  Both experiments and direct numerical simulations have been used to
demonstrate that riblets can reduce turbulent drag by as much as $10\%$, but
their systematic design remains an open challenge. In this paper, we develop a
model-based framework to quantify the effect of streamwise-aligned
spanwise-periodic riblets on kinetic energy and skin-friction drag in turbulent
channel flow. We model the effect of riblets as a volume penalization in the
Navier-Stokes equations and use the statistical response of the
eddy-viscosity-enhanced linearized equations to quantify the effect of
background turbulence on the mean velocity and skin-friction drag. For
triangular riblets, our simulation-free approach reliably predicts
drag-reducing trends as well as mechanisms that lead to performance
deterioration for large riblets. We investigate the effect of height and
spacing on drag reduction and demonstrate a correlation between energy
suppression and drag-reduction for appropriately sized riblets. We also analyze
the effect of riblets on drag reduction mechanisms and turbulent flow
structures including very large scale motions. Our results demonstrate the
utility of our approach in capturing the effect of riblets on turbulent flows
using models that are tractable for analysis and optimization.
