Flow Resistance Equation in Sand-bed Rivers and Its Practical Application in the Yellow River

Rongrong Cai,Luohao Zhang,Hongwu Zhang,Yu Zhang,Hai Huang

doi:10.3390/w12030727

Abstract

To fully reflect the effect of the flow characteristics, sidewall conditions and sediment concentrations on the bed roughness of sand-bed rivers, this study established a new flow resistance equation by introducing a comprehensive influence coefficient presented via a combination of power-function forms of the relative flow velocity, von Karman constant of sediment-laden flows and the ratio of particle size to viscous sublayer thickness. The comprehensive influence coefficient accordingly acts as a synthesized factor representing the combined effects of the flow intensity, bed material movement, energy consumption condition, and relative friction condition in the near-wall region of sediment-laden flows. Based on the field data from sediment-laden flows under scenarios of both high and low sediment concentrations, the performance of the proposed equation was validated to achieve the best accuracy in the calculation of Manning’s roughness coefficient compared with that of several previously presented flow resistance equations. Furthermore, the proposed flow resistance equation was adopted to quantify the stable channel width of the Lower Yellow River (LYR), i.e., the optimum main channel width for sediment transportation in the typical wandering reach of the LYR. The calculated stable channel width is consistent with the current river training width of the LYR, indicating that the proposed equation has great potential as a theoretical tool that can be used to support the determination of the river training strategy for the LYR.

Highlights

Estimating bed roughness with adequate precision is essential in understanding the dynamic and morphological processes (e.g., [1,2]) of rivers and in guiding channel engineering (e.g., [3,4]).In particular, Chang [5] indicated that the parameters of channel morphology, such as the stable channel width, can be obtained through a combination of the minimum stream power concept, the water continuity equation, the sediment transport equation and a proper flow resistance equation
The determination of the stable channel width is crucial in river training, especially for the determination of a river training strategy for the Lower Yellow River (LYR), which is well known for its high sediment concentration [6]
The existing method of Chang [5] applies to channels with low flow discharge and sediment discharge only, and it fails in the calculation of the stable channel width for large sand-bed rivers such as the LYR; in the case of the LYR, this failure is due to the inapplicability of the flow resistance equations and sediment discharge equations recommended by

Summary

Introduction

Chang [5] indicated that the parameters of channel morphology, such as the stable channel width, can be obtained through a combination of the minimum stream power concept, the water continuity equation, the sediment transport equation and a proper flow resistance equation (expression of bed roughness). The wide-river training strategy (leaving adequate space between the main channel and the Grand Levees (the outer boundary of the LYR). Water 2020, 12, 727; doi:10.3390/w12030727 www.mdpi.com/journal/water (constructing various river training structures in the vicinity of the outer boundary of the main channel to maintain a narrow river channel for flood conveyance and sediment transportation) [7] continues (e.g., narrow-river training strategy: Zhang et al [8], and Hu [9]; wide-river training strategy: Wang and Liu [10]).

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Conclusion