Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation

doi:10.1007/s10483-015-1897-9

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (1): 107-120.doi: https://doi.org/10.1007/s10483-015-1897-9

Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation

Wei-jie WANG¹, Wen-xin HUAI¹, Yu-hong ZENG¹, Ji-fu ZHOU²

1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, P. R. China;
2. Institute of Mechanics, Chinese Academy of Sciences, Beijing 100192, P. R. China

收稿日期:2013-12-13 修回日期:2014-06-19 出版日期:2015-01-01 发布日期:2015-01-01
通讯作者: Wen-xin HUAI, Professor, Ph.D., E-mail: wxhuai@whu.edu.cn E-mail:wxhuai@whu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11372232 and 51479007), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130141110016), and the State Water Pollution Control and Management of Major Special Science and Technology (No. 2012ZX07205-005-03)

Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation

Wei-jie WANG¹, Wen-xin HUAI¹, Yu-hong ZENG¹, Ji-fu ZHOU²

1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, P. R. China;
2. Institute of Mechanics, Chinese Academy of Sciences, Beijing 100192, P. R. China

Received:2013-12-13 Revised:2014-06-19 Online:2015-01-01 Published:2015-01-01
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11372232 and 51479007), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130141110016), and the State Water Pollution Control and Management of Major Special Science and Technology (No. 2012ZX07205-005-03)

摘要/Abstract

摘要： An analytical solution for predicting the vertical distribution of streamwise mean velocity in an open channel flow with submerged flexible vegetation is proposed when large bending occurs. The flow regime is separated into two horizontal layers: a vegetation layer and a free water layer. In the vegetation layer, a mechanical analysis for the flexible vegetation is conducted, and an approximately linear relationship between the drag force of bending vegetation and the streamwise mean flow velocity is observed in the case of large deflection, which differes significantly from the case of rigid upright vegetation. Based on the theoretical analysis, a linear streamwise drag force-mean flow velocity expression in the momentum equation is derived, and an analytical solution is obtained. For the free water layer, a new expression is presented, replacing the traditional logarithmic velocity distribution, to obtain a zero velocity gradient at the water surface. Finally, the analytical predictions are compared with published experimental data, and the good agreement demonstrates that this model is effective for the open channel flow through the large deflection flexible vegetation.

关键词: mixing length theory, large deflection, linear drag force, flexible vegetation, analytical velocity distribution

Abstract: An analytical solution for predicting the vertical distribution of streamwise mean velocity in an open channel flow with submerged flexible vegetation is proposed when large bending occurs. The flow regime is separated into two horizontal layers: a vegetation layer and a free water layer. In the vegetation layer, a mechanical analysis for the flexible vegetation is conducted, and an approximately linear relationship between the drag force of bending vegetation and the streamwise mean flow velocity is observed in the case of large deflection, which differes significantly from the case of rigid upright vegetation. Based on the theoretical analysis, a linear streamwise drag force-mean flow velocity expression in the momentum equation is derived, and an analytical solution is obtained. For the free water layer, a new expression is presented, replacing the traditional logarithmic velocity distribution, to obtain a zero velocity gradient at the water surface. Finally, the analytical predictions are compared with published experimental data, and the good agreement demonstrates that this model is effective for the open channel flow through the large deflection flexible vegetation.

Key words: large deflection, analytical velocity distribution, mixing length theory, flexible vegetation, linear drag force

中图分类号:

TV133.1

Wei-jie WANG;Wen-xin HUAI;Yu-hong ZENG;Ji-fu ZHOU. Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(1): 107-120.

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Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation

Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation

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