Journal of Geographical Sciences >
Energy dissipation caused by boundary resistance in a typical reach of the lower Yellow River and the implications for riverbed stability
Xu Haijue (1977-), PhD and Associate Professor, specialized in sediment transport and riverbed evolution. E-mail: ychbai@tju.edu.cn |
Received date: 2021-12-09
Accepted date: 2022-06-02
Online published: 2022-11-25
Supported by
National Natural Science Foundation of China(51979185)
National Natural Science Foundation of China(51879182)
National Natural Science Foundation of China(52109097)
The energy dissipation of boundary resistance is presented in this paper based on the flow resistance. Additionally, the river morphology responses to the resistance energy dissipation are explored using the Gaocun-Taochengpu reach in the lower Yellow River as a prototype. Theoretical analysis, measured data analysis and a one-dimensional hydrodynamic model are synthetically used to calculate the energy dissipation rate and riverbed morphological change. The results show that the energy dissipation rate along the channel will increase in both the mean value and the fluctuation intensity with increasing discharge. However, the energy dissipation rate will first decrease and then increase as the flow section or width-depth ratio increases. In addition, the energy dissipation rate has a significant positive correlation with the riverbed stability index. The results imply that the water and sediment transport efficiency of the river channel can be improved by optimizing the cross-sectional configuration to fulfil the minimum energy dissipation rate of the boundary resistance under stable riverbed conditions.
XU Haijue , LI Yan , HUANG Zhe , BAI Yuchuan , ZHANG Jinliang . Energy dissipation caused by boundary resistance in a typical reach of the lower Yellow River and the implications for riverbed stability[J]. Journal of Geographical Sciences, 2022 , 32(11) : 2311 -2327 . DOI: 10.1007/s11442-022-2049-7
Figure 1 Plan form of the lower Yellow River channel (a) and overview of the study reach (b) |
Figure 2 Schematic diagram of coordinates |
Figure 3 Roughness coefficient distribution at the Gaocun and Sunkou hydrological stations in the lower Yellow River during 2005-2017 |
Figure 4 Comparison of the calculated and measured water levels at Sunkou and Aishan stations in the lower Yellow River |
Figure 5 Variations in the riverbed elevation and thalweg migration from the GC to the TCP stations in the lower Yellow River: (a) bed elevation (Zmin is the thalweg elevation of a cross section, and Zave is the average elevation of riverbed); (b) thalweg migration |
Figure 6 Morphology adjustment of the main channel sections in the lower Yellow River |
Figure 7 Variations in the energy dissipation rate of the boundary resistance from Gaocun to Taochengpu |
Figure 8 Variations in the energy dissipation rate of the boundary resistance from Gaocun to Taochengpu with a flow rate of 4000 m3/s |
Table 1 Average energy dissipation rate and fluctuating intensity in different reaches under a flow rate of 4000 m3/s |
Reach | 2005 | 2016 | ||
---|---|---|---|---|
$\overline{{{P}_{b}}}$(kW/m) | σP | $\overline{{{P}_{b}}}$(kW/m) | σP | |
GC - XMT | 5.56 | 2.11 | 5.51 | 2.68 |
SG - TCP | 4.31 | 1.39 | 4.20 | 1.69 |
Figure 9 Changes in the flow width and water depth from the GC to TCP reaches for different periods: (a) flow width and (b) water depth |
Table 2 Mean flow width, mean water depth and mean fluctuation intensity downstream between the Gaocun and Taochengpu reaches |
Discharge Q (m3/s) | April 2005 | April 2016 | ||||||
---|---|---|---|---|---|---|---|---|
$\bar{B}$(m) | σB | $\bar{h}$(m) | σh | $\bar{B}$(m) | σB | $\bar{h}$(m) | σh | |
1000 | 397 | 111 | 2.53 | 1.19 | 504 | 202 | 2.32 | 0.56 |
2000 | 417 | 129 | 3.02 | 1.04 | 549 | 248 | 3.05 | 0.57 |
3000 | 442 | 134 | 3.56 | 0.93 | 582 | 294 | 3.71 | 0.62 |
4000 | 477 | 139 | 4.02 | 0.86 | 601 | 317 | 4.30 | 0.67 |
Figure 10 Relationship between the energy dissipation rate of the boundary resistance and flow area A and the width-to-depth ratio${\sqrt{B}}/{h}\;$ |
Table 3 Supplementary cross-sections from the Huayuankou-Gaocun reach |
B (m) | h (m) | A (m2) | ${\sqrt{B}}/{h}\;$ | Pb (kW/m) | Section (Year) |
---|---|---|---|---|---|
1020 | 3.3 | 3366 | 9.68 | 2.21 | Babao (2005) |
1210 | 2.92 | 3533 | 11.91 | 3.90 | Liubao (2005) |
1510 | 2.81 | 4243 | 13.83 | 3.88 | Yuanfang (2016) |
1607 | 2.65 | 4259 | 15.13 | 4.20 | Yangxiaozhai (2016) |
1750 | 2.63 | 4603 | 15.91 | 5.10 | Sunzhuang (2005) |
1800 | 2.5 | 4500 | 16.97 | 5.71 | Xiezhaizha (2016) |
Figure 11 Diagrammatic representation of the types of equilibrium (a); sketches of the definitions of stability and instability in an oscillating mechanical system subject to a perturbation (b) (after Knighton, 1984) |
Table 4 Change in the median particle size between the Gaocun and Taochengpu reaches in the lower Yellow River |
Section | Distance from the XLD dam (km) | Median particle size d50 (mm) | |
---|---|---|---|
April 2005 | April 2016 | ||
Gaocun | 303.10 | 0.072 | 0.131 |
Susizhuang | 330.50 | 0.111 | 0.092 |
Gulou | 348.21 | 0.102 | 0.128 |
Yangji | 394.31 | 0.091 | 0.092 |
Sunkou | 421.30 | 0.095 | 0.100 |
Shilipu | 442.00 | 0.076 | 0.088 |
Taochengpu | 456.93 | 0.111 | 0.102 |
Figure 12 Relationship between the energy dissipation rate of the boundary resistance Pb and riverbed stability index KK |
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