Secondary motions in turbulent ribbed channel flows

We present data from direct numerical simulation (DNS) of the fully turbulent flow through nominally two-dimensional channels containing longitudinal, surface-mounted, rectangular ribs whose widths (W) are either one third of or equal to the gap (S - W) between consecutive ribs across the domain, where S is the span (centre-to-centre spacing) of the ribs. A range of the ratio of channel half-height (H) to span (S) is considered, covering 0.25 <= H/S <= 2.5. In each case, a fixed rib height (h) of 0.1H was used, but a number of cases with much smaller heights, h/H = 0.025 or 0.05, were also studied. The secondary flows resulting from the presence of the ribs are examined, along with their sources in terms of the axial vorticity transport equation, which highlights the effects of spanwise inhomogeneity in the Reynolds stresses. We show that the strength of the secondary flows depends strongly on H/S (and, correspondingly, on W/S) and that the major sources of axial vorticity arise near the top corners of the ribs, with convection of that vorticity dominating its spread. We also show that for smaller ribs, the secondary flow strengths are similar to those predicted by Zampino et al. (J. Fluid Mech., vol. 944, 2022, A4) using a linearised model of the Reynolds-averaged equations, which does not include the vorticity convection process; the behaviour of secondary flow topology and strength with varying W/H is thus noticeably different.