A novel mean shear stress model and its application in pressure gradient turbulent boundary layers*

The mean shear stress is one of the most important quantities of interest in turbulent boundary layers (TBL). Kumar and Mahesh (Physical Review Fluids, 6(2), 024603, 2021) developed a model for the mean shear stress in a zero pressure gradient TBL using the governing equations for the mean flow. They derived a relation between the mean total stress and the mean velocity, containing an unknown term, which was modeled using existing TBL data. Their model requires the wall-normal mean velocity profile, which requires modeling if not available. Hence, they also provided a compact fit for the mean wall-normal velocity using scaling arguments and existing data. Both models showed good agreement with reference data for a range of Reynolds numbers. The present work incorporates pressure gradient effects in the mean shear stress and wall-normal velocity models. The proposed models show good agreement with a variety of existing pressure gradient TBL data. Finally, the shear stress model is used to devise a method to indirectly determine friction velocity without requiring any data from the bottom 20 percent of TBL. The accuracy of the proposed method is evaluated for a variety of zero and pressure gradient TBL.