Direct numerical simulation of a turbulent boundary layer with separation and reattachment over a range of Reynolds numbers

Direct numerical simulations (DNSs) are used to examine a turbulent boundary layer with large magnitudes of adverse and favourable pressure gradients, thus involving separation and reattachment. The present DNS datasets have been obtained from the simulations of a pressure-induced turbulent separation bubble (Abe 2017 J. Fluid Mech. 833 563-98). Three values of the inlet Reynolds number ( R e θ 0 = 300 , 600 and 900) are used. These magnitudes increase abruptly with pressure gradients; the maximum values are attained near reattachment (i.e. R e θ = 1060 , 2070 and 2915). Also used are the datasets with varying pressure gradient for a fixed inlet Reynolds number ( R e θ 0 = 300 ). Particular attention is given to effects of Reynolds number and pressure gradient on the momentum transport. In particular, we examine the Reynolds shear stress ( − u v ¯ ) with the use of the transport equation, quadrant analysis and instantaneous fields and discuss how this quantity is generated in the present flow and is associated with mean streamwise velocity ( U ¯ ). It is shown that the magnitude of − u v ¯ increases in the APG and separated regions, while it decreases near top of the bubble due to the convex curvature when the bubble is large. For all three Reynolds numbers, the − u v ¯ peaks are obtained in the outer region in which U ¯ exhibits an inflection point. The similarity to a free shear flow in U ¯ is convincing in the separated shear layer where the effect of the inlet Reynolds number (i.e. the active motion in an incoming boundary layer) is still observed in − u v ¯ . The maximum − u v ¯ is attained after reattachment due to the convective nature of the present flow and depends essentially on the pressure gradient. It is also shown that large-scale structures of streamwise velocity fluctuation become more pronounced with moving downstream and contribute significantly to the momentum transport, which yield a large departure from the log law of mean streamwise velocity.