蜿蜒河流长期演变过程数学模型
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摘要
探索河流长期演变规律是河流动力学中的一个基本问题。数学模型被广泛的应用于蜿蜒河流长期演变过程的研究中,本文希望建立数学模型来模拟和解释自然河流的演变动力过程。通过将河湾长期演变的研究理论运用于实际,指导人们正确的认识、开发和利用河流资源,更好的开展流域规划、河道整治及生态环境修复等工作。
对非线性河流动力学的基本理论原理作了简要概述,介绍了河流演变过程的平衡态及非平衡态问题,并在基础上逐步建立河流平衡及扰动发展方程。
运用自然模型法,采用清水冲刷成功地塑造了室内天然小河。实验研究了不同的初始河流几何边界条件以及水流条件对河流演变的影响。研究发现流量对河流展宽幅值影响最大。水流入射角的大小与河流展宽幅度及河流弯曲度的变化没有必然的联系,300入射角时小河的河流展宽及弯曲度变化最明显。入射角对河流演变的作用只是短期的,且在演变初始阶段影响较大。受初始边界条件的影响,河流向下游演变具有滞后性及曲率变化的传递性等特点。实验分析了河流演变过程中的泥沙分选现象。
运用数学模型模拟了蜿蜒河流长期演变过程,分析了演变过程中的动力特性。模拟结果表明:蜿蜒河流存在着最不稳定波长,河流的演化是从最不稳定波长发育开始,扰动波不能长期保持,河流自身具有滤波功能。模拟了蓟运河长期演变过程,分析了蓟运河地形沉积过程及上、中、下游的演变趋势。简要分析了蓟运河未来长期演变对海河流域生态环境及生产生活的影响。
Explore the long-term evolution is a basic problem of river dynamics. Mathematical model was widely used in the research of the long-term evolution process of meandering rivers, in this article, I want to establish mathematical model to simulate and explain the evolution of natural river dynamic process. Will bend in the evolution of the long-term research theory to practice, guiding people recognize and develop and utilize the river resources correct, better carrying out watershed planning, river regulation and ecological environment restoration and other works.
In this paper, the basic theory of nonlinear river dynamics theory has been briefly discussed. This paper introduces the evolution process of the river equilibrium and non-equilibrium problems and establishes river’s balance and disturbance development equation on the basis of the theory.
Using the natural model method, an indoor natural river has been successfully portrayed with the scouring water. The experiment includes the study of the influence of river channel evolution process duing to different initial river geometric boundary conditions and different flow conditions. Studies reveal that flow is mostly influence to river stretcher amplitude. There are no necessarily relationships among the size of the inflow angle and river’s stretcher range and the changes of river bend degrees, when the inflow angle is 300, changes of river width and curvature are more obvious. The inflow angle affects the river evolution in a short-term and has a greater impact in the initial stage of evolution. Subjecting to initial boundary conditions, river’s evolution downward is lag and transitivity of curvature changes. This paper analyzes the sediment sorting phenomena in the process of river evolution.
The model simulates the long-term evolution process of meandering river and analyzes the dynamic characteristics in the process of evolution. The simulation results show that meandering river has the most unstable wavelength, the evolution of the river start from the most unstable wavelength, disturbance wave can't keep for a long time, the river itself has filter function. Using the mathematical model to simulate the long-term evolution process of Jiyun river, analyzing the deposition process and the evolution trend of upstream, middle reaches and downstream in Jiyun river. Analyzing the effect of the long-term evolution process of Jiyun river on ecological environment and production and life in Haihe basin.
对非线性河流动力学的基本理论原理作了简要概述,介绍了河流演变过程的平衡态及非平衡态问题,并在基础上逐步建立河流平衡及扰动发展方程。
运用自然模型法,采用清水冲刷成功地塑造了室内天然小河。实验研究了不同的初始河流几何边界条件以及水流条件对河流演变的影响。研究发现流量对河流展宽幅值影响最大。水流入射角的大小与河流展宽幅度及河流弯曲度的变化没有必然的联系,300入射角时小河的河流展宽及弯曲度变化最明显。入射角对河流演变的作用只是短期的,且在演变初始阶段影响较大。受初始边界条件的影响,河流向下游演变具有滞后性及曲率变化的传递性等特点。实验分析了河流演变过程中的泥沙分选现象。
运用数学模型模拟了蜿蜒河流长期演变过程,分析了演变过程中的动力特性。模拟结果表明:蜿蜒河流存在着最不稳定波长,河流的演化是从最不稳定波长发育开始,扰动波不能长期保持,河流自身具有滤波功能。模拟了蓟运河长期演变过程,分析了蓟运河地形沉积过程及上、中、下游的演变趋势。简要分析了蓟运河未来长期演变对海河流域生态环境及生产生活的影响。
Explore the long-term evolution is a basic problem of river dynamics. Mathematical model was widely used in the research of the long-term evolution process of meandering rivers, in this article, I want to establish mathematical model to simulate and explain the evolution of natural river dynamic process. Will bend in the evolution of the long-term research theory to practice, guiding people recognize and develop and utilize the river resources correct, better carrying out watershed planning, river regulation and ecological environment restoration and other works.
In this paper, the basic theory of nonlinear river dynamics theory has been briefly discussed. This paper introduces the evolution process of the river equilibrium and non-equilibrium problems and establishes river’s balance and disturbance development equation on the basis of the theory.
Using the natural model method, an indoor natural river has been successfully portrayed with the scouring water. The experiment includes the study of the influence of river channel evolution process duing to different initial river geometric boundary conditions and different flow conditions. Studies reveal that flow is mostly influence to river stretcher amplitude. There are no necessarily relationships among the size of the inflow angle and river’s stretcher range and the changes of river bend degrees, when the inflow angle is 300, changes of river width and curvature are more obvious. The inflow angle affects the river evolution in a short-term and has a greater impact in the initial stage of evolution. Subjecting to initial boundary conditions, river’s evolution downward is lag and transitivity of curvature changes. This paper analyzes the sediment sorting phenomena in the process of river evolution.
The model simulates the long-term evolution process of meandering river and analyzes the dynamic characteristics in the process of evolution. The simulation results show that meandering river has the most unstable wavelength, the evolution of the river start from the most unstable wavelength, disturbance wave can't keep for a long time, the river itself has filter function. Using the mathematical model to simulate the long-term evolution process of Jiyun river, analyzing the deposition process and the evolution trend of upstream, middle reaches and downstream in Jiyun river. Analyzing the effect of the long-term evolution process of Jiyun river on ecological environment and production and life in Haihe basin.
引文
[1]董哲仁.生态水工学探索[M].北京:中国水利水电出版社,2007
[2]白玉川.非现性河流动力学学科研究构想及研究进展[C].第三次全国环境力学研讨会,武汉,2007年10月
[3]张瑞瑾,谢鉴衡,陈文彪等.河流动力学[M].武汉:武汉大学出版社,2007
[4]Frank Engelund. Flow and Bed Topography in Channel Bends[J]. Journal of the Hydraulics Division, 1974, 100(11): 1631-1648
[5]Gottlieb, L.(1976)“Three-dimensional flow pattern and bed topography in meandering channel,”Series paper 11, Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark,1-79.
[6]Ikeda, S., Parker, G., and Sawai, K (1981).“Bend theory of river meanders. Part 1. Linear development,“Journal of Fluid Mechanics, 112,363-377.
[7] Smith JD, McLean SR. A model for flow in meandering streams[J]. Water Resources Research, 1984, 20(9): 1301-1315
[8] Blondeaux P. and G. Seminara. A unified bar-bend theory of river meanders[J]. Journal of Fluid Mechanics, 1985, 157: 449-470
[9]Struiksma, N. (1985).“Prediction of 2-D bed topography in rivers,”Journal of Hydraulic Engineering,111(8), 1116-1182.
[10] Johannesson, H., and G. Parker. Linear theory of river meanders[C]. River Meandering. Water Resources Monograph 12. American Geophysical Union, Washington. 1989: 181-214
[11] Howard A.D. and T.R. Knutson. Sufficient conditions for river meandering: A simulation approach[J]. Water Resource Research, 1984, 20(11): 1659-1667
[12] Howard AD. Modelling channel migration and floodplain development in meandering streams[M]. In Lowland Floodplain Rivers, Carling PA, Petts GE (eds). New York: John Wiley & Sons: Chichester, 1992
[13] Meakin Paul, Tao Sun, et al. A simulation model for meandering rivers and their associated sedimentary environments[J]. Physica A, 1996, 233(2): 606-618
[14] Sun T., P. Meakin and T. J?ssang. Meander migration and the lateral tilting of floodplains[J]. Water Resource Research, 2001, 37(5): 1485–1502
[15] Hickin E.J., Nanson G.C. The character of channel migration on the beatton river, northeast British Columbia, Canada[J]. Bulletin of the Geological Society of America, 1975, 86: 487–494
[16] Syunsuke Ikeda, Gary Parker and Kenji Sawai. Bend theory of river meanders. Part 1. Linear development[J]. Journal of Fluid Mechanics, 1981, 112: 363-377
[17] Odgaard, A. J. (1987).“Streambank erosion along two rivers in Iowa,”Water Resources Research, 23(7), 1224-1236.
[18]Crosato, A. (1987).“Simulation model of meandering processes of rivers,”Extended Abstracts, Euromech 215 Conference, Sept. 14-19, Genova, Italy, 158-1613
[19] Boyd F. Edwards and Duane H. Smith. River meandering dynamics[J]. Physical Review E, 2002, 65, 046303: 1-12
[20]Roher, W. L. M. (1983).“Effects of flow and bank material on meander migration in alluvial rivers,”Proceedings, River Meandering, River’83 Conference, ASCE, Oct. 23-26, New Orleans, U.S.A.,770-782.
[21] S. V. Chitale. Modeling for Width Adjustment in Alluvial Rivers[J]. Journal of Hydraulic Engineering, 2003, 129(5): 403-407
[22] D. Chen, J.G.Duan. Modeling width adjustment in meandering channels[J]. Journal of Hydrology, 2006, 321: 59-76
[23]王随继,倪晋仁,王光谦.河流沉积学研究进展及发展趋势[J].应用基础与工程科学学报,2000,8(4):362-369
[24] Bridge J.S. Computer simulation of sedimentation in meandering streams[J]. Sedimentology, 1975, 22: 3-43
[25] Jackson R.G. Depositional model of point bars in the lower Wabash River[J]. Journal of Sedimentary Petrology, 1976, 46: 579-594
[26] Brian J. Willis. Palaeochannel reconstructions from point bar deposits: a three-dimensional perspective[J]. Sedimentology, 1989, 36(5): 757-766
[27] Allen J.R.L. Studies in fluviatile sedimentation: an exploratory quantitative model for the architecture of avulsion-controlled alluvial suites[J]. Sedimentary Geology, 1978, 21: 129-147
[28]Leeder, M.R.(1978) A quantitative stratigraphic model for alluvium, with special reference to channel deposit density and interconnectedness. In: Fluvial Sedimentology, A.D. Mial (ed.), Calary, Canadian Society of Petroleum Geological Society Special Petroleum Geoligists, 587-596.
[29]Bridge, J.S. (1978) Palaeohydraulic interpretation using mathematical models of contemporary flow and sedimentation in meandering channels. In: Fluvial Sedimentology, A.D. Mial (ed.), Calary, Canadian Society of Petroleum Geological Society Special Petroleum Geoligists, 723-742.
[30]Kesel, R.H., Dunne, K.C., McDonald, R.C. Allison, K.R. and Spicer, B.E.(1974) Lateral erosion and overbank deposition on the Mississippi River in Louisiana caused by 1973 flooding. Geology, 2, 461-494.
[31]Pizzoto, J.E. (1987) Sediment diffusion during overbank flows. Sedimentology, 34, 301-317.
[32]Wolman, M.G. and Leopold, L.B.(1957) River flood plain: some observations on their formation. US Geological Survey Professional Paper 282-C,87-109.
[33]Everitt , B.L. (1986) Use of the cottonwood in an investigation of the recent history of a flood plain. American Journal of Science, 266,417-439.
[34]Nanson, G.C. (1980) Point bar and floodplain formation of the meandering Beatton River, northeastern British Columbia, Canada. Sedimentology,27, 3-29.
[35]白玉川,非线性河流动力学讲义,天津大学,2009
[36]徐海珏,河流弱动力过程非线性理论的基础研究:[博士论文],天津:天津大学,2006
[37]Bai Yuchuan, Han Qiwei, Xu Haijue, etc. Theory and applications of nonlinear river dynamics, The 7th IAHR Symposium on River, Coastal and Estuarine Morphodynamics Processes, Beijing: Tsinghua University Press, 2032-2047
[38] Friedkin J F. A laboratory study of the meandering of alluvial river [R].U S Water Exp Sta,1945. 224- 271.
[39]唐日长.蜿蜒性河段成因的初步分析和造床实验研究[J].地理学报, 1963, 29( 2) : 13- 21.
[40]尹学良.弯曲性河流形成的原因及造床实验的初步研究[J] .地理学报, 1965, 31( 4) : 287- 303.
[41] Yang C T. On river meanders [J]. Journal of hydrology , 1971, 13 (3) : 231～253
[42]倪晋仁.不同边界条件下河型成因的试验研究[D] .北京:清华大学,1989.
[43] Schumm S A. Experimental study of channel patterns .Geol Soc Am Bull, 1972,83, 83 :1755~1770 .
[44]许栋,白玉川.蜿蜒河流横向摆动及河谷地形沉积过程数值模拟[J]泥沙研究, 2010, (04) .
[45]许栋,白玉川,谭艳.正弦派生曲线弯道中水沙运动特性动床试验[J]天津大学学报, 2010, (09) .
[46]钱宁.河床演变学[M] .北京:科学出版社, 1987. 374- 385.
[47]沈玉昌,龚国元.河流地貌学概论[M].北京:科学出版社,1986
[48]王随继,倪晋仁,王光谦.河流沉积学研究进展及发展趋势[J]应用基础与工程科学学报, 2000, (04). 369
[2]白玉川.非现性河流动力学学科研究构想及研究进展[C].第三次全国环境力学研讨会,武汉,2007年10月
[3]张瑞瑾,谢鉴衡,陈文彪等.河流动力学[M].武汉:武汉大学出版社,2007
[4]Frank Engelund. Flow and Bed Topography in Channel Bends[J]. Journal of the Hydraulics Division, 1974, 100(11): 1631-1648
[5]Gottlieb, L.(1976)“Three-dimensional flow pattern and bed topography in meandering channel,”Series paper 11, Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark,1-79.
[6]Ikeda, S., Parker, G., and Sawai, K (1981).“Bend theory of river meanders. Part 1. Linear development,“Journal of Fluid Mechanics, 112,363-377.
[7] Smith JD, McLean SR. A model for flow in meandering streams[J]. Water Resources Research, 1984, 20(9): 1301-1315
[8] Blondeaux P. and G. Seminara. A unified bar-bend theory of river meanders[J]. Journal of Fluid Mechanics, 1985, 157: 449-470
[9]Struiksma, N. (1985).“Prediction of 2-D bed topography in rivers,”Journal of Hydraulic Engineering,111(8), 1116-1182.
[10] Johannesson, H., and G. Parker. Linear theory of river meanders[C]. River Meandering. Water Resources Monograph 12. American Geophysical Union, Washington. 1989: 181-214
[11] Howard A.D. and T.R. Knutson. Sufficient conditions for river meandering: A simulation approach[J]. Water Resource Research, 1984, 20(11): 1659-1667
[12] Howard AD. Modelling channel migration and floodplain development in meandering streams[M]. In Lowland Floodplain Rivers, Carling PA, Petts GE (eds). New York: John Wiley & Sons: Chichester, 1992
[13] Meakin Paul, Tao Sun, et al. A simulation model for meandering rivers and their associated sedimentary environments[J]. Physica A, 1996, 233(2): 606-618
[14] Sun T., P. Meakin and T. J?ssang. Meander migration and the lateral tilting of floodplains[J]. Water Resource Research, 2001, 37(5): 1485–1502
[15] Hickin E.J., Nanson G.C. The character of channel migration on the beatton river, northeast British Columbia, Canada[J]. Bulletin of the Geological Society of America, 1975, 86: 487–494
[16] Syunsuke Ikeda, Gary Parker and Kenji Sawai. Bend theory of river meanders. Part 1. Linear development[J]. Journal of Fluid Mechanics, 1981, 112: 363-377
[17] Odgaard, A. J. (1987).“Streambank erosion along two rivers in Iowa,”Water Resources Research, 23(7), 1224-1236.
[18]Crosato, A. (1987).“Simulation model of meandering processes of rivers,”Extended Abstracts, Euromech 215 Conference, Sept. 14-19, Genova, Italy, 158-1613
[19] Boyd F. Edwards and Duane H. Smith. River meandering dynamics[J]. Physical Review E, 2002, 65, 046303: 1-12
[20]Roher, W. L. M. (1983).“Effects of flow and bank material on meander migration in alluvial rivers,”Proceedings, River Meandering, River’83 Conference, ASCE, Oct. 23-26, New Orleans, U.S.A.,770-782.
[21] S. V. Chitale. Modeling for Width Adjustment in Alluvial Rivers[J]. Journal of Hydraulic Engineering, 2003, 129(5): 403-407
[22] D. Chen, J.G.Duan. Modeling width adjustment in meandering channels[J]. Journal of Hydrology, 2006, 321: 59-76
[23]王随继,倪晋仁,王光谦.河流沉积学研究进展及发展趋势[J].应用基础与工程科学学报,2000,8(4):362-369
[24] Bridge J.S. Computer simulation of sedimentation in meandering streams[J]. Sedimentology, 1975, 22: 3-43
[25] Jackson R.G. Depositional model of point bars in the lower Wabash River[J]. Journal of Sedimentary Petrology, 1976, 46: 579-594
[26] Brian J. Willis. Palaeochannel reconstructions from point bar deposits: a three-dimensional perspective[J]. Sedimentology, 1989, 36(5): 757-766
[27] Allen J.R.L. Studies in fluviatile sedimentation: an exploratory quantitative model for the architecture of avulsion-controlled alluvial suites[J]. Sedimentary Geology, 1978, 21: 129-147
[28]Leeder, M.R.(1978) A quantitative stratigraphic model for alluvium, with special reference to channel deposit density and interconnectedness. In: Fluvial Sedimentology, A.D. Mial (ed.), Calary, Canadian Society of Petroleum Geological Society Special Petroleum Geoligists, 587-596.
[29]Bridge, J.S. (1978) Palaeohydraulic interpretation using mathematical models of contemporary flow and sedimentation in meandering channels. In: Fluvial Sedimentology, A.D. Mial (ed.), Calary, Canadian Society of Petroleum Geological Society Special Petroleum Geoligists, 723-742.
[30]Kesel, R.H., Dunne, K.C., McDonald, R.C. Allison, K.R. and Spicer, B.E.(1974) Lateral erosion and overbank deposition on the Mississippi River in Louisiana caused by 1973 flooding. Geology, 2, 461-494.
[31]Pizzoto, J.E. (1987) Sediment diffusion during overbank flows. Sedimentology, 34, 301-317.
[32]Wolman, M.G. and Leopold, L.B.(1957) River flood plain: some observations on their formation. US Geological Survey Professional Paper 282-C,87-109.
[33]Everitt , B.L. (1986) Use of the cottonwood in an investigation of the recent history of a flood plain. American Journal of Science, 266,417-439.
[34]Nanson, G.C. (1980) Point bar and floodplain formation of the meandering Beatton River, northeastern British Columbia, Canada. Sedimentology,27, 3-29.
[35]白玉川,非线性河流动力学讲义,天津大学,2009
[36]徐海珏,河流弱动力过程非线性理论的基础研究:[博士论文],天津:天津大学,2006
[37]Bai Yuchuan, Han Qiwei, Xu Haijue, etc. Theory and applications of nonlinear river dynamics, The 7th IAHR Symposium on River, Coastal and Estuarine Morphodynamics Processes, Beijing: Tsinghua University Press, 2032-2047
[38] Friedkin J F. A laboratory study of the meandering of alluvial river [R].U S Water Exp Sta,1945. 224- 271.
[39]唐日长.蜿蜒性河段成因的初步分析和造床实验研究[J].地理学报, 1963, 29( 2) : 13- 21.
[40]尹学良.弯曲性河流形成的原因及造床实验的初步研究[J] .地理学报, 1965, 31( 4) : 287- 303.
[41] Yang C T. On river meanders [J]. Journal of hydrology , 1971, 13 (3) : 231～253
[42]倪晋仁.不同边界条件下河型成因的试验研究[D] .北京:清华大学,1989.
[43] Schumm S A. Experimental study of channel patterns .Geol Soc Am Bull, 1972,83, 83 :1755~1770 .
[44]许栋,白玉川.蜿蜒河流横向摆动及河谷地形沉积过程数值模拟[J]泥沙研究, 2010, (04) .
[45]许栋,白玉川,谭艳.正弦派生曲线弯道中水沙运动特性动床试验[J]天津大学学报, 2010, (09) .
[46]钱宁.河床演变学[M] .北京:科学出版社, 1987. 374- 385.
[47]沈玉昌,龚国元.河流地貌学概论[M].北京:科学出版社,1986
[48]王随继,倪晋仁,王光谦.河流沉积学研究进展及发展趋势[J]应用基础与工程科学学报, 2000, (04). 369