Drag reduction in turbulent channel flow over spatially periodic surfaces

Carefully designed surface corrugation is a sensor-free strategy that can reduce skin-friction drag in turbulent flows. In contrast to the traditional approach that relies on numerical simulations and experiments, we develop a model-based framework to quantify the impact of spanwise-periodic surfaces on the dynamics of velocity fluctuations and the resulting mean flow. We model the effect of surface corrugation as a volume penalization on the Navier-Stokes equations and use the statistical response of the stochastically forced linearized equations to quantify the effect of background turbulence on skin-friction drag. For triangular corrugations, we demonstrate that our simulation-free approach reliably predicts drag-reducing trends observed in high-fidelity simulations and experiments.