Predictive modeling and analysis of riblet erosion effects on turbulent drag reduction

Streamwise-elongated surface corrugations, known as riblets, are well-established for their potential to reduce skin-friction drag by modulating near-wall turbulence. However, their drag-reduction performance and long-term effectiveness are highly sensitive to erosion-induced geometric changes, such as tip rounding or groove filling, which can significantly degrade performance. To preserve the economic benefits of riblets, a robust predictive tool is needed to evaluate worn geometries and design erosion-resilient profiles that sustain drag-reduction over time. Direct numerical simulations or experimental studies of such complex, degraded geometries are computationally and experimentally expensive. To address this challenge, we employ a domain transformation approach that maps the surface geometry onto the differential operators of the linearized Navier–Stokes equations. This enables a perturbation analysis of steady-state flow dynamics, providing a computationally efficient method for analyzing high-Reynolds-number flows over eroded riblets. We parameterize typical microscopic erosion patterns of trapezoidal riblets based on experimental observations and quantify the associated drag increase and efficiency loss. Our analysis reveals that tip rounding with a radius of less than one viscous unit can result in a performance degradation of approximately 45%. These predictions are in close agreement with high-fidelity simulation results. Spectral analysis further shows a progressive decline in the suppression of streamwise streaks with λ_x⁺≈800 over eroded riblets, elucidating the underlying degradation mechanism.