Effect of an abrupt rough-to-smooth surface roughness transition on wind farm wakes: An LES and analytical modeling study

Large-eddy simulations (LES) are performed on the flow over a wind farm sited behind an abrupt rough-to-smooth surface roughness jump. The change in surface roughness affects both the first-order and second-order turbulent statistics. The usual deficit, i.e., the difference between the velocities upstream of the entire wind farm and downstream of a turbine, attains negative values close to the ground, which makes it difficult for modeling within the usual Gaussian radial-shape framework. A different definition, i.e., the difference in velocity at the same location with and without a turbine on a heterogeneous surface, is always positive and is amenable to Gaussian shape-based modeling. For the setup considered here, wind farms sited downstream of a surface roughness jump produce more power than a wind farm sited on a homogeneously rough surface. This increase is primarily because of the larger power generated by the downstream turbines and only slightly due to the increased power of the first-row turbine. The farm performance is affected by the distance between the abrupt change in surface roughness and the position of the first row of turbines. The wind farm performance is also dependent on the aerodynamic roughness upstream of the surface roughness jump. Two single-turbine analytical models and three wake-merging strategies are evaluated for their ability to predict the velocity deficits. A corrected form of the standard Gaussian model with a recently proposed wake-merging methodology, applicable for a varying background field, is found to be insensitive to the tunable model parameter and is consistently in line with the LES results.