Turbulence in waked wind turbine wakes: Similarity and empirical formulae

Turbulence of wind turbine wakes increases the power fluctuations and dynamic loads of downwind turbines. In this work, we analyze the large-eddy simulation (LES) data of the Horns Rev wind farm, and find that the streamwise variations of the Reynolds normal stresses in the wakes of the waked wind turbines located in different rows collapse well with each other for both rise and decay portions when they are normalized using the maxima. Empirical formulae in the form of a power function are then proposed to describe the streamwise variations of the Reynolds normal stresses for different blade spanwise positions. Notably, linear relations are observed between the exponent and the coefficient. The LES data of the two tandem wind turbine cases with different inflows and turbine spacings are then employed to test the proposed empirical formulae. The tests show that the empirical formulae can capture the downstream variations of the Reynolds normal stresses especially for the streamwise component.

Automated summary

In this study, the turbulence and Reynolds normal stresses in the wakes of wind turbines were analyzed using large-eddy simulation (LES) data. It was found that the streamwise variations of Reynolds normal stresses in the wakes collapse well with each other when normalized using the maxima. Empirical formulae in the form of a power function were then proposed to describe the streamwise variations of Reynolds normal stresses for different blade spanwise positions, showing linear relations between the exponent and the coefficient. The proposed formulae were validated using LES data of two tandem wind turbine cases, demonstrating their effectiveness in capturing downstream variations of Reynolds normal stresses.