Scaling of velocity fluctuations in statistically unstable boundary-layer flows

Much of our theoretical understanding of statistically stable and unstable flows is from the classical Monin-Obukhov similarity theory: The theory predicts the scaling of the mean flow well, but its prediction of the turbulent fluctuation is far from satisfactory. This study builds on Monin-Obukhov similarity theory and Townsend's attached-eddy hypothesis. We present a model that connects the mean flow and the streamwise velocity fluctuations in both neutral and unstable boundary-layer flows at both moderate and high Reynolds numbers. The model predictions are compared to direct numerical simulations of weakly unstable boundary layers at moderate Reynolds numbers, and large-eddy simulations of unstable boundary-layer flows at high Reynolds numbers. The flow is shear dominated. The range of stability parameter considered in this work is L/\unicode[STIX]{x1D6FF}, where is the Monin-Obukhov length, and is the boundary-layer height. Reasonably good prediction of velocity fluctuations based on knowledge of the mean velocity profile is obtained.