Stereoscopic particle image velocimetry measurements of open-channel flows over streamwise-orientated triangular-shaped ridges were used to explore interactions between ridge-induced secondary currents (SCs) and turbulence. Terms in the double-averaged (in space and in time) momentum and energy conservation equations were analysed for a range of ridge spacings (s) between 0.4 and 4.0 flow depths (H). The double-averaged equations neatly partition momentum and energy fluxes into turbulence and SC contributions, making them well suited to this study. The obtained data indicate that for a range of s/H between 0.4 and 2.0, the normalised momentum and energy fluxes due to SCs approximately collapse when plotted as functions of (z−d)/s, where z is the vertical coordinate and d a constant that aligns the elevations of SC cell centres. The SCs controlled the shape of the mean velocity distribution with the vertical gradient of the double-averaged streamwise velocity found to be inversely proportional to s near the elevations of SC cell centres. Partitioning the total kinetic energy into double-mean (DMKE), dispersive (DKE) and turbulent (SATKE) components and considering the balance equation for each component indicated that at the elevation of SC cell centres the production rate of SATKE via exchange with DMKE was comparable in magnitude to the production rate via exchange with DKE (due to SCs). For all ridge spacings, SATKE was reduced compared to a no-ridge benchmark case due to suppression of very-large-scale turbulent motions by the SCs. Finally, it is demonstrated that energy is supplied to SCs by turbulence.
Bibliographical noteAcknowledgements. Discussions with I. Marusic (University of Melbourne) and B. Ganapathisubramani (University of Southampton) are greatly appreciated.
Funding. Financial support was provided by the EPSRC/UK grant ‘Bed friction in rough-bed free-surface flows: a theoretical framework, roughness regimes, and quantification’ (grant EP/K041088/1).
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