Scaling of turbulent separating flows

The present work investigates the scaling of the turbulent boundary layer in regions of adverse pressure gradient flow. For the first time, direct numerical simulation and experimental data are applied to the theory presented in Cruz and Silva Freire [Cruz, D. O. A., & Silva Freire, A. P. (1998). On single limits and the asymptotic behaviour of separating turbulent boundary layers. International Journal of Heat and Mass Transfer, 41, 2097-2111] to explain how the classical two-layered asymptotic structure reduces to a new structure consistent with the local solutions of Goldstein and of Stratford at a point of zero wall shear stress. The work discusses in detail the behaviour of an adaptable characteristic velocity (uR) that can be used in regions of attached as well as separated flows. In particular, uR is compared to velocity scales based on the local wall shear stress and on the pressure gradient at the wall. This is also made here for the first time. A generalized law of the wall is compared with the numerical and experimental data, showing good agreement. This law is shown to reduce to the classical logarithmic solution and to the solution of Stratford under the relevant limiting conditions.