Receptivity analysis of flows over structured corrugated surfaces

We develop a model-based approach to quantify the receptivity of laminar and turbulent channel flows over corrugated surfaces. For small-amplitude roughness elements, we utilize perturbation analysis to determine the modification to the mean flow. The dynamics of velocity fluctuations around the resulting base velocity profile are studied using the linearized Navier-Stokes equations. In turbulent regime, the effect of background turbulence on the mean velocity is captured by a turbulent viscosity which can be determined from second-order statistics of velocity fluctuations. We utilize the second-order statistics resulting from the stochastically forced linearized model to compute a correction to the turbulent viscosity. This correction in turn influences the turbulent mean velocity and modifies skin-friction drag. Our simulation-free approach paves the way for a systematic analysis of energy amplification and skin-friction drag in the presence of roughness elements of various height and spacing.