Theoretical analyses on hydrodynamic instability in narrow deep river with variable curvature

doi:10.1007/s10483-015-1971-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (9): 1147-1168.doi: https://doi.org/10.1007/s10483-015-1971-6

Theoretical analyses on hydrodynamic instability in narrow deep river with variable curvature

Haijue XU^1,2, Yuchuan BAI^1,2

1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China;
2. Institute for Sedimentation on River and Coastal Engineering, Tianjin University, Tianjin 300072, China

收稿日期:2014-05-30 修回日期:2015-01-28 出版日期:2015-09-01 发布日期:2015-09-01
通讯作者: Yuchuan BAI E-mail:ychbai@tju.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 51279124 and 50979066) and the Science Fund for Creative Research Groups of the National Natural Science Foun- dation of China (No. 51021004)

Theoretical analyses on hydrodynamic instability in narrow deep river with variable curvature

Haijue XU^1,2, Yuchuan BAI^1,2

1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China;
2. Institute for Sedimentation on River and Coastal Engineering, Tianjin University, Tianjin 300072, China

Received:2014-05-30 Revised:2015-01-28 Online:2015-09-01 Published:2015-09-01
Contact: Yuchuan BAI E-mail:ychbai@tju.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 51279124 and 50979066) and the Science Fund for Creative Research Groups of the National Natural Science Foun- dation of China (No. 51021004)

摘要/Abstract

摘要： Bending river is the most common river type in nature, and it is also a typical example for river evolution. The transform of the flow pattern can affect the development of the riverbed form. In return, the variation in the riverbed form can affect the hydrodynamic characteristics of the flow, thereby leading to the continuous evolution of the bending river. Based on this, a theoretical model for the bending river is established. The hydrodynamic instability characteristics of the laminar flow in the channel with a variable curvature, a typical model as the meandering river, are studied, and the variations of some parameters such as the curvature, the wave number, and the wave frequency are also discussed.

关键词: bending river, hydrodynamic stability, self-adaptability, nonlinear river dynamics

Abstract: Bending river is the most common river type in nature, and it is also a typical example for river evolution. The transform of the flow pattern can affect the development of the riverbed form. In return, the variation in the riverbed form can affect the hydrodynamic characteristics of the flow, thereby leading to the continuous evolution of the bending river. Based on this, a theoretical model for the bending river is established. The hydrodynamic instability characteristics of the laminar flow in the channel with a variable curvature, a typical model as the meandering river, are studied, and the variations of some parameters such as the curvature, the wave number, and the wave frequency are also discussed.

Key words: nonlinear river dynamics, self-adaptability, bending river, hydrodynamic stability

中图分类号:

O158

Haijue XU, Yuchuan BAI. Theoretical analyses on hydrodynamic instability in narrow deep river with variable curvature[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(9): 1147-1168.

参考文献

[1] Frank, E. Flow and bed topography in channel bends. Journal of the Hydraulics Division, 100, 1631-1648(1974)
[2] Parker, G. and Andrews, E. D. Sorting of bedload sediments by flow in meander bends. Water Resource Research, 21, 1361-1373(1985)
[3] Zhao, Y. A. and Long, P. L. Channel Pattern Dynamics, Yellow River Institute of Hydraulic Research, Zhengzhou, 43-46(2005)
[4] Hou, H. C. Basic Problem of River Dynamics, Water Resource Press, Beijing (1982)
[5] Shao, X. J. and Wang, G. Q. The impact of upper yellow river hydropower development on downstream fluvial processes. Journal of Hydroelectric Engineering, 76, 128-138(2002)
[6] Syunsuke, I., Gary, P., and Kenji, S. Bend theory of river meanders, part 1:linear development. Journal of Fluid Mechanics, 112, 363-377(1981)
[7] Parker, G., Sawai, K., and Ikeda, S. Bend theory of river meanders, part 2:nonlinear deformation of finite-amplitude bends. Journal of Fluid Mechanics, 115, 303-314(1982)
[8] Chang, H. H. Fluvial Processes in River Engineering, Krieger Publishing Company, New York (1988)
[9] Bai, Y. C. and Luo, J. S. The loss of stability of laminar flow in open channel and the mechanism of sand ripple formation. Applied Mathematics and Mechanics (English Edition), 23(2), 276-293(2002) DOI 10.1007/BF02438335
[10] Bai, Y. C. and Xu, H. J. A study on the stability of laminar open-channel flow over a sandy rippled bed. Science in China, Series E:Engineering & Materials Science, 35, 53-73(2005)
[11] Shi, X. G. Turbulence, Tianjin University Press, Tianjin (1994)
[12] Bai, Y. C. and Andreas, M. A linear disturbance theory for coherent structure and mechanic sand waves in open-channel flow. International Journal of Sediment Research, 16, 234-243(2001)
[13] Hou, H. C. Analysis on the dynamic process of the laminar boundary layer. Journal of Sun Yatsen University, 4, 35-52(1977)
[14] Bai, Y. C. and Xu, D. Numerical simulation of the lateral migration of meandering rivers and floodplain development processes. Journal of Sediment Research, 4, 68-72(2010)
[15] Yalin, M. S. River Mechanics, Pergamon Press, Oxford (1992)
[16] Bai, Y. C. Nonlinear River Dynamics, Tianjin University, Tianjin (2009)
[17] Monson, D. J., Seegmiller, H. L., and McConnaughey, P. K. Comparision of experiment with calculations using curvature-corrected zero and two equation turbulence models for a two-dimensional U-duct. AIAA 21st Fluid Dynamics, Plasma Dynamics and Lasers Conference, Seattle (1990)
[18] Jiang, L. and Lakashminarayana, B. Prediction of strongly curved turbulent duct flows with Reynolds stress model. AIAA Journal, 35, 91-98(1997)
[19] Zhang, R. J., Xie, J. H., and Chen, W. B. River Dynamics, Wuhan University Press, Wuhan (2007)
[20] Zhao, G. F. Secondary instability of large scale structure in free turbulent shear layer. Applied Mathematics and Mechanics (English Edition), 16(4), 383-389(1995) DOI 10.1007/BF02456952
[21] Herbert, T. Secondary instability of boundary layers. Annual Review of Fluid Mechanics, 20, 487-526(1988)
[22] Wang, F. M. Accurate solution of the Orr-Sommerfeld eigenvalue equation. Chinese Journal of Computational Physics, 2, 489-497(1985)
[23] Wang, F. M. and Huang, Z. Y. An expansion solution of Orr-Sommerfeld eigenvalue problem for Poiseuille flow (in Chinese). Journal on Numerical Methods and Computer Application, 1, 37-51(1991)
[24] Shen, Y. M., Wu, X. G., and Zheng, Y. H. Algebraic-stress turbulent model for 2-D plane flow in curvilinear coordinates. Journal of Hydraulic Engineering, 36, 383-390(2005)
[25] Orszag, S. A. Accurate solution to the Orr-Sommerfeld stability equation. Journal of Fluid Mechanics, 50, 689-703(1971)
[26] Reynolds, W. C. and Potter, M. C. Finite-amplitude instability of parallel shear flows. Journal of Fluid Mechanics, 27, 465-492(1967)
[27] Nishioka, M. and Ichikawa, Y. An experimental investigation of the stability of plane Poiseuille flow. Journal of Fluid Mechanics, 72, 731-751(1975)

Theoretical analyses on hydrodynamic instability in narrow deep river with variable curvature

Theoretical analyses on hydrodynamic instability in narrow deep river with variable curvature

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