Modeling effective transpiration over riblets to improve drag predictions

Riblets are flow-aligned micro-grooves that reduce turbulent skin friction below that of a smooth wall. The drag reduction has been quantified by viscous protrusion-heights theory (Luchini et al., J. Fluid Mech., vol 228, 1991, pp. 87-109). The theory uses viscous (Stokes) flow to characterize the offsets of the mean flow and turbulence above small riblets, where the flow is similar to that above a smooth wall (Luchini, Comp. Meth. Appl. Sci., vol. 3, 1996, pp. 466-470). In this talk, I will assess direct numerical simulation data against the theory and propose an extension to the theory. The assessment points to the importance of crest-transpiration effects (Ibrahim et al., J. Fluid Mech., vol. 915, 2021, pp. A56), which is not accounted for in the protrusion-heights theory, and I will discuss a reduced-order calculation of turbulence structures to incorporate this effect.