Mean velocity profiles and total shear stress profiles in adverse-pressure-gradient turbulent boundary layers considering history effect

This study focuses on developing a predictive model for mean velocity profiles and total shear stress profiles in turbulent boundary layers subjected to adverse pressure gradients, especially with history effects. A new scaling using friction velocity modified by Clauser pressure gradient parameter is introduced to restore streamwise self-similarity. Furthermore, an estimation-correction model is developed, explicitly incorporating a streamwise derivative of pressure gradient, which effectively captures history effect beyond the reach of Reynolds-averaged Navier-Stokes equations. With the help of the model, the total shear stress is decomposed into four parts, representing respectively the Reynolds number effects, equilibrium pressure gradient effects, the coupling between free-stream velocity and pressure gradient, and local non-equilibrium pressure gradient effects. The latter two are considered first-order history effects, and can account for up to approximately half of the total stress. Validation against multiple DNS/LES datasets across a wide range of pressure gradients and Reynolds numbers demonstrates the model’s accuracy in predicting both mean velocity profiles and total shear stress profiles.