Experimental evidence of the dispersion relation of Kelvin waves along a free-surface vortex*

Kelvin waves are waves that propagate along vortices in turbulent flows or in quantum turbulence. Although ubiquitous in nature, they are challenging to access experimentally.  Here, we investigate a free-surface vortex, like a bathtub vortex, that forms at the interface between water and air, within a container with a hole at its bottom, in response to injectors arranged circularly around the outlet. In this out-of-equilibrium stationary state, the vortex extends vertically over 50 cm with a diameter of the order of the millimeter. When excited using a wavemaker, we experimentally evidence Kelvin waves propagating along such a vortex and report their full dispersion relation for the first time. The latter exhibits a rich spectral structure with several branches, as helical bending modes. Our findings pave the way for the experimental investigation of Kelvin wave turbulence predicted theoretically.