长河段河床纵剖面分形特征研究

doi:10.3969/j.issn.1674-0696.2017.07.10

重庆交通大学学报（自然科学版） ›› 2017, Vol. 36 ›› Issue (7): 58-65.DOI: 10.3969/j.issn.1674-0696.2017.07.10

• 港口航道·水利水电·资源环境 • 上一篇下一篇

长河段河床纵剖面分形特征研究

倪志辉1,2，王伟1，吴立春3

（1. 重庆交通大学水利水运工程教育部重点实验室国家内河航道整治工程技术研究中心，重庆 400074； 2. 重庆交通大学西南水运工程科学研究所，重庆 400016；3.重庆第二师范学院，重庆 400067）

收稿日期:2015-09-12 修回日期:2016-11-12 出版日期:2017-07-31 发布日期:2017-07-31
作者简介:倪志辉（1980—），男，湖南衡阳人，博士，副研究员，主要从事河流海岸水动力学、环境及数值模拟方面的研究。
基金资助:
国家重点基础研究发展计划项目（2016YFC0402104）；重庆市基础与前沿研究计划项目（cstc2016jcyjA0380）；省部共建水利水运工程教育部重点实验室暨国家内河航道整治工程技术研究中心开放基金项目（SLK2016B03）；内河航道整治技术交通行业重点实验室开放基金项目（NHHD-201514）

Fractal Characteristics of Longitudinal Section of River Bed

NI Zhihui1, 2, WANG Wei1, WU Lichun3

(1. Key Laboratory of Hydraulic and Waterway Engineering of the Ministry of Education, National Engineering Research Center for Inland Waterway Regulation, Chongqing Jiaotong University, Chongqing 400074, P. R. China; 2. Southwestern Research Institute of Water Transportation Engineering, Chongqing Jiaotong University, Chongqing 400016, P. R. China; 3. Chongqing University of Education, Chongqing 400067, P. R. China)

Received:2015-09-12 Revised:2016-11-12 Online:2017-07-31 Published:2017-07-31

摘要/Abstract

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。

关键词: 航道工程, 纵剖面, 非恒定流, 分形维数, 变维分形, 数值模拟

Abstract: 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.

Key words: waterway engineering, longitudinal section, unsteady flow, fractal dimension, variable dimension fractal, numerical simulation

中图分类号:

TU612.3

倪志辉1,2，王伟1，吴立春3. 长河段河床纵剖面分形特征研究[J]. 重庆交通大学学报（自然科学版）, 2017, 36(7): 58-65.

NI Zhihui1, 2, WANG Wei1, WU Lichun3. Fractal Characteristics of Longitudinal Section of River Bed[J]. Journal of Chongqing Jiaotong University(Natural Science), 2017, 36(7): 58-65.

参考文献

［1］许模,王迪,漆继红,等.基于分形理论的卡斯特地貌形态分析［J］.成都理工大学学报（自然科学版）,2011,38(3):328-333.
XU Mu, WANG Di, Qi Jihong. Study on morphological characteristics of karst landform based on the fractal theory［J］. Journal of Chengdu University of Technology
(Science & Technology Edition, 2011, 38(3): 328-333.
［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 of 3D 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.

[1]	郑植1,2，耿波2，袁佩2，李嵩林2，胡正涛3. 桥墩复合材料防船撞装置新型连接试验研究[J]. 重庆交通大学学报（自然科学版）, 2021, 40(05): 66-73.
[2]	王杰，费鹏，陈凯. 基于混合时间窗下动态需求的补给船航线规划[J]. 重庆交通大学学报（自然科学版）, 2021, 40(01): 53-58.
[3]	曹力桥1，王志斌2，周丁恒3. PBA车站扣拱施工顺序对上部跨河桥沉降影响分析[J]. 重庆交通大学学报（自然科学版）, 2021, 40(01): 79-86.
[4]	徐建国，冯越. 新型气囊式避险车道消能过程数值分析[J]. 重庆交通大学学报（自然科学版）, 2020, 39(12): 94-98.
[5]	江朝华1,3，李智成1,3，方佳敏2，李函1,3. 废弃疏浚沙土固化利用研究[J]. 重庆交通大学学报（自然科学版）, 2020, 39(12): 111-116.
[6]	赵天龙1,2，马廷森1，付长静1,2，冼才麟1. 非恒定流条件下宽级配土石料冲刷过程试验研究[J]. 重庆交通大学学报（自然科学版）, 2020, 39(10): 93-99.
[7]	李文杰1，张浩游1，张文2，杨胜发1，胡江3. 基于模糊贝叶斯网络的长江上游航道整治建筑物技术状况评价研究[J]. 重庆交通大学学报（自然科学版）, 2020, 39(09): 112-118.
[8]	常继峰1，陈彦君2，孙全胜3. 多年岛状冻土路基坡向性热效应数值模拟分析[J]. 重庆交通大学学报（自然科学版）, 2020, 39(07): 100-107.
[9]	段纪淼1，刘慧姝1，赫曼求2，徐硕3，李江1. 舰用燃料油流动传热耦合特性数值模拟[J]. 重庆交通大学学报（自然科学版）, 2020, 39(07): 138-146.
[10]	杜晓庆1, 2，刘延泰1，施定军1，马文勇3. 低雷诺数下类方柱绕流的数值模拟研究[J]. 重庆交通大学学报（自然科学版）, 2020, 39(05): 49-57.
[11]	计明军，王恒，高振迪，张金伟. 考虑潮汐的长江航道矿石散装船航线优化[J]. 重庆交通大学学报（自然科学版）, 2020, 39(05): 108-116.
[12]	任兆丹. 软岩隧道拉锚结构数值分析与支护机理研究[J]. 重庆交通大学学报（自然科学版）, 2020, 39(03): 113-122.
[13]	李培楠1,2，石来2，刘俊3，李晓军2. 基于iS3的复杂地质建模与数值数字一体化研究[J]. 重庆交通大学学报（自然科学版）, 2020, 39(03): 142-148.
[14]	唐红梅，王平，王林峰. 变化裂隙岩体的压缩破坏RFPA数值模拟[J]. 重庆交通大学学报（自然科学版）, 2020, 39(02): 103-110.
[15]	蒋孜伟1,2，许光祥1，童思陈1. 引航道导墙透空技术改善流态的数值模拟研究[J]. 重庆交通大学学报（自然科学版）, 2020, 39(01): 98-102.

长河段河床纵剖面分形特征研究

Fractal Characteristics of Longitudinal Section of River Bed

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics