Rapidly characterizing drag reduction when riblets are yawed or tip-rounded

The drag reduction that riblets provide in the viscous regime can be rapidly quantified with two-dimensional Stokes flow computations. Wong et al. (A viscous vortex model for predicting the drag reduction of riblet surfaces, J.Fluid Mech., under review) recently improved the accuracy of these computations for flow-aligned riblets by modifying the boundary forcing to represent a nearby quasi-streamwise vortex. However, setting the vortex wavelength constrained the riblet spacing to its integer factors. This constraint is relaxed herein by employing a Floquet–Bloch formulation, which redefines the boundary forcing across a single riblet period. Yawed flow conditions are also efficiently addressed, as the computations remain two-dimensional even when the Bloch wave is not aligned with the riblets. Modeled drag reduction trends agree well with direct numerical simulations for both yawed and tip-rounded riblets.