrate allowing for a systematic study of waves along its inner and outer border under curved and periodic conditions [1,2]. By exciting the torus border, we recover the displacements of the two 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 borders for sufficiently strong forcing. We stress the observation of subsonic elevation solitons which are due to a strong influence of periodic boundary conditions through a Korteweg-de Vries equation, giving a non-trivial dependence of the soliton velocity on its amplitude and torus curvature. Finally, a triadic resonance instability is observed between two different dispersion branches, namely the sloshing and gravity-capillary modes. Nonlinear interactions allow for a transfer of energy between the two branches and the decay of a mother wave into daughter waves. Additional secondary and tertiary waves are also formed leading to a discrete cascade to smaller scales, potentially allowing a route towards wave turbulence.
- 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). - F. Novkoski, C.-T. Pham and E. Falcon, Experimental Periodic Korteweg-de Vries solitons along a
torus of fluid, submitted to Europhys. Lett., (2022).