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.