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We experimentally investigate the effects on scaling ofseparating/reattaching flows of the ratio $\delta_e/h$, where $\delta_e$ is thethickness at separation of the incoming boundary layer and $h$ thecharacteristic cross-stream scale of the flow. In the present study, we proposean original approach based on mean mass entrainment, which is the drivingmechanism accounting for the growth of the separated shear layer. The focus ison mass transfer at the Turbulent/Non-Turbulent Interface (TNTI). Inparticular, the scaling of the TNTI, which is well documented in turbulentboundary layers, is used to trace changes in the scaling properties of theflow. To emphasise the influence of the incoming boundary layer, twogeometrically similar, descending ramps with sizeably different heights $h$ butfundamentally similar values of $\delta_e$ are compared. The distribution inspace of the TNTI highlights a sizeable footprint of the incoming boundarylayer on the separated flow, the scaling of which results of the competitionbetween $h$ and $\delta_e$. On the basis of a simple mass budget within theneighbourhood of separation, we propose to model this competition byintroducing the scaling factor $C_{h,\delta} = 1 + \delta_e/h$. With thismodel, we demonstrate that the relationship between shear layer growth and massentrainment rates established for free shear layers (i.e. $\delta_e = 0$) mightbe extended to flows where $\delta_e/h > 0$. Since many control systems rely onmass entrainment to modify separation properties, our findings suggest that theparameter $\delta_e/h$ needs to be taken into account when choosing the mostrelevant strategies for controlling or predicting separating/reattaching flows.

On scaling of mass entrainment in separated shear layers: the footprint of the incoming boundary layer