Scaling and statistics of large-defect adverse pressure gradient turbulent boundary layers

The purpose of this article is to test similarity laws and scaling ideas, as well as characterize turbulence behaviour of large-defect adverse-pressure gradient turbulent boundary layers using six experimental and numerical databases including a new direct numerical simulation of a strongly decelerated non-equilibrium turbulent boundary layer. In the latter flow, at a moderate Reynolds number, the mean velocity profiles depart from the classical law of the wall throughout the inner region including in the viscous sublayer and they do not follow the log law. However, the agreement is excellent with the extended law of the wall that accounts for the pressure gradient for the viscous sublayer. The Reynolds stress components are not self-similar in the viscous sublayer when the velocity defect is important, but they scale reasonably well with the pressure-viscous scales.Detailed comparisons of the six different flows are made in the outer region. In order to do such comparisons, an outer region velocity scale analogous to the commonly defined free shear layer velocity scales is introduced. It is found that the investigated one-point velocity statistics in the upper half of large-defect boundary layers resemble those of a mixing layer: mean velocity defect, Reynolds stresses, turbulent kinetic energy budgets, uv correlation factor and structure parameter -〈uv〉/2k. The dominant peaks of turbulence production and Reynolds stresses are located roughly in the middle of the boundary layer. The profiles of the uv correlation factor reveal that u and v become less correlated throughout the boundary layer as the mean velocity defect increases, especially near the wall. The structure parameter is low in the large-defect disequilibrium boundary layers, similar to large-defect equilibrium flows and mixing layers and decreases as the mean velocity defect increases. All large-velocity-defect boundary layers analysed are found to be less efficient in extracting turbulent energy from the mean flow than zero-pressure-gradient turbulent boundary layers, even throughout the outer region.