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.

• The paper demonstrates that riblets optimized for ZPG drag reduction can incur up to a 124% drag penalty under acceleration due to geometry-induced local shear.
• It employs DNS with immersed boundary methods to isolate the effect of riblet-induced viscous shear that decouples groove drag from the outer turbulent flow.
• The study identifies Kelvin-Helmholtz rollers as a key mechanism driving earlier retransition, calling for revised scaling models in non-equilibrium flows.

Drag Modulation and Transition Dynamics in Accelerating Turbulent Boundary Layers over Riblets

Introduction

The study investigates the effects of streamwise-aligned riblet geometries on turbulent boundary layers (TBLs) subjected to strong favorable pressure gradients (FPGs). Using direct numerical simulation (DNS) with immersed boundary methods, the paper provides detailed insight into drag modulation mechanisms and turbulence dynamics during relaminarization and retransition phases. The riblet configuration and flow regime are chosen to match canonical drag-reducing conditions under zero pressure gradient (ZPG), establishing a benchmark for contrasting performance under non-equilibrium acceleration.

Methodology

The DNS methodology employs a sinusoidal riblet geometry with optimal viscous-scaled parameters for drag reduction in ZPG TBLs. Two cases are simulated: a smooth wall and a fully ribleted wall, each exposed to identical inflow conditions and a prescribed freestream acceleration profile. The computational domain resolves both riblet-scale and boundary-layer turbulence, with ensemble and time-averaged statistics used for analysis. The riblet size, spacing, and cross-sectional area are selected based on established ZPG literature to ensure comparability in upstream flow conditions.

Drag Modulation: Departure from Canonical Scaling

The simulations demonstrate that riblets, which reduce drag in ZPG conditions, generate significant drag penalties under modest acceleration. The drag penalty arises primarily from geometry-induced concentration of viscous shear near the riblet crests, rather than Reynolds or dispersive stresses, which remain negligible prior to retransition. Despite this increase in total drag, the overlying TBL remains statistically similar to the smooth wall when scaled with the shear stress at the groove opening.

This finding reveals a fundamental decoupling: the groove drag, although dominant in total wall friction, does not transmit directly to the turbulence above. The effective shear at the crest acts as a partial-slip boundary for the TBL, with the outer turbulence governed by this local scale rather than the elevated drag within the grooves. Conventional viscous scaling of riblet size and spacing, as used in ZPG flows, loses predictive accuracy in the presence of strong pressure gradients, especially when groove drag is not communicated to the outer flow.

Transition Dynamics: Relaminarization and Retransition

The evolution of turbulence and coherent structures is tracked through relaminarization and retransition. In both cases, FPG-induced thinning of the boundary layer suppresses turbulence and elongates near-wall streaks. For the smooth wall, retransition proceeds via bypass mechanisms—sinuous and varicose instabilities of streamwise streaks lead to turbulent spot formation, consistent with canonical transition pathways.

In contrast, the riblet case exhibits a fundamentally distinct retransition mechanism. Spanwise Kelvin-Helmholtz (KH) rollers form near the riblet crest, promoted by geometry-imposed local shear layers and increasing FPG amplification. These KH rollers interact dynamically with residual near-wall streaks, undergoing amplification under high-speed streaks and local suppression under low-speed streaks due to differing convection velocities. The result is earlier retransition, more intense turbulence, and rapid breakdown of previously elongated structures. This mechanism enhances drag penalty and turbulence generation within the groove, shifting the canonical understanding of riblet-turbulence interactions in developing boundary layers.

Statistical, Structural, and Scaling Implications

Quantitative turbulence statistics reveal that, prior to retransition, the overlying TBL responds to the effective groove-opening shear rather than the total groove drag. Reynolds stress profiles, joint distributions, and spectral analyses confirm collapse between smooth and riblet cases under appropriate scaling. Dispersive stresses, dominant in sandgrain roughness cases, remain suppressed in riblet flows aligned with the direction of acceleration, facilitating relaminarization.

Once KH rollers initiate breakdown, inertial momentum transport increases within the grooves, mixing previously decoupled groove and TBL flows. Piecewise linear relationships between slip length and groove scale, normalized by effective viscous scales, capture transitions between regimes and identify dynamically relevant scaling for riblet characterization in non-equilibrium flows.

Numerical Results and Contradictory Claims

A strong numerical result is the rapid departure of drag modulation from canonical ZPG curves—drag penalty increases to 124% at peak retransition, compared to modest drag reduction in ZPG. The onset of riblet drag penalty occurs with only a 3% increase in freestream velocity, even when viscous-scaled riblet parameters remain within the conventional drag-reduction range. Contradictory to ZPG-based predictions, riblet performance under acceleration cannot be reliably forecast by viscous scaling alone; non-equilibrium effects and geometry-induced local shear dominate drag outcomes.

Practical and Theoretical Implications

Practically, these findings question the robustness of riblet-based drag reduction strategies in aeronautical and energy applications exposed to varying pressure gradients and boundary-layer development. Predictive models and engineering simulations that rely on ZPG-based correlations require reformulation, incorporating dynamically relevant scaling such as groove-opening shear and KH instability thresholds. Theoretically, the study advances understanding of partial-slip boundaries, geometric control of turbulence, and the role of secondary instability modes in boundary-layer transition.

Future Directions

Future developments include parametric exploration of riblet geometries and flow histories to establish general conditions for KH roller onset and interaction dynamics. Reynolds number dependencies, scale separation effects, and history-driven turbulence modulation in non-equilibrium boundary layers remain unresolved. Broader validation across multiple surface configurations, including airfoils, compressor blades, and complex geometric roughness, is necessary for comprehensive modeling and application guidance.

Conclusion

Direct numerical simulations reveal that riblets optimized for drag reduction under ZPG conditions can induce substantial drag penalties and modify transition dynamics in accelerating turbulent boundary layers. The mechanisms underlying drag modulation and earlier retransition are governed by geometry-induced local shear, partial-slip boundary effects, and Kelvin-Helmholtz instability, which collectively invalidate canonical viscous scaling approaches in non-equilibrium flows. These results necessitate re-examination of predictive riblet performance models and point to dynamically relevant scaling for engineering and theoretical analysis of turbulent boundary layers over structured surfaces (2604.21981).