Analytical model of a wind turbine in sheared inflow

The vertical wind profile is not uniform due to the friction of the atmosphere with the earth surface. The gradient of velocity with respect to height induces shear stresses in the fluid and vorticity is present in the transverse direction. By extension, one will refer to wind shear or sheared inflow to describe such velocity profile.

The simplest model of a shear profile consists in a step of wind speed, which in turn can be modelled by a vortex sheet. The current chapter adds the effect of this vortex sheet to the vortex cylinder model presented in Chap. 17. The results are expected to be published in a more detailed article (Gaunaa et al., Modelling the Influence of Wind Shear Using a Simple Vortex Rotor Model, 2015) [2].

The chapter starts with a literature review on the topic of shear. The following questions are raised: Does the power coefficient increase and does the wake follow an upward movement under sheared conditions? The key elements and results of the cylindrical vortex model in shear are presented. It is found that the results from the axial momentum theory is valid in the local sense and hence the power coefficient is unaltered by the presence of shear.

Further, the analytical model predicts no upward motion of the wake. This result is further confirmed by the analytical and numerical investigations performed in Chap. 30 using vorticity-based methods.