Relating statistical moments and entropy in the stable boundary layer

Fourth order moments and their connection with other statistics, including second order moments, skewness and entropy, in stable boundary layers are investigated with a large eddy simulation model (LES), wind tunnel experiment data (WT) and measurements on a meteorological tower in an urban area (MT). The relationship between skewness and kurtosis has been studied through two formulae, whose coefficients are determined for the three data sets. Shannon entropy is analysed as an index of the turbulent flow organization in order to further understand the possible reason for the failure of the QN hypothesis. To quantify this relationship between Shannon entropy and kurtosis, a power function is proposed.