On determining characteristic length scales in pressure-gradient turbulent boundary layers

In the present work, we analyze three commonly used methods to determine the edge of pressure gradient turbulent boundary layers: two based on composite profiles, the one by Chauhan et al. [Criteria for assessing experiments in zero pressure gradient boundary layers, Fluid Dyn. Res. 41, 021404 (2009)] and the one by Nickels [Inner scaling for wall-bounded flows subject to large pressure gradients, J. Fluid Mech. 521, 217-239 (2004)], and the other one based on the condition of vanishing mean velocity gradient. Additionally, a new method is introduced based on the diagnostic plot concept by Alfredsson et al. [A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the 'outer' peak, Phys. Fluids 23, 041702 (2011)]. The boundary layers developing over the suction and pressure sides of a NACA4412 wing section, extracted from a direct numerical simulation at chord Reynolds number Re-c = 400 000, are used as the test case, besides other numerical and experimental data from favorable, zero, and adverse pressure-gradient flat-plate turbulent boundary layers. We find that all the methods produce robust results with mild or moderate pressure gradients, although the composite-profile techniques require data preparation, including initial estimations of fitting parameters and data truncation. Stronger pressure gradients (with a Rotta-Clauser pressure-gradient parameter beta larger than around 7) lead to inconsistent results in all the techniques except the diagnostic plot. This method also has the advantage of providing an objective way of defining the point where the mean streamwise velocity is 99% of the edge velocity and shows consistent results in a wide range of pressure gradient conditions, as well as flow histories. Collapse of intermittency factors obtained from a wide range of pressure-gradient and Re conditions on the wing further highlights the robustness of the diagnostic plot method to determine the boundary layer thickness (equivalent to delta(99)) and the edge velocity in pressure gradient turbulent boundary layers. Published by AIP Publishing.