Simplified model for helical vortex instabilities with applications to asymmetric rotor wakes

Helical vortices, such as those generated in the wake of a rotor, are subject to various instabilities including displacement instabilities, which occur when the vortex core is shifted from its baseline position. After being perturbed, the vortices deform and begin to break down. The zero-wavenumber displacement instability mode can be triggered by introducing an asymmetry to the rotor producing the vortices. The vortex dynamics in this case are highly complex, so a simplified model based on an infinitely-repeating strip of point vortices is developed to reproduce the nonlinear instability evolution. The model is validated against a more sophisticated filament model and water channel experiments, showing remarkable agreement for a range of parameters relevant to industrial rotors. It is then used to investigate the effectiveness of different types of rotor asymmetries at accelerating vortex breakdown. Even small initial displacements around 5% of the vortex spacing substantially disturb the vortices, and the direction of the perturbation plays an important role in the speed of the instability development. These findings can then be used to design wind turbine rotors that minimize the detrimental effects of their wakes on downstream turbines within a wind farm.