Short-wave displacement instability of a helical vortex

This article presents results from an experimental, numerical and theoretical study of the short-wave instability of a helical vortex generated by a rotating blade. Experimental dye visualisations and corresponding numerical simulation show unstable displacement perturbations with wavelengths that are small compared with the helix radius and pitch, but can be large compared with the vortex core size. Stability analysis based on the experimental vortex profiles identifies large bands of unstable wavenumbers across different vortex bending modes, a result not compatible with existing theory on short-wave vortex instability. Similar modes are found for an array of straight vortices, showing that they are not related to vortex curvature. A theoretical analysis of the dispersion relation of Kelvin modes for the experimental vortex reveals the existence of a new family of modes, related to the specific vorticity profile of the vortex. Their non-resonant interaction via the strain field could explain the observed instability features.