Drag penalty during relaminarization and Kelvin-Helmholtz-promoted retransition in an accelerating turbulent boundary layer over initially drag-reducing riblets

Abstract

Direct numerical simulations of an accelerating turbulent boundary layer (TBL) over a smooth wall and a wall fully covered with streamwise-aligned riblets are performed to investigate drag modulation and its underlying mechanisms. The riblet-scale flow is resolved using an immersed boundary method. Starting from a zero-pressure-gradient (ZPG) TBL at Re=6800, the flow undergoes a threefold freestream acceleration over seventy-five boundary-layer thicknesses, matching the development reported by Warnack and Fernholz (1998), and consequently experiences relaminarization followed by retransition farther downstream. The riblets, defined by a sinusoidal spanwise profile with initial s+=15.2 and lg+=10.5, correspond to near-optimal drag-reducing size in ZPG flows. However, even modest acceleration renders them drag-increasing, showing that the conventional ZPG interpretation based on total-drag viscous scaling does not apply directly in this non-equilibrium flow. During relaminarization, the drag penalty arises primarily from geometry-determined concentration of viscous shear near the riblet crest, with negligible direct Reynolds- and dispersive-stress contributions prior to retransition. Despite the drag increase, the overlying TBL remains statistically similar to the smooth-wall case when scaled with the total shear stress at the groove opening, demonstrating that this shear sets the relevant scaling for the TBL, while the additional drag generated within the grooves remains largely decoupled from the outer-layer turbulence dynamics. This partial decoupling persists until the onset of retransition, when spanwise Kelvin-Helmholtz rollers develop near the riblet crest and promote earlier, stronger retransition through their interaction with the residual near-wall streaks. These findings provide a revised physical picture of riblet performance in non-equilibrium turbulent flows.