Database Study of Turbulent Boundary Layer Flows in Pressure-Gradients: Testcase Overview and Parametrization of History Effects

Abstract

The accurate prediction of turbulent boundary layers (TBLs) subjected to streamwise pressure gradients remains a central challenge in fluid mechanics. In contrast to canonical zero-pressure-gradient (ZPG) flows, streamwise changes of adverse or favorable pressure gradients (APG/FPG) can drive the flow out of equilibrium, introducing ''history effects'' whereby the local state of the boundary layer depends on its upstream evolution. These effects complicate data interpretation, scaling, and model validation, as two boundary layers with identical local parameters may exhibit distinct behaviors due to different histories. This work provides a unified overview and parametrization of steady pressure-gradient TBLs from a wide set of well-documented experimental and numerical databases. The comparison includes cases with different wall geometries, pressure-gradient distributions, and degrees of non-equilibrium. The datasets cover a broad range of Reynolds numbers and Clauser pressure-gradient parameters, from mild favorable to strong adverse regimes, with and without flow separation. A consistent framework of pressure-gradient parameters is introduced, encompassing global, inner, outer, and cumulative definitions such as the Clauser parameter beta-C, the Zagarola–Smits parameter beta-ZS, and their integral (accumulated) counterparts. Their ability to capture local disequilibrium and cumulative history effects is assessed across all cases. The resulting analysis supports the development of common reference metrics and provides a basis for improved comparison, modeling, and interpretation of non-equilibrium turbulent boundary layers.