Scaling of velocity fluctuations in statistically unstable boundary-layer flows
Xiang I. A. Yang, Sergio Pirozzoli, Mahdi Abkar
Abstract
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 is the boundary-layer height. Reasonably good prediction of velocity fluctuations based on knowledge of the mean velocity profile is obtained.