Long- and short-wave instabilities in helical vortices

Abstract

We review two instability mechanisms that may be active in wind turbine wakes and contribute to their downstream evolution, by considering simplified configurations of one or several spatially uniform helical vortices. One category of instabilities involves displacement perturbations of the vortices, with wavelengths that are large compared to the size of their cores; they can be analysed using a filament approach. Previous theoretical results, confirmed by our recent experiments, show that the predicted instability modes are related to the pairing phenomenon found in periodic arrays of vortices. A second group of instabilities involves internal perturbations of the vortex cores, with wavelengths scaling on the core size. They result from deformations of the cores due to curvature, torsion or the strain induced by neighbouring helix loops. Our experiments show that the non-linear evolution of the shortwave instabilities, combined with the pairing mechanism, leads to a rapid destruction of the helical wake vortices.