Secondary Currents and Turbulent Motions in Open-channel Flows over Streamwise Ridges

Streamwise ridges on the bed of open channels are capable of generating time-averaged counter rotating vortices, known in hydraulics as secondary currents (e.g., Nezu and Nakagawa, 1993). These flow features represent a distinct mechanism of momentum delivery to the bed and may also interfere with momentum exchange due to turbulence. The effects of streamwise ridges on flow dynamics remain poorly understood. Preliminary friction factor measurements carried out by the authors suggest that the streamwise ridges may lead to either increase or decrease of hydraulic resistance depending on their spanwise spacing. The aim of this work is to study the effects of streamwise ridges in open-channel flow, with particular focus on secondary currents and their effects on the turbulence structure.

Long-duration (2 hours) high-resolution particle image velocimetry (PIV) measurements were carried out for a range of ridge spacings between 0.4 and 4.0 flow depths; these were supplemented with PIV measurements in the absence of ridges to provide a reference case for comparison. The long measurement time was required to fully resolve spectral wavelengths characterising the largest turbulent scales in the flow, including very large scale motions (long meandering regions of uniform momentum, e.g., Cameron et al., 2017).

The data revealed that streamwise ridges generate secondary currents that scale proportionally to the ridge spacing, with upflows above the ridges and downflows in the inter-ridge gaps (see Figure below). For all studied ridge spacings, the ridges were found to supress the very-large-scale motions which were detected in the reference case without ridges. A previously unknown “secondary current instability” length scale, caused by the low amplitude transverse meandering of the secondary currents, is identified and assessed. The study presents evidence of the effects that secondary currents have on the mean flow, turbulence structure, and overall momentum delivery to the bed. As a result, streamwise ridges modify hydraulic resistance (as preliminary friction factor measurements carried out by the authors show) by generating secondary currents scaled with the ridge spacing.

Figure: Contour maps of time-averaged streamwise velocity u (overbar denotes averaging in time) normalised by bulk flow velocity U. Vectors represent time-averaged velocities in the transverse (y) and vertical (z) directions, while s is spanwise spacing of the ridges.

References

Cameron, S. M., Nikora, V. I., Stewart, M. T. (2017). “Very-large-scale motions in rough-bed open-channel flow.” J. Fluid Mech., 814, 416-429.

Nezu, I., and Nakagawa, H. (1993). Turbulence in open-channel flows, Balkema, Rotterdam, Netherlands.