Model-based analysis of turbulent drag reduction in channel flow over corrugated surfaces

We develop a model-based approach to quantify the effect of spatially periodic surface corrugation on skin-friction drag in turbulent channel flow. The effect of surface corrugation is modeled as a volume penalization on the Navier-Stokes equations and the dynamics of velocity fluctuations around the resulting base velocity profile are studied using the eddy-viscosity enhanced linearized equations. We utilize the second-order statistics of velocity fluctuations resulting from the stochastically forced linearized model to compute a correction to the turbulent viscosity of flow over the corrugated surface. This correction in turn influences the turbulent mean velocity and modifies skin-friction drag. For triangular surface corrugation, our simulation-free approach reliably predicts drag-reducing trends observed in high-fidelity simulations and experiments. We investigate the effect of height and spacing of triangular riblets on these drag-reducing trends and demonstrate similar trends for the turbulent kinetic energy of velocity fluctuations. Finally, we examine the flow structures that are extracted from a modal decomposition of the velocity covariance matrix and uncover the influence of periodic surface corrugation on the energetic near-wall cycle.