The log behaviour of the Reynolds shear stress in accelerating turbulent boundary layers

Direct numerical simulation of highly accelerated turbulent boundary layers (TBLs) reveals that the Reynolds shear stress, uv⁺ , monotonically decreases downstream and exhibits a logarithmic behaviour (e.g. -uv⁺=-(1/Aᵤᵥ)ln y⁺+Bᵤᵥ ) in the mesolayer region (e.g. 50 y⁺ 170 ). The thickness of the log layer of uv⁺ increases with the streamwise distance and with the pressure gradient strength, extending over a large portion of the TBL thickness (up to 55 %). Simulations reveal that V⁺\,∂ U⁺/∂ y⁺~ 1/y⁺~ ∂ uv⁺/∂ y⁺ , resulting in a logarithmic uv⁺ profile. Also, V⁺~ -y⁺ is no longer negligible as in zero-pressure-gradient (ZPG) flows. Other experimental/numerical data at similar favourable-pressure-gradient (FPG) strengths also show the presence of a log region in uv⁺ . This log region in uv⁺ is larger in sink flows than in other spatially developing FPG flows. The latter flows exhibit the presence of a small power-law region in uv⁺ , which is non-existent in sink flows.