长河段河床纵剖面分形特征研究
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摘要
以长江干流水富至朱沱段为研究对象,建立一维非恒定分形数学模型,将研究河段分作3段,以岷江、沱江汇流口作为分界,计算各分段河道纵剖面分维数。研究表明:纵剖面分维数呈二阶分维特性,且整体分维数小于分段分维数;整体分维数不等于各分段分维数算术平均值;纵剖面分维数随流量增大而不断减小;各分段河道纵坡降随纵剖面分形维数的变化形态类似波形。
Taking Shuifu to Zhutuo section in mainstream of the Yangtze River as the research object,an unsteady and fractal mathematics model with one-dimension was established. The studied section was divided into 3 segments,and the confluence of Minjiang River and Tuojiang River was taken as a demarcation. The fractal dimension of longitudinal section in river profile was calculated. The research indicates that: the fractal dimension of longitudinal section has two order fractal characteristics,and the overall fractal dimension is smaller than that of the piecewise. The value of overall fractal dimension is not equal to the arithmetic mean of fractal dimension of various sections. Fractal dimension of longitudinal section decreases as the flow increases. The longitudinal slope in various sections of river course is changing with the fractal dimension of longitudinal section,whose morphology is similar to the wave shape.
Taking Shuifu to Zhutuo section in mainstream of the Yangtze River as the research object,an unsteady and fractal mathematics model with one-dimension was established. The studied section was divided into 3 segments,and the confluence of Minjiang River and Tuojiang River was taken as a demarcation. The fractal dimension of longitudinal section in river profile was calculated. The research indicates that: the fractal dimension of longitudinal section has two order fractal characteristics,and the overall fractal dimension is smaller than that of the piecewise. The value of overall fractal dimension is not equal to the arithmetic mean of fractal dimension of various sections. Fractal dimension of longitudinal section decreases as the flow increases. The longitudinal slope in various sections of river course is changing with the fractal dimension of longitudinal section,whose morphology is similar to the wave shape.
引文
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[22]吴立春,倪志辉.长江重庆主城段河流长度分维数与洪水的关系[J].重庆交通大学学报(自然科学版),2012,31(5):1042-1045.WU Lichun,NI Zhihui.Relationship between fractal dimension of the length in section of Chongqing city of Yangtze River and the flood[J].Journal of Chongqing Jiaotong University(Natural Science),2012,31(5):1042-1045.
[23]倪志辉,吴立春,张绪进,等.潮流流速垂线分布的分类及其分形规律[J].人民黄河,2012,34(3):13-16.NI Zhihui,WU Lichun,ZHANG Xujin,et al.Patterns of vertical velocity profile of tidal current and their fractal law[J].Yellow River,2012,34(3):13-16.
[2]范林峰,胡瑞林,张小艳,等.基于GIS和DEM的水系三维分形计盒维数的计算[J].地理与地理信息科学,2012,28(6):28-30.FAN Linfeng,HU Ruilin,ZHANG Xiaoyan,et al.Calculation of3D box dimension of river system based on GIS and DEM[J].Geography and Geo-Information Science,2012,28(6):28-30.
[3]倪志辉,吴立春,舒小红.基于分形理论的挟沙水流掺混长度分析[J].人民黄河,2009,31(9):32-33.NI Zhihui,WU Lichun,SHU Xiaohong.Analysis of water sediment mixing length based on fractal theory[J].Yellow River,2009,31(9):32-33.
[4]倪志辉,张绪进,胥润生.长江黄河含沙量垂线分布的分形研究[J].人民长江,2011,42(19):73-76.NI Zhihui,ZHANG Xujin,XU Runsheng.Fractal study on the vertical concentration distribution of sediment flow in Yangtze River and Yellow River[J].Yangtze River,2011,42(19):73-76.
[5]江齐英,牛瑞卿.长江三峡库岸几何形态的分形分维研究[J].人民长江,2010,41(9):42-44.JIANG Qiying,NIU Ruiqing.Research on fractal and fractal dimension of Three Gorges Reservoir bank’s geometric shape[J].Yangtze River,2010,41(9):42-44.
[6]王卫红,徐鹏,田世民.分形理论在河型研究中的应用探讨[J].泥沙研究,2010(2):35-42.WANG Weihong,XU Peng,TIAN Shimin.Application of the fractal theory in the river pattern study[J].Journal of Sediment Research,2010(2):35-42.
[7]高义,苏奋振,周成虎,等.基于分形的中国大陆海岸线尺度效应研究[J].地理学报,2011,66(3):331-339.GAO Yi,SU Fenzhen,ZHOU Chenghu,et al.Scale effects of China mainland coastline based on fractal theory[J].Acta Geographica Sinica,2011,66(3):331-339.
[8]周银军,陈立,欧阳娟,等.三峡蓄水后典型河段分形维数的变化分析[J].水科学进展,2010,21(3):299-306.ZHOU Yinjun,CHEN Li,OUYANG Juan,et al.Changes in fractal dimensions of representative reaches after the impoundment of Three Gorges Project[J].Advances in Water Science,2010,21(3):299-306.
[9]许光祥,钟亮.河道剖面轮廓的一元分形插值模拟[J].人民长江,2012,43(3):20-23.XU Guangxiang,ZHONG Liang.Unary fractal interpolation simulation of channel profiles[J].Yangtze River,2012,43(3):20-23.
[10]郭碧云,傅旭东,张正峰.震后龙溪河流域河床纵剖面变化和沟谷分形[J].应用基础与工程科学学报,2014,22(1):118-125.GUO Biyun,FU Xudong,ZHANG Zhengfeng.The Longitudinal change and gully bed fractality of Longxi river valley after the earthquake[J].Journal of Basic Science and Engineering,2014,22(1):118-125.
[11]NIKORA V I,SAPOZHNIKOV V B,NOEVER D A.Fractal geometry of individual river channels and its computer simulation[J].Water Resources Research,1993,29(29):3561-3568.
[12]SAPOZHNIKOV V,FOUFOULA-GEORGIOU E.Self-affinity in braided rivers[J].Water Resources Research,1996,32(5):1429-1439.
[13]FOUFOULA-GEORGIOU E,SAPOZHNIKOV V B.Anisotropic scaling in braided rivers:an integrated theoretical framework and results from application to an experimental river[J].Water Resources Research,1998,34(4):863-868.
[14]NYKANEN D K,FOUFOULA-GEORGIOU E,SAPOZHNIKOV V B.Study of spatial scaling in braided river patterns using synthetic aperture radar imagery[J].Water Resources Research,1998,34(7):1795-1807.
[15]KINSNER W.A unified approach to fractal dimensions[J].International Journal of Cognitive Informatics and Natural Intelligence,2007,1(4):26-46.
[16]王欣凯,贾建军.浙江海岛岸线分维数与其人工岸线比例的关系[J].海洋学研究,2011,29(4):25-31.WANG Xinkai,JIA Jianjun.Relationship between the fractal dimension and percentage of artificial coastlines of islands in Zhejiang Province[J].Journal of Marine Sciences,2011,29(4):25-31.
[17]ZHOU Z,YANG J,DENG Y,et al.Shortest-path fractal dimension for percolation in two and three dimensions[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2012,86(1):1-5.
[18]NI Z H,WU L C,ZHANG X J,et al.A new model for the regulation width of waterway based on hydraulic geometry relation[J].Mathematical Problems in Engineering,2013(4):883-907.
[19]NI Z H,WU L C,WANG M H.The fractal dimension of river length based on the observed data[J].Journal of Applied Mathematics,2013(1):361-376.
[20]MANDELBROT B B.How long is the coast of britain?Statistical self-similarity and fractional dimension[J].Science,1967,156(3775):636.
[21]吴立春,倪志辉.河流长度整体分维与局部分维关系研究——以长江重庆主城段为例[J].四川师范大学学报(自然科学版),2013,36(1):147-151.WU Lichun,NI Zhihui.Study on the relationship between overall fractal dimension and partial fractal dimension of river length for example of the section of Chongqing City of Yangtze River[J].Journal of Sichuan Normal University(Natural Science),2013,36(1):147-151.
[22]吴立春,倪志辉.长江重庆主城段河流长度分维数与洪水的关系[J].重庆交通大学学报(自然科学版),2012,31(5):1042-1045.WU Lichun,NI Zhihui.Relationship between fractal dimension of the length in section of Chongqing city of Yangtze River and the flood[J].Journal of Chongqing Jiaotong University(Natural Science),2012,31(5):1042-1045.
[23]倪志辉,吴立春,张绪进,等.潮流流速垂线分布的分类及其分形规律[J].人民黄河,2012,34(3):13-16.NI Zhihui,WU Lichun,ZHANG Xujin,et al.Patterns of vertical velocity profile of tidal current and their fractal law[J].Yellow River,2012,34(3):13-16.