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Abstract
The prediction of the velocity distribution in adverse-slope flow is improved by analytical and experimental study of the wake and dip effects, based on the log-wake-dip velocity law. This improved equation allows accurate prediction of the wake phenomenon and dip phenomenon. The equation compares very well with the experimental data obtained in the present study and some reference data, and it predicts better than other formulations available in the literature. This study shows that the wake-parameter can be expressed by the linear equation for the pressure-gradient parameter, under the conditions of the respective Reynolds number and aspect ratio. The dip-parameter can be determined as constants using the known position of the maximum velocity point. When the pressure gradient is relatively small, the wake effect is a boost to velocity. In contrast, when the pressure gradient is relatively large, the wake effect is an impediment to velocity.
Acknowledgements
The authors thank the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering of Hohai University for use of the tiltable recirculating rectangular flume. The authors also thank the editor and the anonymous reviewers for taking the time to review the paper and for their constructive comments and suggestions for the improvement of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notation
| a | = | flow acceleration (m s−2) |
| B | = | channel width (m) |
| c | = | intercept constant of relationship between Π and β (−) |
| F | = | Froude number (−) |
| g | = | gravity acceleration (m s2) |
| H | = | water depth (m) |
| J | = | energy slope (−) |
| ks | = | bed roughness (m) |
| p* | = | piezometric pressure (Pa) |
| Q | = | flow discharge (m3 s−1) |
| R | = | hydraulic radius (m) |
| Re | = | Reynolds number (−) |
| S | = | channel bed slope (−) |
| u | = | longitudinal point velocity (m s−1) |
| u* | = | friction velocity (m s−1) |
| U | = | depth-average flow velocity (m s−1) |
| x | = | distance in the longitudinal direction (m) |
| X | = | distance in the longitudinal direction in coordinate figure (m) |
| z | = | distance perpendicular to the bed surface (m) |
| Z | = | distance perpendicular to the bed surface in coordinate figure (m) |
| z0 | = | reference-bed level (m) |
| α | = | dip-parameter (−) |
| β | = | pressure-gradient parameter (−) |
| δ | = | distance from the reference level to the maximum velocity point (m) |
| θ | = | channel bed angle (°) |
| κ | = | von Karman’s constant (−) |
| ν | = | kinematic viscosity (m2 s−1) |
| Π | = | Coles’ wake-parameter (−) |
| ρ | = | water density (kg m−3) |
| τ0 | = | bed shear stress (Pa) |