Influence of riblet shapes on the occurrence of Kelvin-Helmholtz rollers

We investigate turbulent flow over streamwise-aligned riblets (grooves) of various shapes and sizes. Small riblets with spacings of typically less than viscous units are known to reduce skin-friction drag compared to a smooth wall, but larger riblets allow inertial-flow mechanisms to appear and cause drag reduction to break down. One of these mechanisms is a Kelvin-Helmholtz instability that Garcia-Mayoral & Jimenez (J. Fluid Mech., vol. 678, 2011, pp. 317-347) identified in turbulent flow over blade riblets. In order to evaluate its dependence on riblet shape and thus gain a broader understanding of the underlying physics, we generate an extensive data set comprising 21 cases using direct numerical simulations of fully developed minimal-span channel flow. The data set contains six riblet shapes of varying sizes between maximum drag reduction and significant drag increase. Comparing the flow fields over riblets to that over a smooth wall, we find that in this data set only large sharp-triangular and blade riblets have a drag penalty associated with the Kelvin-Helmholtz instability and that the mechanism appears to be absent for blunt-triangular and trapezoidal riblets of any size. We therefore investigate two indicators for the occurrence of Kelvin-Helmholtz rollers in turbulent flow over riblets. First, we confirm for all six riblet shapes that the groove cross-sectional area in viscous units serves as a proxy for the wall-normal permeability that is necessary for the development of Kelvin-Helmholtz rollers. Additionally, we find that the occurrence of the instability correlates with a high momentum absorption at the riblet tips. The momentum absorption can be qualitatively predicted using Stokes flow.

Automated summary

Research has shown that only large sharp-triangular and blade riblets increase drag due to the Kelvin-Helmholtz instability, while blunt-triangular and trapezoidal riblets do not exhibit this mechanism. This study also found that the cross-sectional area of the grooves in viscous units serves as a proxy for the necessary wall-normal permeability for the development of Kelvin-Helmholtz rollers. Additionally, the occurrence of the instability is correlated with high momentum absorption at the riblet tips, which can be predicted qualitatively using Stokes flow.