MEAN-VELOCITY SCALING IN AND AROUND A MILD, TURBULENT SEPARATION BUBBLE

This paper examines the question of the scaling of mean-velocity profi les in adverse-pressure-gradient flows. In these flows, the mean veloc ity scaling must be different than in zero-pressure-gradient flows, be cause the friction velocity used in the latter case can become vanishi ngly small in the former. Two decades ago, Ferry 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 sho wn 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 se t of scaling laws has been proposed by Durbin and Belcher [J. Fluid Me ch. 238, 699 (1992)] as a result of their asymptotic analysis, in whic h they assumed the appropriate near-wall velocity scale to be based on the local strength of the pressure gradient. The resulting scaling la ws are different than Ferry and Schofield's scaling and, in fact, pred ict a three-layered rather than a two-layered boundary-layer structure . Here, experimental results are shown for an adverse-pressure-gradien t boundary layer which separates from and then reattaches to a smooth surface. These data provide a wide range of flow conditions for compar ing the conflicting scaling laws mentioned above, under conditions of both decreasing and increasing skin friction, with and without instant aneous reverse flow. It is found that the Perry-Schofield coordinates provide better collapse, over a wider range of streamwise positions an d 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 p rovide a test of the range of validity of the (zero-pressure-gradient) logarithmic law of the wall. The law is violated here when instantane ous reverse flow exists in the boundary layer and/or when the local pr essure gradient is strong enough, as is consistent with earlier work. However, after reattachment these criteria are insufficient to indicat e the return to the log law, and several bubble lengths are required a fter 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. (C) 1995 American Institute of Physics.