Experimental characterisation of Kelvin–Helmholtz rollers over riblet surfaces

The formation of Kelvin–Helmholtz-like rollers (referred to as K–H rollers) over riblet surfaces has been linked to the drag-increasing behaviour seen in certain riblet geometries, such as sawtooth and blade riblets, when the riblet size reaches sufficiently large viscous scales (Endrikat et al. (2021 a ), J. Fluid Mech . 913 , A37). In this study, we focus on the sawtooth geometry of fixed physical size, and experimentally examine the response of these K–H rollers to further increases in viscous scaled riblet sizes, by adopting the conventional approach of increasing freestream speeds (and consequently, the friction Reynolds number). Rather than continual strengthening, the present study shows a gradual weakening of these K–H rollers with increasing sawtooth riblet size. This is achieved by an analysis of the roller geometric characteristics using both direct numerical simulations and hot-wire anemometry databases at matched viscous scaled riblet spacings, with the former used to develop a novel methodology for detecting these rollers via streamwise velocity signatures (e.g. as acquired by hot wires). Spectral analysis of the streamwise velocity time series, acquired within riblet grooves, reveals that the frequencies (and the streamwise wavelengths) of the K–H rollers increase with increasing riblet size. Cross-correlation spectra, estimated from unique two-point hot-wire measurements in the cross-plane, show a weakening of the K–H rollers and a reduction in their wall-normal coherence with increasing riblet size. Besides contributing to our understanding of the riblet drag-increasing mechanisms, the present findings also have implications for the heat transfer enhancing capabilities of sawtooth riblets, which have been associated previously with the formation of K–H rollers. The present study also suggests conducting future investigations by decoupling the effects of viscous scaled riblet spacing and friction Reynolds numbers, to characterise their influence on the K–H rollers independently.