Large-scale control in turbulent flows over surface riblets

The drag reduction efficacy of a large-scale flow control over a rough surface is studied via direct numerical simulations of turbulent channels (at friction Reynolds numbers $Reτ=180$⁠) by combining together wall riblets and streamwise counter-rotating swirls. In particular, the height of triangular riblets is $h+≈10$ (+indicating wall units), while the number of riblets (⁠ $NRib$ in the range 1–56) along the periodic spanwise direction is varied to find the optimum. The swirls are generated by the spanwise opposed wall-jet forcing (SOJF) in the Navier–Stokes equation, whose controlling parameters follow the optimal ones as for the smooth wall. In total, 12 cases of combined SOJF and riblets are performed to investigate the coupling effects between the two methods. We find a range of $NRib=7$–14 (with the spanwise width $z+≈140−280$⁠) yields the largest drag reduction (up to 20%) for $Reτ=180$⁠, much higher than riblets control only (about 3%). Compared to SOJF control only, riblets suppress the secondary swirls of SOJF hence decreasing drag, while the lateral and down washing motions of SOJF impinging on riblets would increase drag—the opposite two effects thus giving rise to an optimal. Through examinations on coherent structures, we elucidate that the attenuation of both large-scale coherent motions and small-scale random fluctuations leads to the net drag reduction. We conclude that large-scale control is a robust approach in the cases of rough surfaces, and the parameters can be selected for maximum drag reduction in each particular situation.