Analyzing Kelvin-Helmholtz-Induced Drag-Reduction Degradation in Large Riblets Using Linearized Navier-Stokes

Numerical and experimental studies have shown that small riblets with appropriate spacing reduce skin-friction drag in wall-bounded flows. Recent efforts in reduced-order modeling have demonstrated the efficacy of the eddy viscosity-enhanced linearized Navier-Stokes equations in capturing this drag reduction. In these studies, the immersed boundary method in conjunction with a constructive turbulence modeling procedure were used to capture the effect of riblets on the flow. This approach, however, struggles to capture the flow mechanisms surrounding large sharp riblets, especially at high Reynolds numbers, as the problem size can become prohibitively large. In this paper, we employ a domain transformation that facilitates a perturbation analysis and significantly reduces computational complexity. We first show that this approach captures previously reported drag reduction trends of {scalloped and triangular} riblets. We then use our simulation-free approach to examine flow mechanisms, such as the Kelvin-Helmholtz instability, that affect the drag reducing benefits of riblets.