Log-Linear Overlap Parameters Extracted from Pressure Gradient Boundary Layers

Following on the recent paper "The hunt for the Kármán ‘constant’ revisited", by Peter Monkewitz and Hassan Nagib, in Journal of Fluid Mechanics 967, A15, 2023, and utilizing experimental data obtained under various favorable and adverse pressure gradients in the NDF wind tunnel at IIT and the MTL wind tunnel at KTH, we extracted the parameters of the "Log-Linear" overlap region. Different schemes to extract the parameters from the mean velocity profiles were evaluated on hot-wire meassured profiles over a wide range of pressure gradients, including the Zero Pressure Gradient (ZPG) boundary layers from the NDF. The Kármán “coefficient” κ, the slope of the linear component of the overlap region S₀ and the constant B₀ are presented as functions of the pressure-gradient parameter β, and compared to trends from ZPG boundary layers, and fully-developed channel and pipe flows. The Log-Linear overlap parameters are also contrasted with the trends of the traditional "Pure-Log" overlap parameters κ and B from "Variations of von Kármán coefficient in canonical flows" by Hassan Nagib and Kapil Chauhan, in Physics of Fluids, 20, 101518, 2008. The results and their trends are valuable not only for our basic understanding of a wide range of wall-bounded turbulent flows, but also are proposed as input to turbulence models and computational turbulence in general.