Andrés Castillo - Long-wave instabilities of elongated vortices - ENS Paris-Saclay

Helical vortex systems, such as those found in the wakes of wind turbines, helicopter rotors, and propellers, are subject to instabilities that lead to pairing between adjacent vortex loops. Certain modes of these instabilities can

be triggered by an asymmetry in the rotor generating the vortices. In three-vortex systems, like those formed by many industrial rotors, the nonlinear vortex interactions are highly complex, introducing the need for a simple
model to predict their dynamics. The current study presents a model for  helical vortex systems based on spatially periodic helical vortices. This highly simplified model is shown to accurately reproduce the helical vortex dynamics observed in water channel experiments on model rotors. These findings can be used to design asymmetric rotors that induce vortex breakdown more effectively, mitigating detrimental wake effects such as increased fatigue loading on downstream structures.

In a second part, we consider the stability and motion of inviscid thin vortex filaments in the shape of toroidal coils. These vortex structures, which approximate thin vortex rings subject to a finite-amplitude Kelvin wave, translate and rotate at uniform rates without deformation, from which a dispersion relation may be deduced. The temporal linear stability properties are studied using the numerical approach of Castillo-Castellanos & Le Dizès (J. Fluid Mech. (2022), vol. 946, A10). Vortex coils are linearly unstable, but growth rates vary drastically with the amplitude. For small and intermediate amplitudes, the most unstable modes are explained by a coupling between Kelvin waves with the external field. For large amplitudes, unstable modes are consistent with a local pairing instability between the consecutive loops of a bent helical vortex.