河流网络的分形与自组织及其物理机制

汪富泉; 曹叔尤; 丁晶

河流网络的分形与自组织及其物理机制

1.
茂名学院教务处, 广东, 茂名, 525000;
2.
四川大学水利水电工程学院, 四川, 成都, 610065

基金项目: 国家自然科学基金(59890200);水利部重大基金;国家重点实验室访问学者基金(教育部教技司[1999]153号);四川大学高速水力学国家重点实验室开放基金

详细信息

作者简介:
汪富泉(1955- ),男,四川南充人,茂名学院教授,博士.主要从事水文学、河流动力学研究.

中图分类号: P512.31

Fractal, self-organization and its physical mechanism of river networks

1.
Dean's office of Maoming University, Maoming 525000, China;
2.
The Hydraulic and Hydropower College of Sichuan University, Chengdu 610065, China

Funds: The project is supported by National Natural Science Fund of China(No.59890200).

摘要: 扼要地评述近年来国内外在流域、水系等方面的分形及自组织研究的有关成果,指出其中存在的问题和可能的改进途径.从地球内外营力及河网系统的开放性、非线性、随机性、耗散性等角度探讨河网系统自组织及分形结构产生的物理机制.在流域侵蚀与生态环境恢复、流域产流与汇流、泥沙产生与输移、河床形态演变等方面提出了进一步的研究方向及有关课题.
- 河网 /
- 分形 /
- 自组织 /
- 物理机制
Abstract: This paper briefly introduces and reviews the achievements of fractal and self-organization of river networks,points out existing questions in the articles and possible improvement ways at the same time,discusses the physical mechanism of production and evolution of the self-organized fractal structure of river networks from the viewpoint of internal and external force of the earth as well as the opening property,the nonlinear property,the stochastic property and the dissipative property of the river network system,and proposes the further study projects in the field of basin erosion and ecosystem restoring,flow production and flow together of the basin,sediment production and transport,the evolution of the riverbed form and so on.
- river networks /
- fractal /
- self-organization /
- physical mechanism

[1]	汪富泉,李后强.分形——大自然的艺术构造[M].济南:山东教育出版社,1996.10-164.
[2]	Mandelbrot B B.How long is the coast of Britain? Statistical self-similarity and fractional dimension[J].Science,1967,155:636-638.
[3]	Mandelbrot B B.Fractals:Form,Chance and Dimension[M].New York:W.H.Freeman,1975,1-20.
[4]	Mandelbrot B B.The Fractal Geometry of Nature[M].New York:W.H.Freeman,1992,5-70.
[5]	Gupta V K.Statistical self-similarity in river networks parameterixed by elevation[J].Water Resources Bulletin,1989,25(3):752-758.
[6]	Snow R S.Fractal sinuosity of stream channels[J].Pure and Applied Geophysics,1989,131,(1-2):15-21.
[7]	Hjelmfelt.Fractals and the river length-catchment area ratio[J].Water Resources Bulletin,1988,24,(2):455-458.
[8]	Robert A,Roy A G.On the fractal interpretation of the main-stream length-drainage area relationship[J].Water Resources Res,1990,26,(9):839-842.
[9]	Feder J.Fractals[M].New York & London,Plumum,1988,20-100.
[10]	Barbera P L,Rosso R.On the fractal dimensions of stream networks[J].Water Resources Res,1989,25(4).
[11]	Garcia J M,Otalora F.Fractal trees and Horton law[J].Math Goeol,1992,24(1):19-25.
[12]	Tarboton D G,Bras R L,Rodriguez-Iturbe I.The fractal nature of river networks[J].Water Resources Res,1988,24(9):1 317-1 332.
[13]	Tarboton D G,Bras R L,Rodriguez-Iturbe I.Coment on "On the Fractal Dimensions of Stream Networks" by Paolo La Barbera and Renzo Rosso[J].Water Resources Res,1990,26(9):2 243-2 244.
[14]	Barbera P L,Rosso R.Reply[J].Water Resources Res,1990,26(9):2 245-2 249.
[15]	Rosso B,Bacchi B,Barbera P L.Fractal relation of mainstream length to catchment area in river networks[J].Water Resources Res,1991,27(3):391-397.
[16]	Nikora V.Fractal structures of river plan forms[J].Water Resources Res,1991,27(6):1 327-1 333.
[17]	Nikora V I,Sapozhnikov V B.River network fractal geometry and its computer simulation[J].Water Resources Res,1993,29(10):3 569-3 575.
[18]	李后强,艾南山.分形地貌学及地貌发育的分形模型[J].自然杂志,1992,(7):516-519.
[19]	冯平,冯炎.河流形态特征的分维计算方法[J].地理学报,1997,52(4):324-330.
[20]	Moussa R.Is the drainage network a fractal Sierpinski space?[J].Water Resources Res,1997,33(10):2 399-2 409.
[21]	金德生,陈浩,郭庆伍.河道纵剖面分形-非线性形态特征[J].地理学报,1997,52(2):154-161.
[22]	汪富泉,李后强.分形几何与动力系统[M].哈尔滨:黑龙江教育出版社,1993.5-60.
[23]	汪富泉,李后强.一类分形集及其刻画[J].应用数学,1994,7(1):60-64.
[24]	Nikora V I,Sapozhnikov V B,Noever D A.Fractal geometry of individual river channels and its computer simulation[J].Water Resources Res,1993,29(10):3 561-3 569.
[25]	Sapozhnikov V B,Foufoula-Georgiou E.Study of self-similar and self-affine object using logarithmic correlation integral[J].J Phys A,Math Gen,1995,28:559-571.
[26]	Sapozhnikov V B,Foufoula-Georgiou E.Self-affinity in braided rivers[J].Water Resources Res,1996,32(5).
[27]	Grebogi C,McDonald S W,Ott E,et al.Exterior dimension of fractals[J].Phys Letters,1985,110A(1):1-4.
[28]	Umberger D K,Farmer J D.Fat fractals on the energy surface[J].Phys Rev Letters 1985,55(7):661-664.
[29]	Nikora V I.On Self-similarity and self-affinity of drainage basins[J].Water Resources Res,1994,30(1):133-137.
[30]	汪富泉,李后强.有面积的曲线的性质及高维推广[J].数学研究与评论,1994,14(4):579-584.
[31]	Lavalle'e D,Lovejoy S,Schertzer D,et al.Nonlinear variability of landscape topography:Multifractal analysis and simulation[M].in:Fractals in Geography,Ed by N.Lam and L.De Cola,Prentice-Hall,Englewood Cliffs,N J 1993.158-192.
[32]	Rodriguez-Iturbe I,Marnani M,Rigon R,et al.Self-organized river basin landscapes:Fractal and multifractal characteristics[J].Water Resources Res.1994,30(12).
[33]	Marnani A,Rigon R,Rinaldo A.A Note on fractal channel networks[J].Water Resources Res,1991,27(12):3#531-3#539.
[34]	Robert A.Statistical properties of sediment bed profiles in alluvial channels[J].Math Geology,1988,20(3).
[35]	Robert A.Fractal properties of sediment bed profiles in coarse-grained channels[J].Math Geology,1988,20(3).
[36]	Liu T.Fractal structrue and properties of stream networks[J].Water Resources Res,1992,28(11):2 981-2 988.
[37]	Rodriguez-Iturbe I,Valdes J B.The geomorphologic structure of hydrologic response[J].Water Resources Res,1979,15(6):1 409-1 420.
[38]	Rosso R.Nash model relation to Horton order ratios[J].Water Resources Res,1984,20(7):914-920.
[39]	Leheny R L,NagelS R.Model for the evolution of river networks[J].Phys Rev Letters,1993,71(9):1 470-1 473.
[40]	Kramer S,Marder M.Evolution of river networks[J].Phys Rev Letters,1992,68(2):205-209.
[41]	汪富泉,丁晶,曹叔尤,等.论悬移质含沙量沿垂线的分布[J].水利学报,1998,(11):44-49.
[42]	Wang F Q,Li H Q,Ding J.Nonlinear analysis on distribution along the depth of suspended load[J].Nonlinear Sci & Num Sim Comm,1998,3(2):74-79.
[43]	Bak P,Tang C,Wiesenfeld K.Self-organized criticality:an explanation of 1/f noise[J].Phys Rev Letters,1987,59(4):391-394.
[44]	Bak P,Tang C,Wiesenfeld K.Self-organized criticality[J].Phys Rev A,1988,38(1):364-374.
[45]	Murray A B.A cellular model of braided rivers[J].Nature,1994,371(1):54-57.
[46]	Rodriguez-Iturbe I,Ijja'sz-Va'squez E J,Bras R L,et al.Power law distribution of discharge mass and energy in river basins[J].Water Resources Res,1992,28(4):1 089-1 093.
[47]	Rodriguez-Iturbe I,Rinaldo A,Rigon R,et al.Energy dissipation,runoff production,and the three-dimensional structrue of river basins[J].Water Resources Res,1992,28(4):1 095-1 103.
[48]	Rinaldo A,Rodriguez-Iturbe I,Rigon R,et al.Minimum energy and fractal structrues of drainage networks[J].Water Resources Res,1992,28(9):2 183-2 195.
[49]	Takayasu H,Inaoka H.New type of self-organized criticality in a model of erosion[J].Phys Rev Letters,1992,68(7):966-969.
[50]	Rinaldo A,Rodriguez-Iturbe I,Rigon R,et al.Self-organized fractal river networks[J].Phys Rev Letters,1993,70(6):922-925.
[51]	Sun Y,Meakin P,Ssang T J.A minimum energy dissipation model for river basin geometry[J].Phys Rev E,1994,49(6):4 965-4 872.
[52]	Rigon R,Rinaldo A,Rodriguez-Iturb I,et al.On landscape self-organization[J].J Geophys Res,1994,99(11):971-11 993.
[53]	Sapozhnikov V B,Foufoula-Georgiou E.Do the current landscape evolution models show self-organized criticality?[J].Water Resources Res,1996,32(4):1 109-1 112.
[54]	Maslov S,Paczuski M,Bak P.Avalanches and 1/f noise in evolution and growth models[J].Phys Rev Letters,1994,73:2 162-2 165.
[55]	Sapozhnikov V B,Foufoula-Georgiou E.Experimental evidence of dynamic scaling and idications of self-organized criticality in braided rivers[J].Water Resources Res,1997,33(8):1 983-1 991.
[56]	汪富泉.泥沙运动及河床演变的分形特征与自组织规律研究[D].成都:四川大学,1999.59-103.
[57]	汪富泉,曹叔尤,刘兴年.悬移颗粒运动特征值的分形分布[J].水利学报,2000,(9):65-69.
[58]	汪富泉,曹叔尤,丁晶.河湾形态演变的自组织及其稳定性[J].水科学进展,2001,12(1):7-16.

[1]	陈一帆, 程海洋, 万晓丽, 方华建. 结合糙率校正的河网水情数据同化 . 水科学进展, 2015, 26(5): 731-738. doi: 10.14042/j.cnki.32.1309.2015.05.015
[2]	陈一帆, 程伟平, 徐庆华, 万晓丽. 一个稳健的河网水情数据同化耦合模型 . 水科学进展, 2014, 25(6): 842-847.
[3]	左俊杰, 蔡永立. 平原河网地区汇水区的划分方法——以上海市为例 . 水科学进展, 2011, 22(3): 337-343.
[4]	唐洪武, 雷燕, 顾正华. 河网水流智能模拟技术及应用 . 水科学进展, 2008, 19(2): 232-237.
[5]	王船海, 向小华. 通用河网二维水流模拟模式研究 . 水科学进展, 2007, 18(4): 516-522.
[6]	谢先红, 崔远来, 蔡学良. 灌区塘堰分布分形描述 . 水科学进展, 2007, 18(6): 858-863.
[7]	罗翔宇, 贾仰文, 王建华, 王浩, 秦大庸, 周祖昊. 基于DEM与实测河网的流域编码方法 . 水科学进展, 2006, 17(2): 259-264.
[8]	吴作平, 杨国录, 甘明辉. 湖泊调蓄作用对河网计算的影响 . 水科学进展, 2004, 15(5): 603-607.
[9]	吴作平, 杨国录, 甘明辉. 复杂河网水沙数学模型研究 . 水科学进展, 2004, 15(3): 336-340.
[10]	刘建国, 王洪涛, 聂永丰. 多孔介质中溶质有效扩散系数预测的分形模型 . 水科学进展, 2004, 15(4): 458-462.
[11]	朱晓华, 蔡运龙. 中国水系的盒维数及其关系 . 水科学进展, 2003, 14(6): 731-735.
[12]	诸裕良, 严以新, 李瑞杰, 郑金海. 河网海湾水动力联网数学模型 . 水科学进展, 2003, 14(2): 131-135.
[13]	黄冠华, ZHAN Hong-bin, 叶自桐. 水力传导度空间变异性的分形模拟研究进展 . 水科学进展, 2003, 14(2): 236-241.
[14]	刘建立, 徐绍辉, 刘慧, 郭飞. 确定田间土壤水力传导率的分形方法 . 水科学进展, 2003, 14(4): 464-470.
[15]	吴作平, 杨国录, 甘明辉. 河网水流数值模拟方法研究 . 水科学进展, 2003, 14(3): 350-353.
[16]	刘晓丽, 梁冰, 薛强. 多孔介质渗透率的分形描述 . 水科学进展, 2003, 14(6): 769-773.
[17]	刘建国, 聂永丰. 非饱和土壤水力参数预测的分形模型 . 水科学进展, 2001, 12(1): 99-106.
[18]	汪富泉, 曹叔尤, 丁晶. 河湾形态演变的自组织及其稳定性 . 水科学进展, 2001, 12(1): 7-16.
[19]	汤一波, 金忠青. 脉动压力的紊流分形特征 . 水科学进展, 1998, 9(4): 361-366.
[20]	郑孝宇, 褚君达, 朱维斌. 河网非稳态水环境容量研究 . 水科学进展, 1997, 8(1): 25-31.

点击查看大图

计量

文章访问数: 17
HTML全文浏览量: 5
PDF下载量: 884
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

河流网络的分形与自组织及其物理机制

作者简介:
汪富泉(1955- ),男,四川南充人,茂名学院教授,博士.主要从事水文学、河流动力学研究.

Fractal, self-organization and its physical mechanism of river networks

计量

河流网络的分形与自组织及其物理机制

1. 茂名学院教务处, 广东, 茂名, 525000;

2. 四川大学水利水电工程学院, 四川, 成都, 610065

作者简介:
汪富泉(1955- ),男,四川南充人,茂名学院教授,博士.主要从事水文学、河流动力学研究.

English Abstract

Fractal, self-organization and its physical mechanism of river networks

1. Dean's office of Maoming University, Maoming 525000, China;

2. The Hydraulic and Hydropower College of Sichuan University, Chengdu 610065, China

全文HTML

目录

留言板

河流网络的分形与自组织及其物理机制

作者简介: 汪富泉(1955- ),男,四川南充人,茂名学院教授,博士.主要从事水文学、河流动力学研究.

Fractal, self-organization and its physical mechanism of river networks

计量

出版历程

河流网络的分形与自组织及其物理机制

1. 茂名学院教务处, 广东, 茂名, 525000; 2. 四川大学水利水电工程学院, 四川, 成都, 610065

作者简介: 汪富泉(1955- ),男,四川南充人,茂名学院教授,博士.主要从事水文学、河流动力学研究.

English Abstract

Fractal, self-organization and its physical mechanism of river networks

1. Dean's office of Maoming University, Maoming 525000, China; 2. The Hydraulic and Hydropower College of Sichuan University, Chengdu 610065, China

全文HTML

目录

作者简介:
汪富泉(1955- ),男,四川南充人,茂名学院教授,博士.主要从事水文学、河流动力学研究.

1. 茂名学院教务处, 广东, 茂名, 525000;

2. 四川大学水利水电工程学院, 四川, 成都, 610065

作者简介:
汪富泉(1955- ),男,四川南充人,茂名学院教授,博士.主要从事水文学、河流动力学研究.

1. Dean's office of Maoming University, Maoming 525000, China;

2. The Hydraulic and Hydropower College of Sichuan University, Chengdu 610065, China