Tip-vortex breakdown of wind turbines subject to sheared inflow.*

The breakdown of the triple-helix tip-vortex structure behind wind turbines under uniform inflow has been investigated extensively in earlier studies, leading to the determination of the most unstable modes with the largest growth rates. Wind turbines are, however, located in atmospheric boundary layers where shear leads to an asymmetric breakdown of the tip-vortex structure. This talk presents results of a wind turbine subject to both uniform and sheared inflow. A harmonic perturbation is imposed at each blade tip and the response of the tip vortices is investigated using a Fourier transform. The growth rate of the response varies significantly along the vertical axis. However, when the growth rates are scaled with the local pitch, convection velocity and circulation the growth rates collapse to one value along the entire azimuth. For azimuthal wavenumbers corresponding to exact vortex pairing this value is close to π/2, which is the maximum growth rate for helical vortices subject to uniform inflow. This knowledge enables an estimation of the stable wake length of wind turbines located in sheared flows similar to that of unsheared flows which is of large importance in wind farms impacted by wake interaction.