Logarithmic and Log-Linear Overlap Regions in Adverse Pressure Gradient Boundary Layers

We analyze the mean velocity profiles of developing high Reynolds number turbulent boundary layers under adverse pressure gradient (APG) measured in three wind tunnel facilities to establish the co-existence of the classical logarithmic (log) overlap region and the recently established* logarithmic plus linear (log+lin) extended overlap region. The pressure gradient parameter for the APG boundary layers, β, ranged up to 10. Independent wall shear stress measurements using oil film interferometry permits an unbiased extraction of the fitting parameters, and the wall-normal bounds related to both of these scaling laws. Increasing β is found to result in shrinking of the upper bound of the pure log overlap region from 0.13 to 0.12 of the boundary layer thickness (δ), alongside a decrease in the additive parameter (4.63 > B > 3.13), while keeping the von Kármán coefficient (κ) nearly constant around 0.38 to 0.39. On the other hand, the extended log+lin overlap region broadens with increasing β, as it starts immediately above the pure log region and remains valid until 0.25 δ, with a log-term parameter κ_o > 0.5, and the linear term parameter S_o and the constant B_o ranging from 9.6 to 15.2 and 11.4 to 8.9, respectively. Some comparisons with developing rough wall boundary layers will also be presented.



*Baxerres et al. 2024 Evidence of quasiequilibrium in pressure-gradient turbulent boundary layers. J. Fluid Mech. 987, R8.