Reorganisation of turbulence by large and spanwise-varying riblets

Abstract

We study the flow above non-optimal riblets, specifically large drag-increasing and two-scale trapezoidal riblets. In order to reach large Reynolds numbers and large scale separation while retaining access to flow details, we employ a combination of boundary-layer hot-wire measurements and direct numerical simulation (DNS) in minimal-span channels. Although the outer Reynolds numbers differ, we observe fair agreement between experiments and DNS at matched viscous–friction-scaled riblet spacings $s^+$ in the overlapping physical and spectral regions, providing confidence that both data sets are valid. We find that hot-wire velocity spectra above very large riblets with $s^+ \gtrsim 60$ are depleted of near-wall energy at scales that are (much) greater than $s$ . Large-scale energy likely bypasses the turbulence cascade and is transferred directly to secondary flows of size $s$ , which we observe to grow in strength with increasing riblet size. Furthermore, the present very large riblets reduce the von Kármán constant $\kappa$ of the spanwise uniform mean velocity in a logarithmic layer and, thus, reduce the accuracy of the roughness-function concept, which we link to the near-wall damping of large flow structures. Half-height riblets in the groove, which we use as a model of imperfectly repeated (spanwise-varying) riblets, impede in-groove turbulence. We show how to scale the drag optimum of imperfectly repeated riblets based on representative measurements of the true geometry by solving inexpensive Poisson equations.