Mean velocity profiles and total shear stress profiles in adverse-pressure-gradient turbulent boundary layers considering local disequilibrating effects

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 local disequilibrating effects. A new scaling using friction velocity modified by the Clauser pressure gradient parameter is introduced, and an estimation–correction model is developed, explicitly incorporating a streamwise derivative of pressure gradient, which effectively captures local disequilibrating effects 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 effect, the equilibrium pressure gradient effect, the coupling between free-stream velocity and pressure gradient, and the local non-equilibrium pressure gradient effect. The latter two are considered first-order local disequilibrating effects, and can account for up to approximately half of the total stress. The model’s accuracy in predicting both mean velocity profiles and total shear stress profiles is validated against a wide range of DNS/LES datasets, with Clauser pressure gradient parameter β reaching a maximum of $4.53$ , Re_θ peaking at 9.65× 10³ , and the non-dimensional second-order streamwise pressure gradient γ ranging from -4.57× 10⁻³ to 2.82× 10⁻⁴ .