Characterizing Spatially Heterogeneous Wind Turbine Wakes Under Yaw and Tilt Misalignment

The formation of a counter-rotating vortex pair in the wake of a misaligned wind turbine produces a spatially heterogeneous flow with interactions across a range of physical scales. We apply lacunarity analysis to identify the dominant length scales in response to wake deflection and characterize overall flow complexity through a heterogeneity index. Flow data were obtained from large eddy simulations for a single turbine in a neutrally-stable atmospheric boundary layer flow. We considered a range of nacelle misalignment angles including yaw, tilt, and yaw-tilt combinations to parameterize heterogeneity across the full range of possible deflection angles. In addition, we varied roughness height to determine the influence of surface characteristics. Wake flow was isolated from the background by subtracting the boundary layer profile. Spatial heterogeneity was computed from the advection and Reynolds stress budgets at each downstream location. We found the dominant length scales and spatial heterogeneity vary with misalignment in the near wake and are driven by surface interactions in certain cases. Misalignment angles which direct the wake towards the ground experience significant shear which introduces further deformation and compounds heterogeneity from deflection. The streamwise point where these interactions occur is revealed through the heterogeneity index and depends on turbine aspect ratio, misalignment angle, and surface roughness.