Testing of Reynolds-stress-transport closures by comparison with DNS of an idealized adverse-pressure-gradient boundary layer

Results are used from direct numerical simulation (DNS) of incompressible plane-channel flow subjected to a uniform straining field typical of a two-dimensional adverse pressure gradient (APG) to investigate the accuracy of three second-moment closures specially designed to account for wall-bounded turbulence. Since the DNS statistics satisfy a one-dimensional unsteady problem with rigorously defined boundary and initial conditions, and since the flow contains many of the essential features found in suddenly decelerated boundary layers, this allows an efficient and straightforward but non-trivial assessment of the closures. The Reynolds-stress budgets from the DNS are used to examine the individual production/dissipation/transport terms used by each closure. This reveals shortcomings in all three schemes, especially in the near-wall behavior of their pressure–strain models. One of the major findings of this study is the degree to which the individual modeling shortcomings are offset by the tendency for them to cancel each other. The Wilcox Stress-ω model best captures the cumulative effect of the APG straining, compared to the models of Launder and Shima and So et al., in terms of giving mean velocities and the time at which the surface shear stress reverses sign that most closely agree with the DNS. However, its prediction of the streamwise and wall-normal Reynolds stresses is much less accurate than that given by the other two schemes.