Numerical study on secondary currents of the second kind in wide shallow open channel flows

A theoretically based relationship for the Darcy–Weisbach friction factor $f$ for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.

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Flow structure in compound open-channel flows in the presence of transverse currents

E3S Web of Conferences ◽

10.1051/e3sconf/20184005024 ◽

2018 ◽

Vol 40 ◽

pp. 05024 ◽

Cited By ~ 1

Author(s):

Sébastien Proust ◽

Vladimir Nikora

Keyword(s):

Coherent Structures ◽

Large Scale ◽

Open Channel ◽

Mixing Layer ◽

Free Surface Flows ◽

Channel Flows ◽

Two Dimensional ◽

Open Channel Flows ◽

Secondary Currents ◽

Flow Modification

The structure of free-surface flows is experimentally investigated in a laboratory flume with a compound cross-section consisting of a central main channel (MC) and two adjacent floodplains (FPs). The study focuses on the effects of transverse currents on: (i) mixing layers and quasi-two-dimensional coherent structures at the interfaces between MC and FPs; (ii) secondary currents developing across the channel; and (iii) large and very-large-scale motions that were recently observed in non-compound open channel flows. Transverse currents represent spanwise depth- and time-averaged flow from MC to FPs or vice versa. The study is based on one-point and two-point ADV measurements. Streamwise non-uniform flows are generated by imposing an imbalance in the discharge distribution between MC and FPs at the flume entrance, keeping the total flow rate the same for all scenarios. It is shown that even small transverse currents can be very effective in flow modification, as they can significantly displace the mixing layer, shear-layer turbulence, and coherent structures towards MC or FP, depending on the current direction. They can also alter the distribution and strength of the secondary currents. The interactions of quasi-two-dimensional coherent structures, very-large-scale motions, and secondary currents at different conditions are also part of this study.

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