On the extension of streamwise turbulence intensity profile beyond the atmospheric surface layer under neutral to unstable stratifications

Turbulence intensity (TI) is a key factor that affects both the energy production and the performance of individual wind turbines and wind farms. In particular, accurate energy production estimation from wind sources requires a reliable TI model at turbine hub height. Modern multi-megawatt wind turbines operate at heights well above the atmospheric surface layer (ASL). However, most existing analytical TI models are merely valid in the ASL or under neutral atmospheric conditions. Therefore, this paper aims to derive an analytical expression for streamwise TI under neutral to unstable stratifications, which can reasonably model TI at heights beyond the ASL. To this end, the Monin-Obukhov similarity theory, Townsend's attached eddy hypothesis, and a modification proposed in the literature to the eddy population density of Townsend for unstable conditions are utilized. The proposed models are validated against datasets from four tall meteorological towers in Denmark, Sweden, and China. The sites constitute a considerable difference in Coriolis parameter and surface roughness. Results show that the proposed models reasonably follow the measured velocity variance and TI data under neutral to unstable conditions in the ASL and beyond.