ALBERT

Notes: This paper examines the question of the scaling of mean-velocity profiles in adverse-pressure-gradient flows. In these flows, the mean velocity scaling must be different than in zero-pressure-gradient flows, because the friction velocity used in the latter case can become vanishingly small in the former. Two decades ago, Perry and Schofield [Phys. Fluids 16, 2068 (1973)] proposed a new outer-region scaling law to be used when the boundary layer approaches separation. Since that time, a number of sets of experimental data close to separation have been shown to fall on a universal curve when the profiles are plotted in Perry–Schofield coordinates, and the profile shape was given by Dengel and Fernholz [J. Fluid Mech. 212, 615 (1990)]. Recently, however, a new set of scaling laws has been proposed by Durbin and Belcher [J. Fluid Mech. 238, 699 (1992)] as a result of their asymptotic analysis, in which they assumed the appropriate near-wall velocity scale to be based on the local strength of the pressure gradient. The resulting scaling laws are different than Perry and Schofield's scaling and, in fact, predict a three-layered rather than a two-layered boundary-layer structure. Here, experimental results are shown for an adverse-pressure-gradient boundary layer which separates from and then reattaches to a smooth surface. These data provide a wide range of flow conditions for comparing the conflicting scaling laws mentioned above, under conditions of both decreasing and increasing skin friction, with and without instantaneous reverse flow.It is found that the Perry–Schofield coordinates provide better collapse, over a wider range of streamwise positions and over a larger fraction of the boundary layer, than the scaling laws of Durbin and Belcher. Other proposed scaling laws are also evaluated. Yaglom's half-power law is shown to hold for a subset of the profiles which fall on Dengel and Fernholz's universal profile. And the data provide a test of the range of validity of the (zero-pressure-gradient) logarithmic law of the wall. The law is violated here when instantaneous reverse flow exists in the boundary layer and/or when the local pressure gradient is strong enough, as is consistent with earlier work. However, after reattachment these criteria are insufficient to indicate the return to the log law, and several bubble lengths are required after reattachment before the universal log law is satisfied. The wake region responds to reattachment more slowly and does not appear fully recovered six bubble lengths (twenty boundary-layer thicknesses) after reattachment. © 1995 American Institute of Physics.

Notes: This paper describes experimental results measured in a low-shear turbulent boundary layer. The low-shear condition is exerted after the boundary layer reaches Reθ(approximately-equal-to)2000 and has the effect of removing the inner layer; thus, these are the first results to show the behavior of an outer-layer-only turbulent boundary layer. The removal of the inner layer causes the gradual decay of the turbulent stresses over eleven boundary-layer thicknesses (roughly 20 large-eddy length scales) of streamwise distance, with the decay beginning at the wall and propagating into the outer flow with increasing downstream distance. However, the structure of the outer layer is little affected by the perturbation, as demonstrated by stress (anisotropy) ratios, quadrant analysis, and spectral measurements. Although the lack of near-wall production implies this flow must eventually decay into isotropic turbulence, this decay occurs relatively slowly because the dissipation is also greatly reduced with the decrease in near-wall shear. In addition, the outer-layer production is significant in maintaining the turbulence level. These results show that, once formed, the outer-layer characteristics are not explicitly dependent on the presence of the inner layer. These results are compared with similar studies of isotropic turbulence near a shear-free wall. Very close to the wall the two flows both show that the normal-stress components respond differently to the presence of the wall. However, away from the wall the isotropic results underpredict the distance to which the tangential stresses are damped by the impermeability condition at the wall. Finally, the results show general similarities to those in a boundary layer just downstream of reattachment, after a similar low-shear condition over the separation bubble. This raises the possibility that many of the important features of the reattaching flow can be captured by the present, simpler experiment. © 1996 American Institute of Physics.