Drag reduction by riblets

The interaction of the overlying turbulent flow with riblets, and its impact on their drag reduction properties are analysed. In the so-called viscous regime of vanishing riblet spacing, the drag reduction is proportional to the riblet size, but for larger riblets the proportionality breaks down, and the drag reduction eventually becomes an increase. It is found that the groove cross section A(g)(+) is a better characterization of this breakdown than the riblet spacing, with an optimum A(g)(+1/2) ≈ 11. It is also found that the breakdown is not associated with the lodging of quasi-streamwise vortices inside the riblet grooves, or with the inapplicability of the Stokes hypothesis to the flow along the grooves, but with the appearance of quasi-two-dimensional spanwise vortices below y(+) ≈ 30, with typical streamwise wavelengths λ(x)(+) ≈ 150. They are connected with a Kelvin-Helmholtz-like instability of the mean velocity profile, also found in flows over plant canopies and other surfaces with transpiration. A simplified stability model for the ribbed surface approximately accounts for the scaling of the viscous breakdown with A(g)(+).