Stability analysis of the tip vortices of a wind turbine

The aim of the present paper is to obtain a better understanding of the stability properties of wakes generated by wind turbine rotors. To accomplish this, a numerical study on the stability of the tip vortices of the Tjaereborg wind turbine has been carried out. The numerical model is based on large eddy simulations of the Navier-Stokes equations using the actuator line method to generate the wake and the tip vortices. To determine critical frequencies, the flow is disturbed by inserting harmonic perturbations, giving rise to spatially developing instabilities. The results show that the instability is dispersive and that growth arises only for some specific frequencies and type of modes, in agreement with previous instability studies. The result indicates two types of modes; one where oscillations of neighboring vortex spirals are out of phase and one where oscillations in every vortex spiral in phase. The mode with spirals out of phase results in the largest growth with the main extension of the disturbance waves in radial and downstream directions. The out-of-phase disturbance leads to vortex pairing once the development leaves the linear stage. The study also provides evidence of a relationship between the turbulence intensity and the length of the near wake. The relationship, however, needs to be calibrated against measurements. Copyright (C) 2010 John Wiley & Sons, Ltd.