Energy-based drag decomposition analyses for a turbulent channel flow developing over convergent–divergent riblets

Direct numerical simulations of a turbulent channel flow developing over convergent–divergent (C–D) riblets are performed at a Reynolds number of Re_b = 2800, based on the half channel height δ and the bulk velocity. To gain an in-depth understanding of the origin of the drag generated by C–D riblets, a drag decomposition method is derived from kinetic energy principle for a turbulent channel flow with wall roughness. C–D riblets with a wavelength, Λ, ranging from $0.25δ$ to $1.5δ$⁠, are examined to understand the influence of secondary flow motions on the drag. It is found that as Λ increases, the intensity of the secondary flow motion increases first and then decreases, peaking at $Λ/δ=1$⁠. At $Λ/δ≥1$⁠, some heterogeneity appears in the spanwise direction for the turbulent kinetic energy (TKE) and vortical structures, with the strongest enhancement occurring around regions of upwelling. All the riblet cases examined here exhibit an increased drag compared to the smooth wall case. From the energy dissipation/production point of view, such a drag increase is dominated by the TKE production and the viscous dissipation wake component. While the drag contribution from the TKE production shear component decreases as Λ increases, the drag contribution from the wake component of both the TKE production and viscous dissipation follows the same trend as the intensity of the secondary flow motion. From the work point of view, the drag increase in the riblet case at $Λ/δ=0.25$ comes mainly from the work of the Reynolds shear stresses, whereas at $Λ/δ≥1$⁠, the drag augmentation is dominated by the work of the dispersive stresses. At $Λ/δ=0.5$⁠, both components play an important role in the increase in the drag, which also exhibits a peak.