河床形态冲刷调整量化及其对阻力的影响初步研究
|
摘要
河床作为河道水沙运动的边界,其特殊在于随时可动性和形态的三维性、复杂性。河床形态的变化,及其所带来的水流结构、河床阻力及输沙能力调整等问题均是河流动力学学科的基础研究内容。对于水库下游河道而言,来水来沙等条件的改变必将引起其河床形态的冲刷调整,这将对坝下游河道的防洪、灌溉、航运等诸多方面造成影响。因此,研究河床形态冲刷调整及其相关影响具有重要的理论意义和工程价值。
本文采用实测资料分析和概化模型试验的方法,将GIS技术、非线性-分形理论引入河流动力学,对河床形态冲刷调整规律及其度量方法进行了研究,并以此为基础对河型划分、河道阻力估算,以及三峡工程坝下游河段河床形态冲刷调整及其对阻力的影响进行了探讨,具体研究内容和所得主要结论如下。
(1)采取实测资料分析的手段,对不同类型分汉河段河床形态的特点及其冲刷调整规律进行了分析。在边界约束较强情况下,不同类型的分汊河道冲刷调整规律的共性是汊道冲刷为主,且各汊道冲刷具有不均衡性,此外,其江心洲及凸岸边滩亦会受到一定程度的冲刷蚀退,其差异在于两汊冲刷的相对幅度不同,虽然二者冲刷发展较快的均是洪水期水流动力轴线所经之汊道,但是发展的结果却不同：水流动力轴线年内交替型分汊河段的分汊格局会发生调整,而年内非交替型分汉河段则更加稳定。
(2)提出以河床表面分形维数来量化河床形态,并根据表面积——尺度法原理,在对其表面积估算、边界处理及无标度区判断等方面进行改进的基础上,结合GIS技术,给出了以DWG格式河道水下地形图为数据源计算河床表面分形维数的方法,该方法对河床表面分形计算具有较好的适用性,并具有高效、准确的特点,同时结合典型河段,分析了河床表面形态的分形特征。
(3)通过不同河型的概化模型试验,并结合实测资料,对河床表面分形维数与河床形态调整的关系进行了研究。河床表面分形维数与河段平面形态、横断面形态及深泓纵剖面形态之间是整体与部分的必然关系,各二维剖面仅是从不同的侧面或局部来反映床面形态的变化,而河床表面分形维数是从整体上描述河床表面形态冲淤起伏的剧烈程度,并且能较好地反映河床形态的演变特点,由于不同类型河段具有不同的河床形态,故河床表面分形维数可在一定程度上体现河型、以及河型亚类之间的差异,在收集更多实测河段资料并统一分维算法后,河床表面分形维数可作为河型的判据之一。同时,对河段深泓纵剖面分形维数的物理意义亦进行了研究,认为深泓纵剖面分形维数可定量反映河段深泓纵剖面的起伏程度,并与枯水糙率存在一定联系。
(4)基于概化模型试验,对不同因素影响下河床冲刷调整过程中阻力的变化规律与机理进行了研究。来流条件强度的增加或侵蚀基准面的下降,使得河床形态冲淤变化幅度加大,能加剧河道阻力的调整；不同河型的阻力调整过程基本是相似的,都有一个先增大而后减小的基本过程,较之顺直河型,分汊河型和弯曲河型因水流结构的复杂以及河床变形的迅速,其综合阻力调整进程较快,变化幅度较大。河床表面分形维数与河床糙率之间存在较好的正相关关系,并基于试验给出了河床表面分形维数与河床糙率之间的量化关系,该量化关系可适用于同一河段糙率变化的估算。
(5)从三峡工程蓄水后宜昌至杨家脑河段的冲刷分布特点及河段形态调整对宜昌枯水位的变化机理进行了分析和探讨。宜昌至杨家脑河段冲刷的沿程分布与河道形态有密切关系,相对而言,弯道段及分汊段冲刷强度大于整体河段平均值；河段纵向节点多为分汊河段,且交替型分汊河段较非交替型分汊河段的节点作用更为稳定；由于长河段深泓纵剖面分形维数的加大,节点河段河床表面分形维数的普遍加大以及床沙的粗化使得下游河道阻力有所加大,这对宜昌河段枯水位的下降起到了抑制作用；在下游水位进一步下降幅度不大,并在采取一定工程措施的情况下,宜昌枯水位将可以保持稳定。
As the boundary of river water and sediment movement, the characters of Riverbed are movable and complexity of its 3D space structure. The variety of river bed form and the problems such as flow structure, channel resistance and sediment transport capacity adjustment which is caused by its shape changes are the contents of fundamental research in the river dynamics field. For the channels downstream reservoir, the changes of water and sediment conditions will lead to erosion adjustment of their bed form, which will impact the flood control, irrigation, navigation and many other implications of the river. Therefore, it has important theoretical and engineering value to study erosion adjustment of channel form and some related effects.
In this paper, GIS technology and theory of non-linear-fractal are introduced into the river dynamics, the law and measurement method of river bed form erosion adjustment is studied by the approach of observed data analysis and generalized model experiment, and on this basis, the river-type classification, channel resistance estimation, as well as the river bed erosion adjustment and related effects on resistance of the river downstream Three Gorges Project (TGP) were also discussed, the specific contents and main results are as follows:
(1) The bed form features of different typical braided river and the law of its erosion adjustment are analyzed by the observed data analysis. In the case of strong constraint boundary, the commonness of erosion adjustment among different types of braided river is erosion of the inlet, and each inlet has a unbalanced turn of erosion, in addition, the central bar and sand bar nearby convex bank often will be a degree of erosion; the difference is that the relative erosion rate of the two branches is different. Although the larger one is still after the local flood dynamic axis, the results are also different, the diversion pattern of the alternate braided river should be changed, the one of non-alternant braided river will be stability.
(2) The riverbed surface fractal dimension (BSD) is put forword to measure river bed. Based on improvements in some aspects of Surface area-Scale Method, such as, estimation of surface area, boundary treatment and judgment of non-scale range, and GIS technology was combined to bring up a method on the bed surface fractal dimension calculation that the data sources is DWG format underwater topographic map. The new method is effective and accurate, and has good applicabiliton on the bed surface fractal dimension calculation. The fractal characteristics of river bed surface morphology is discussed by combination with river-pattern, local river regime and river process of typical reach.
(3) Based on the combination of general model about different river patterns and observed data, the relationship between bed surface fractal dimension and the adjustment of bed form is studied. There is whole and part relationship between riverbed surface fractal dimension and flat shape, cross-sectional shape as well as longitudinal profile form of the river, the two-dimensional profiles reflect changes in bed form only from a different side or in part, therefore, the bed surface fractal dimension can describe overall adjustment intensity of river bed surface morphology, and reflect characteristic of the river process sensitivity. As different river has different bed form, the river bed surface fractal dimension can reflect the difference among river-patterns, even subclass to some extent. The bed surface fractal dimension should be a distinguished criterion of river-pattern after gather more actual information and unified fractal algorithm. Meanwhile, the fractal characteristics of the Yangtze River middle reaches is studied, the thelweg longitudinal profile profile fractal dimension (TD) can quantitatively reflect thecomplexity of river longitudinal profile sharp.
(4) The law and mechanism of resistance changes in the adjustment process under the variational factors is studied. The increase of intensity of flow conditions or the decrease of base-level can make the range of river bed changes greater, and exacerbate the adjustment of channel resistance; the resistance adjustment process of different river pattern are basically similar, there is a first increases and then decreases in the basic process, compared with straight river pattern, as the complexity of the flow structure and rapidity of bed deformation in braided river and bending river, their resistance adjustment process is faster and the variation range is bigger. There is a positive relationship between river bed surface fractal dimension and the bed roughness. The quantitative relationship between them is obtained based on the experiment, the quantitative relationship can be applied to estimate changes of roughness in the same river.
(5) The mechanism of low water level changes in Yichang was analyzed and discussed from distribution of erosion and river morphology adjustment on Yichang to Yangjianao channel after the impoundment of Three Gorges Project(TGP). There is a closely relationship between distribution of erosion along the river and the channel morphology on this channel, in comparison, the erosion intensity of bending reach and the branching reach is greater than the overall average; the longitudinal nodes of the channel are mostly braided reach, and the node of alternating-type braided reach is more stable than the one of non-alternating type braided reach; due to the increase of thalweg longitudinal profile fractal dimension in the long channel, the general increase of riverbed surface fractal dimension in node reaches,and coarsening of bed material, the bed resistance downstream TGP has increased, and the increace played inhibition to this low water level decline in Yichang; in the case of in downstream water level can not decline furtherly, Yichang low water level will remain stable with some engineering measures be carried on.
本文采用实测资料分析和概化模型试验的方法,将GIS技术、非线性-分形理论引入河流动力学,对河床形态冲刷调整规律及其度量方法进行了研究,并以此为基础对河型划分、河道阻力估算,以及三峡工程坝下游河段河床形态冲刷调整及其对阻力的影响进行了探讨,具体研究内容和所得主要结论如下。
(1)采取实测资料分析的手段,对不同类型分汉河段河床形态的特点及其冲刷调整规律进行了分析。在边界约束较强情况下,不同类型的分汊河道冲刷调整规律的共性是汊道冲刷为主,且各汊道冲刷具有不均衡性,此外,其江心洲及凸岸边滩亦会受到一定程度的冲刷蚀退,其差异在于两汊冲刷的相对幅度不同,虽然二者冲刷发展较快的均是洪水期水流动力轴线所经之汊道,但是发展的结果却不同：水流动力轴线年内交替型分汊河段的分汊格局会发生调整,而年内非交替型分汉河段则更加稳定。
(2)提出以河床表面分形维数来量化河床形态,并根据表面积——尺度法原理,在对其表面积估算、边界处理及无标度区判断等方面进行改进的基础上,结合GIS技术,给出了以DWG格式河道水下地形图为数据源计算河床表面分形维数的方法,该方法对河床表面分形计算具有较好的适用性,并具有高效、准确的特点,同时结合典型河段,分析了河床表面形态的分形特征。
(3)通过不同河型的概化模型试验,并结合实测资料,对河床表面分形维数与河床形态调整的关系进行了研究。河床表面分形维数与河段平面形态、横断面形态及深泓纵剖面形态之间是整体与部分的必然关系,各二维剖面仅是从不同的侧面或局部来反映床面形态的变化,而河床表面分形维数是从整体上描述河床表面形态冲淤起伏的剧烈程度,并且能较好地反映河床形态的演变特点,由于不同类型河段具有不同的河床形态,故河床表面分形维数可在一定程度上体现河型、以及河型亚类之间的差异,在收集更多实测河段资料并统一分维算法后,河床表面分形维数可作为河型的判据之一。同时,对河段深泓纵剖面分形维数的物理意义亦进行了研究,认为深泓纵剖面分形维数可定量反映河段深泓纵剖面的起伏程度,并与枯水糙率存在一定联系。
(4)基于概化模型试验,对不同因素影响下河床冲刷调整过程中阻力的变化规律与机理进行了研究。来流条件强度的增加或侵蚀基准面的下降,使得河床形态冲淤变化幅度加大,能加剧河道阻力的调整；不同河型的阻力调整过程基本是相似的,都有一个先增大而后减小的基本过程,较之顺直河型,分汊河型和弯曲河型因水流结构的复杂以及河床变形的迅速,其综合阻力调整进程较快,变化幅度较大。河床表面分形维数与河床糙率之间存在较好的正相关关系,并基于试验给出了河床表面分形维数与河床糙率之间的量化关系,该量化关系可适用于同一河段糙率变化的估算。
(5)从三峡工程蓄水后宜昌至杨家脑河段的冲刷分布特点及河段形态调整对宜昌枯水位的变化机理进行了分析和探讨。宜昌至杨家脑河段冲刷的沿程分布与河道形态有密切关系,相对而言,弯道段及分汊段冲刷强度大于整体河段平均值；河段纵向节点多为分汊河段,且交替型分汊河段较非交替型分汊河段的节点作用更为稳定；由于长河段深泓纵剖面分形维数的加大,节点河段河床表面分形维数的普遍加大以及床沙的粗化使得下游河道阻力有所加大,这对宜昌河段枯水位的下降起到了抑制作用；在下游水位进一步下降幅度不大,并在采取一定工程措施的情况下,宜昌枯水位将可以保持稳定。
As the boundary of river water and sediment movement, the characters of Riverbed are movable and complexity of its 3D space structure. The variety of river bed form and the problems such as flow structure, channel resistance and sediment transport capacity adjustment which is caused by its shape changes are the contents of fundamental research in the river dynamics field. For the channels downstream reservoir, the changes of water and sediment conditions will lead to erosion adjustment of their bed form, which will impact the flood control, irrigation, navigation and many other implications of the river. Therefore, it has important theoretical and engineering value to study erosion adjustment of channel form and some related effects.
In this paper, GIS technology and theory of non-linear-fractal are introduced into the river dynamics, the law and measurement method of river bed form erosion adjustment is studied by the approach of observed data analysis and generalized model experiment, and on this basis, the river-type classification, channel resistance estimation, as well as the river bed erosion adjustment and related effects on resistance of the river downstream Three Gorges Project (TGP) were also discussed, the specific contents and main results are as follows:
(1) The bed form features of different typical braided river and the law of its erosion adjustment are analyzed by the observed data analysis. In the case of strong constraint boundary, the commonness of erosion adjustment among different types of braided river is erosion of the inlet, and each inlet has a unbalanced turn of erosion, in addition, the central bar and sand bar nearby convex bank often will be a degree of erosion; the difference is that the relative erosion rate of the two branches is different. Although the larger one is still after the local flood dynamic axis, the results are also different, the diversion pattern of the alternate braided river should be changed, the one of non-alternant braided river will be stability.
(2) The riverbed surface fractal dimension (BSD) is put forword to measure river bed. Based on improvements in some aspects of Surface area-Scale Method, such as, estimation of surface area, boundary treatment and judgment of non-scale range, and GIS technology was combined to bring up a method on the bed surface fractal dimension calculation that the data sources is DWG format underwater topographic map. The new method is effective and accurate, and has good applicabiliton on the bed surface fractal dimension calculation. The fractal characteristics of river bed surface morphology is discussed by combination with river-pattern, local river regime and river process of typical reach.
(3) Based on the combination of general model about different river patterns and observed data, the relationship between bed surface fractal dimension and the adjustment of bed form is studied. There is whole and part relationship between riverbed surface fractal dimension and flat shape, cross-sectional shape as well as longitudinal profile form of the river, the two-dimensional profiles reflect changes in bed form only from a different side or in part, therefore, the bed surface fractal dimension can describe overall adjustment intensity of river bed surface morphology, and reflect characteristic of the river process sensitivity. As different river has different bed form, the river bed surface fractal dimension can reflect the difference among river-patterns, even subclass to some extent. The bed surface fractal dimension should be a distinguished criterion of river-pattern after gather more actual information and unified fractal algorithm. Meanwhile, the fractal characteristics of the Yangtze River middle reaches is studied, the thelweg longitudinal profile profile fractal dimension (TD) can quantitatively reflect thecomplexity of river longitudinal profile sharp.
(4) The law and mechanism of resistance changes in the adjustment process under the variational factors is studied. The increase of intensity of flow conditions or the decrease of base-level can make the range of river bed changes greater, and exacerbate the adjustment of channel resistance; the resistance adjustment process of different river pattern are basically similar, there is a first increases and then decreases in the basic process, compared with straight river pattern, as the complexity of the flow structure and rapidity of bed deformation in braided river and bending river, their resistance adjustment process is faster and the variation range is bigger. There is a positive relationship between river bed surface fractal dimension and the bed roughness. The quantitative relationship between them is obtained based on the experiment, the quantitative relationship can be applied to estimate changes of roughness in the same river.
(5) The mechanism of low water level changes in Yichang was analyzed and discussed from distribution of erosion and river morphology adjustment on Yichang to Yangjianao channel after the impoundment of Three Gorges Project(TGP). There is a closely relationship between distribution of erosion along the river and the channel morphology on this channel, in comparison, the erosion intensity of bending reach and the branching reach is greater than the overall average; the longitudinal nodes of the channel are mostly braided reach, and the node of alternating-type braided reach is more stable than the one of non-alternating type braided reach; due to the increase of thalweg longitudinal profile fractal dimension in the long channel, the general increase of riverbed surface fractal dimension in node reaches,and coarsening of bed material, the bed resistance downstream TGP has increased, and the increace played inhibition to this low water level decline in Yichang; in the case of in downstream water level can not decline furtherly, Yichang low water level will remain stable with some engineering measures be carried on.
引文
[1]钱宁,张仁,周志德.河床演变学[M].北京：科学出版社,1987.
[2]张瑞瑾.河流泥沙动力学[M].北京：中国水利水电出版社,1989.6.
[3]陈立,明宗富.河流动力学[M].武汉：武汉大学出版社,2001.
[4]王兴奎,邵学军,王光谦,等.河流动力学[M].北京：科学出版社,2004.
[5]钱宁,万兆惠.泥沙运动力学[M].北京：科学出版社,1983.182-415.
[6]天津水运工程科学研究所,清华大学.葛洲坝枢纽下游水位变化对船闸与航道影响及对策研究[A].国务院三峡工程建设委员会办公室泥沙课题专家组,中国长江三峡工程开发总公司三峡工程泥沙专家组.长江三峡工程泥沙问题研究(1996.2000第六卷长江三峡工程坝下游泥沙问题(一))[C].北京：知识出版社,2002,1-34.
[7]李云中.长江宜昌河段低水位变化研究[J].中国三峡建设,2002(5)：12-14.
[8]孙昭华,李义天,李明,等.长江中游宜昌-沙市段河床冲淤与枯水位变化[J].水利水运工程学报,2007(4)：14-20.
[9]李义天,葛华,孙昭华.葛洲坝下游局部卡口对宜昌枯水水位影响的初步分析[J].应用基础与工程科学学报,2007,]5(4)：435-444.
[10]孙昭华,李义天,葛华,等.三峡下游沙卵石河段纵剖面形态对枯水位影响[J].泥沙研究,2007(3)：9-16.
[11]葛华,李义天,朱玲玲,等.三峡蓄水初期宜昌枯水位稳定机理初步分析[J].四川大学学报(工程科学版),2009,41(1)：47-53.
[12]王光谦,张红武,夏军强,著.游荡型河流演变及模拟[M].北京：科学出版社,2005.
[13]孙赞盈,曲少军,苏运启,等.描述黄河中下游河道横断面形态的新指标[J].山地学报,2004,22(2)：161-164.
[14]蔡大富,曾庆云,段文忠.长江荆江河段河弯平面形态变化规律研究[J].水道港口,2006,27(2)：84-88.
[15]Brice.G.C. Channel Patterns and terraces of the Loup River in Nebraska, U.S.Geol.Survey, 1964,422.
[16]谢鉴衡,主编.河床演变及整治[M].北京：中国水利水电出版社,1997.
[17]中国水利学会泥沙专业委员会,主编.泥沙手册[M].北京：中国环境科学出版社,1989.
[]8]张俊勇.河流再造床河型变化过程与结果的初步研究[D].武汉：武汉大学博士论文,2006.
[19]倪晋仁,王随继.论顺直河流[J].水利学报,2000,(12)：14-20.
[20]赵晓马.顺直冲积型河道河相关系和稳定指标研究[D].重庆：重庆交通大学硕士论文,2009.
[21]刘金,陈立,周银军,等.三峡蓄水后宜昌河段河床演变分析[J].水运工程,2009.11(434)：116-120.
[22]吴娱,陈立,桂波,等.汉江兴隆至新泗港河段河道演变及浅滩碍航机理分析[J].水运工程,2008(4)：76-79.
[23]长江航道规划设计研究院,长江重庆航运工程勘察设计院.长江三峡工程航道泥沙原型观测2006-2007年度分析报告[R].2007.10.
[24]韩其为,杨克诚.三峡水库建成后下荆江河型变化趋势的研究[J].泥沙研究,2000(3)：1-11.
[25]长江水利委员会水文局.2007年度三峡工程坝下游宜昌至湖口河段冲淤及河床组成变化分析[R].2008.4
[26]覃莲超,余明辉,谈广鸣,等.河湾水流动力轴线变化与切滩撇弯关系研究[J].水动力学研究与进展A辑.2009,24(1)：29-35.
[27]韩其为,何明民.三峡水库建成后长江中下游河道演变的趋势[J].长江科学院院报,1997(1)：12-16
[28]潘庆燊.长江中下游河道演变趋势及对策[J].人民长江,1997(5)：22-25.
[29]许炯心.汉江丹江口下游游荡段河岸侵蚀及其在河床调整中的意义[J].科学通报,1998,40(8)：1689-1693.
[30]许炯心.汉江丹江口水库下游河床调整过程中的复杂响应[J].科学通报,1989(6).
[31]冯源.年内交替型分汊河道冲刷调整规律与机理的初步研究[D].武汉大学博士论文,2009.5
[32]陈立,鲍倩,何娟,吴娱.枢纽下游近坝段不同类型河段的再造床过程及其对航道条件的影响[J].水运工程,2008(7)：109-115.
[33]何娟,陈立,周银军,等.河床边界条件改变对强约束型分汊河道冲刷调整的影响[J].水运工程,2009.5(428)：92-97.
[34]何娟,陈立,关洪林.水库下游不同约束条件分汊河道冲刷调整规律研究[J].长江科学 院院报,2009,26(5)：5-8.
[35]龚国元.汉江丹江口水库下游河床演变[J].地理研究,1982,1(1)：69-78.
[36]夏军强,吴保生,王艳平.近期黄河下游河床调整过程及特点[J].水科学进展,2008,19(3)：301-308.
[37]贾锐敏.从丹江口、葛洲坝水库下游河床冲刷看三峡工程下游河床演变对航道的影响[J].1996,(3)：1-13
[38]许炯心.黄河下游游荡河段清水冲刷时期河床调整的复杂响应现象[J].水科学进展,2001,12(3)：291-299.
[39]张敏.黄河下游河道横断面形态演变特点及调整规律探讨[D].太原理工大学硕士论文,2006.
[40]陆中臣,陈劭锋,陈浩.黄河下游游荡段河道平面形态与河势变化趋势预测[J].地理学报,2000,55(6)：729-736.
[41]H W Shen, Henry M. F. and Cesar M.Bed Form Resistances in open Channel Flows[J]. Journal of Hydraulic Engineering,1990,116(6):799-815.
[42]Yalin M.S. Mechanics of Sediment Transport.Oxford:Pergamon Press,1972,1-223.
[43]Brownlie W R. Flow depth in sand-bed channels[J]. Journal of the Hydraulics Division,1983,109 (7):959-990.
[44]Lovera F and Kennedy J F. Friction factors for flat-bed flows in sand channels[J]. Journal of the Hydraulics Division,1969,95 (4):1227-1234.
[45]Alam AMZ and Kennedy J F. Friction factors for flow in sand bed channels[J]. Journal of the Hydraulics Division,1969,95 (6):1973-1992.
[46]Vanoni V. A., and Hwang L. S. (1967). Relation between bed forms and friction in streams[J]. Journal of the Hydraulics Division,1967,93 (3):121-144.
[47]郭俊克,惠遇甲.沙垄阻力的理论分析与试验研究[J].水动力学研究与进展A辑,1990,6(1)：1-12.
[48]Shu-Qing Yang and Soon-Keat Tan. Flow Resistance over Mobile Bed in an Open-Channel Flow[J]. Journal of the Hydraulic Engineering,2008,134 (7):937-947.
[49]乐培九,李献忠.沙波阻力问题的研究[J].水道港口,1989,(1)：1-7.
[50]喻国良,敖汝庄,郑丙辉,等.冲积河床的河床阻力[J].水利学报,1999,30(4)：1-8.
[51]George A. G. Form Resistance in Gravel Channels with Mobile Beds[J]. Journal of the
Hydraulic Engineering,1989,115 (3):340-355.
[52]Wang S Q, White W R. Alluvial resistance in transition regime[J]. Journal of the Hydraulic Engineering,1993,119 (6):725-741.
[53]赵连白,袁美琦.床面形态与河床阻力关系[J].水道港口.1999年6月第2期：19-24.
[54]黄才安,顾春锋.动床沙粒阻力计算的研究[J].水力发电学报.2008,27(1)：74-78.
[55]黄才安,严恺.动床阻力的研究进展及发展趋势[J].泥沙研究,2002(4)：76-81.
[56]王士强.冲积河渠床面阻力试验研究[J].水利学报,1990,21(12)：18-29.
[57]F Karim.Bed Configuration and Hydraulic Resistance in Alluvial-Channel Flows[J].Journal of Hydraulic Engineering,1995,121 (1):15-25.
[58]White, W.R., Paris, E., and Bettess R. The Frictional Characteristics of Alluvial Streams:A New Approach.Proc.Inst.Civ.En.grs,1980,69 (2):737-700.
[59]Simons D. B., and Richardson, E. V. Forms of bed roughness in alluvial channels[J]. Trans. Am. Soc. Civ. Eng.,1963,128 (1):284-323.
[60]H Afzalimehr and F Anctil. Estimation of gravel-bed river flow resistance[J]. Journal of Hydraulic Engineering,1998,124(10):1054-1058.
[61]苏启东,韩慧卿,王学金.黄河山东段复式河槽动床阻力分布特性[J].水文,1999(6)：48-50.
[62]秦荣昱,刘淑杰,王崇浩.黄河下游河道阻力与输沙特性的研究[J].泥沙研究,1995(4)：10-18.
[63]黄才安,赵晓冬,龚敏飞.基于水流功率理论的动床阻力计算方法[J].扬州大学学报(自然科学版),20047(4)：71-74.
[64]黄才安,周济人,张瑾,等.均匀沙床面动床阻力计算的人工神经网络模型[J].水利学报,2009,40(11)：1351-1356.
[65]Van Rijn, L.C.Equivalent. Roughness of Alluvial Bed[J].Journal of the Hydraulics Division, 1982,108 (10):1215-1218.
[66]James P B.Algorithm for resistance to flow and transport in sand-bed channels[J]. Journal of Hydraulic Engineering,1995,121 (8):578-590.
[67]Raudkivi A. J. Ripples on stream bed[J].Journal of Hydraulic Engineering,1997,123 (1): 58-64.
[68]Scott Wright and Gary Parker.Flow Resistance and Suspended Load in Sand-Bed Rivers:Simplified Stratification Model[J]. Journal of Hydraulic Engineering,2004,130(8): 796-805.
[69]Richard D. Hey.Bar Form Resistance in Gravel-Bed Rivers[J]. Journal of Hydraulic Engineering,1988,114(12):1498-1508.
[70]Hayashi T.Resistance to Flow in Alluvial Channels[C].In:Proceedings of the Fourth International Symposium on River Sedimentation, Beijing, China,1989:514-521.
[7]]赵连军,张红武.黄河下游河道摩阻特性的研究[J].人民黄河,1997,19(9)：17-20.
[72]周国栋,刘琼轶,王桂仙,等.床沙组成对水流阻力的影响[J].水动力学研究与进展A辑,2003,18(5)：576-583.
[73]V. Ferro and G. Giordano. Experimental Study of Flow Resistance in Gravel-Bed Rivers[J]. Journal of Hydraulic Engineering,1991,117(10):1239-1246.
[74]Song T., Chiew Y.M.,and Chin C.O. Effect of Bed-Load Movement on Flow Friction Factor[J]. Journal of Hydraulic Engineering,1998,124(2):165-175.
[75]周志德.中细沙平整动床的阻力[J].水利学报,1983,(5)：58-64.
[76]Smith J.D.,and McLean S.R. Spatially Averaged Flow over a Wavy Surface[J].Journal of Geophysical Research,1977,82(12):1735-1746.
[77]Wiberg P.L.,and Rubin D.M.Bed Roughness Produced by Saltating Sediment[J]. Journal of Geophysical Research,1989,94(4):5011-5016.
[78]D.A.Lyn. Resistance in Flat-Bed Sediment-Laden Flows[J]. Journal of Hydraulic Engineering,1991,117(1):94-114.
[79]Arora A.K,Rangaraju K.G,and Garde R.J.Resistance to Flow and Velocity Distribution in Rigid Boundary Channels Carrying Sediment-Laden Flow[J].Water Resources Research, 1986,22(6):943-951.
[80]Kereselidze N.B.,and Kutavaia V.I.Experimental Research on Kinematics of Flows withHigh Suspended Solid Concentration[J].Journal of Hydraulic Research,1995,33(1):65-75.
[81]Parker G.,and Coleman N.L.Simple Model of Sediment-Laden Flows[J].Journal of Hydraulic Engineering,1986,112(5):356-375.
[82]Chanson H. Drag Reduction in Open Channel Flow by Aeration and Suspended Load[J].Journal of Hydraulic Research,1994,32(1):87-101.
[83]Liu Q.Q.,Chen L,and Liu D.Effects of Existance of Sediment Particles on EnergyLoss of the
Sediment-Laden Flow[J].International Journal of Sediment Research,1996,11 (3):18-24.
[84]金忠青,韩龙喜,张健.复杂河网的水力计算及参数反问题[J].水动力学研究与进展A辑,1998,13(3)：280-285.
[85]郑邦民,齐鄂荣.天然河道非恒定流条件下阻力系数变化规律的研究[J].水动力学研究与进展A辑,1990,5(3)：49-59.
[86]董文军,杨则.一维圣维南方程的反问题研究与计算方法[J].水利学报,2002(9)：61-65.
[87]姜志群,王佩兰.河道洪水演进有限差分模型糙率系数的率定[J].水文,1996(6)：56-58.
[88]杨永德,刘炳衡.糙率变化过程的推算模型与长江三峡糙率探讨[J].人民长江,1991(22)12： 9-15.
[89]Fread, D. L. and Smith, G. F., Calibration Technique for 1-D Unsteady Flow Models, Journal of the Hydraulics Division[J].1978,104 (7):1027-1043.
[90]韩龙喜,朱羿,蒋莉华.山区型河道一维水力数值模拟糙率确定方法[J].水文,2002,22(6)：16-18.
[91]李义天,赵明登,曹志芳.河道平面二维水沙数学模型[M].北京：中国水利水电出版社,2001：24-27.
[92]要 威,李义天.游荡型河道阻力沿河宽分布的研究[J].四川大学学报：工程科学版,2007,39(1)：38-43.
[93]刘 臣,平克军.河道二维数值模拟糙率横向分布研究[J].水道港口,2008,29(2)：113-118.
[94]吴伟明.天然河流平面二维动床阻力问题研究[J].武汉水利电力大学学报,1996,9(3)：7-12.
[95]倪晋仁,马蔼乃,著.河流动力地貌学[M].北京：北京大学出版社,1998.
[96]邵学军,王兴奎,编著.河流动力学概论[M].北京：清华大学出版社,2005.
[97]余文畴.长江中下游长河段阻力系数分析[J].人民长江,1995,26(4)：8-14.
[98]秦荣昱,王崇浩,刘淑杰,刘峡.峡谷河道综合糙率变化规律的预报[J].泥沙研究,1995.3：59-69.
[99]沈玉吕,龚国元,编著.河流地貌学概论[M].北京：科学出版社,1986.
[100]Howard H. Chang.Variation of Flow Resistance Through Curved Channels[J]. Journal of Hydraulic Engineering,1984,112(10):1772-1782.
[101]叶青超,陆中臣,杨毅芬,等著.黄河下游河流地貌[M].北京：科学出版社,1990.
[102]V.A.范诺尼,候乐如.冲积河流河床形态和输沙率计算动态介绍.水利水电科技进展,1983(1)：151-182.
[103]P. Y. Julien, G. J. Klaassen, W. B. M. Ten Brinke and A. W. E. Wilbers.Case Study:Bed Resistance of Rhine River during 1998 Flood[J].Journal of Hydraulic Engineering,2002, 128(12):1042-1050.
[]04] 许炯心.基于对Leopold-Wolman关系修正的河床河型判别[J].地理学报2004,59(3)：462-467.
[105]Mandelbrot B B.The Fractal Geometry of Nature.San Francisco[M].Freeman,1982
[106]Mandelbrot B B.How long is the coast of Britain[J].Science,1967,155:636-638.
[107]谢和平,张永平,宋晓秋著.分形几何——数学基础与应用[M].重庆：重庆大学出版社,1991.
[108]Hastings H M and Sugihara G. Fractals:a user's guide for the natural sciences.Oxford University Press, Oxford, England,1993
[109]张济忠.分形[M].北京：清华大学出版社,1995,111-140.
[110]孙霞,吴自勤,黄畇编著.分形原理及应用[M].合肥：中国科学技术大学出版社,2003.
[111]Noordwijk MV, Purnomosidhi P, Van NM, et al. Root architecture in relation to tree-soil-crop interactions and shoot pruning in agroforestry. Agroforestry Systems,1995, 30:1-2,161-173
[112]邹明清.分形理论的若干应用[D].武汉：华中科技大学,2007：5-15.
[113]常福宣.分形理论在水文水资源研究中的应用[D].成都：四川大学,2001.
[114]孙霞,吴自勤.规则表面形貌的分形和多重分形描述.物理学报,2001,50(11)：2126-2131.
[115]张少文,王文圣,丁 晶,等.分形理论在水文水资源中的应用[J].水科学进展,2005,16(1)： 141-146.
[116]Gupta VK, Waymire E. Multiscaling properties of spatial rainfall and river flow distributions [J]. J Geophys Res,1990,95 (3):1999-2009.
[117]Samuele G. D., Massimo V., Leonardo P.. Estimated generalized dimensions of river networks[J]. Journal of Hydrology,2006,322:181-191.
[118]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,1992,15(7)：
516-519.
[119]Vincent D., Marc S. Topography of large-scale watersheds:fractal texture and global drift.Application to the Mississippi basin. Earth and Planetary Letters,1996,143:257-267.
[120]王倩,邹欣庆,朱大奎.基于GIS技术的秦淮河流域水系分维研究[J].水科学进展,2002,11 (6)： 751-756.
[121]张宏才,汤国安.基于GIS的河网分形研究[J].西北大学学报(自然科学版),2006,36(4)：659-662.
[122]崔灵周,肖学年,李占斌.基于GIS的流域地貌形态分形盒维数测定方法研究[J].水土保持通报,2004,24(2)：38-40.
[123]Nikota V I. Fractal sturctures of river plan forms[J].Water Resour. Res.,1991,27(6): 1327-1333.
[124]Nikora V I, Sapozhnikov V B, Noever D A-Fractal geometry of individual river channels and its computer simulation[J].Water Resour Res,1993,29 (10):3561-3568.
[125]Nikora V I, SapozhnikovVB. River network fractal geometry and its computer simulation[J].Water Resour Res,1993,29 (10):3569-3575.
[126]Sapozhnikov V B, Foufpula-Georgou E. Self-affinity in braided rivers[J]-Water Resour Res,1996,32 (5):1429-1439.
[127]冯平,冯焱.河流形态特征的分维计算方法[J].地理学报,1997,7(4)：324-330.
[128]白玉川,黄涛,许栋.蜿蜒河流平面形态的几何分形及统计分析[J].天津大学学报,2008,41(9)：1052-1056.
[129]朱嘉伟,赵云章等黄河下游河道地貌分形分维特征研究[J].测绘科学,2005,30(5)：28-30.
[130]Robert.A. Statistical properties of sediment bed profiles in alluvial channels [J]. Math. Geol.,1988,20:205-225.
[131]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)： 154-162.
[132]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[J].水科学进展,2002,13(3)：368-376.
[133]周银军,陈立,刘欣桐,等.河床表面分形特征及其分形维数计算方法研究[J].华东师范大学学报(自然科学版),2009,3：170-178.
[134]Tokinaga S, MoriyasuH, Miyazaki A, et al. Forecasting of time serieswith fractal geometry by using scale transformations and parameter esti-mations obtained by the wavelet transform[J].Electronics and Communications in Japan, Part 3,1997,80(9):2054-2062.
[135]刘德平.分形理论在水文过程形态特征分析中的应用[J]·水利学报,1998(2)：20-25.
[]36] 丁 晶,刘国东.日径流过程分维估计[J]·四川水力发电,1999,18(4)：74-76.
[137]冯 平,王仁超.水文干旱的时间分形特征探讨[J]·水利水电技术,1997,28(11)：48-51.
[138]冯利华,许晓路.金衢盆地旱涝统计特征初步分析[J]·水科学进展,1999,10(1)：84-88.
[139]方崇惠,郭生练,段亚辉,等.应用分形理论划分洪水分期的两种新途径[J].科学通报,2009,54(1])：1613-1617.
[140]张之湘,惠仕兵,沈焕荣,等.宽级配卵石推移质输移随机过程的分维研究[J].泥沙研究,2000(4)：60-64.
[141]杨清书,傅家谟,罗章仁.西北江三角洲来水来沙的非线性分形特征[J].泥沙研究,2002(6)：15-18.
[142]P.J. Shang, Santi K..Fractal nature of time series in the sediment transport phenomenon[J].Chaos, Solitons and Fractals,2005,26:997-1007.
[143]钟 亮,许光祥.分形理论在紊流与泥沙研究中的应用现状[J].重庆交通大学学报(自然科学版),2008,27(5)：806-811.
[144]FujisakaH, MoriH.Amaximum principle fordetermining the intermittency exponent of fully developed steady turbulence[J]. ProgTheorphys,1979,62 (8):54-60.
[145]Tabelling P. Sudden increase of the fractal dimension in a hydrodynamic system[J]. Phys Rev,1985,31 (5):3460-3462.
[146]Sreenivasan K R, Meneveau C.The fractal facets of turbulence[J].FluidMech,1986, 173 (3):357-386.
[147]Prasad T, MurayamaM, Tanida Y. Fractal analysis of turbulent premixed flame surface[J]. Experiment in Fluids,1997,245 (10):61-71.
[148]Ali R. K., Ali N. Z., Emdad H., et al. Fractal-Markovian scaling of turbulent bursting process in open channel flow[J].Chaos, Solitons and Fractals,2005,25 (2) 307-318
[149]D. Queiros-Conde, F. Foucher, C. Mounaim-Rousselle, et al. A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall[J].Physica A, 2008,387 (27):6712-6724.
[150]黄真理,李玉梁,余常昭.紊动射流的分维测量[J].科学通报,1994,39(6)：567-570.
[151]汤一波,金忠青.脉动压力的紊流分形特征[J].水科学进展,1998,9(4)：361-365.
[152]王玲玲,金忠青.分形理论及其在紊流研究中的应用[J].河海大学学报,1997,25(1)：1-5.
[153]李玉梁,田晓东,梁东方.二维半岛紊动尾流的分维量测与分析[J].水力发电学报,2004,23(4)：60-64.
[154]杨铁笙,张正红.泥沙淤积物颗粒排列结构的分形模式研究[J].应用基础与工程科学学报,1994,2(2、3)：152-156.
[155]李洪,李嘉,李克锋,等.泥沙的分形表面和分形吸附模型[J].水利学报,2003,34(3)： 14-18.
[156]王毅力,芦家娟,周岩梅,等.沉积物颗粒表面分形特征的研究[J].环境科学学报,2005，25(4)：457-463.
[157]方红卫,陈明洪,陈志和.泥沙颗粒污染前后表面孔隙力学特征分析[J].中国科学G 辑,2008,38(6)：714-720.
[158]李泳,陈晓清,胡凯衡,等.泥石流颗粒组成的分形特征[J].地理学报,2005,60(3)：495-502.
[159]陶高梁, 张季如.表征孔隙及颗粒体积与尺度分布的两类岩土体分形模型[J]_科学通报,2009,54(6)：838-846
[160]James.P.H., Luis.E. V..Fractal analysis of the roughness and size distribution of granular materials[J].Engineering Geology,1997,48 (4):231-244.
[161]武生智,魏春玲,马崇武,等.沙粒粗糙度和粒径分布的分形特性.兰州大学学报(自然科学版),1999,35(1)：53-56.
[162]王协康,方铎,姚令侃.非均匀沙床面粗糙度的分形特征[J].水利学报,1999,30(7)：70-74.
[163]姚令侃,方铎.非均匀沙自组织临界性及其应用研究[J].水利学报,1997,28(3)：26-32.
[164]王协康,方铎,曹叔尤.宽级配卵石泥沙颗粒特性的分维值及其应用[J].长江科学
院院报,1999,16(5)：9-12.
[1]何娟,陈立,关洪林.水库下游不同约束条件分汊河道冲刷调整规律研究[J].长江科学院院报,2009,26(5)：5-8.
[2]冯源.年内交替型分汊河道冲刷调整规律与机理的初步研究[D].武汉大学博士论文,2009.5
[3]张炯,陈立,何娟,等.三峡水库蓄水后宜都水道演变及航道变化[J].水运工程,2006(8)： 83-86.
[4]熊治平,邓良爱.关洲、芦家河水道演变的几点认识[J].水运工程.1996(11)：27-29.
[5]罗优,陈立,周银军.三峡蓄水后芦家河河段演变分析.水运工程,2009.12(435)：154-158.
[1]王兴奎,邵学军,王光谦,等编著.河流动力学[M].北京：科学出版社,2004.
[2]Mandelbrot B B.The Fractal Geometry of Nature [M].New York:W.H.Freeman,1992.
[3]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.
[4]余文畴,卢金友,编著.长江河道演变与治理[M].北京：中国水利水电出版社,2005.
[5]崔灵周,肖学年,李占斌.基于GIS的流域地貌形态分形盒维数测定方法研究[J].水土保持通报,2004,24(2)：38-40.
[6]Andreas C.W.Baas. Chaos,fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments[J]. Geomorphology.2002,200 (48):309-328.
[7]周宏伟,谢和平,KWASNIEWSKI M A.粗糙表面分维计算的立方体覆盖法[J].摩擦学学报,2000,20(6)：455-459.
[8]沈中原,李占斌,李鹏,等.流域地貌形态特征多重分形算法研究[J].水科学进展,2009,20(3)： 385-391
[9]王强.GIS在河道冲淤及河床演变分析中的应用[D].武汉：武汉大学,2004.5-13.
[10]兰宇.数字河流的河槽演变空间分析方法[D].南京：河海大学,2007.12-13.
[11]王建,白世彪,陈哗编著Surfer8地理信息制图[M].北京：中国地图出版社,2004.1-8.
[12]陆志波,陆雍森Surfer 8.0在环境评价和规划中的应用[J].同济大学学报(自然科学版).2005,33(2)：191-195.
[13]张强,施雅风,姜彤,等.长江中游马口——田家镇河段40年来河道演变[J].地理学报,2007,62(1)：62-71.
[14]何娟,陈立,黄荣敏,王鑫.DWG图形文件直接生成DEM的方法和实现[J].计算机应用研究.2007,(24)5：295-297.
[15]谢和平,等著.分形几何——数学基础与应用[M].重庆：重庆大学出版社,1991.
[16]Xie H, Wang J A, Stein E. Direct fractal measurement and multifractal properties of fracture surface[J].Physics Letters A,1998,242:41-50.
[17]张亚衡,周宏伟,谢和平.粗糙表面分形维数估算的改进立方体覆盖法[J].岩石力学与工程学报,2005,24(17)：3192-3196.
[18]周银军,陈立,刘欣桐,等.河床表面分形特征及其分形维数计算方法研究[J].华东师范大学学报(自然科学版),2009,3：170-178.
[19]Russ. J. C. Fractal Surfaces [M]. Plenum Prcss.1994.
[20]陈立,冯源,何娟,等.武桥水道水动力特性与汉阳边滩演变[J].武汉大学学报(工学版),2008,41(5)
[21]刘金,陈立,周银军,等.三峡蓄水后宜昌河段河床演变分析[J].水运工程,2009.11(434)：116-120.
[1]钱宁,张仁,周志德.河床演变学[M],北京：科学出版社,1987
[2]冯源.年内交替型分汊河道冲刷调整规律与机理的初步研究[D].武汉：武汉大学博士论文,2009.5
[1]冯源.年内交替型分汉河道冲刷调整规律与机理的初步研究[D].武汉：武汉大学博士论文,2009.5
[2]王兴奎,邵学军,王光谦,等编著.河流动力学[M].北京：科学出版社,2004.
[3]倪晋仁,马蔼乃,著.河流动力地貌学[M].北京：北京大学出版社,1998.
[4]沈玉昌,龚国元,编著.河流地貌学概论[M].北京：科学出版社,1986.
[5]叶青超,陆中臣,杨毅芬,等著.黄河下游河流地貌[M].北京：科学出版社,1990.
[6]许炯心.砂质河床与砾石河床的河型判别研究[J].水利学报,2002,(10)：14-20.
[7]许炯心.基于对Leoplod-Wolman关系修正的河床河型判别.地理学报[J].2004,59(3)：462-467.
[1]陈立,明宗富.河流动力学[M].武汉：武汉大学出版社,2001.
[1]Howard H.Chang.River morphology and thresholds [J]. Journal of Hydraulic Engineering, 1985, 111(3):503-519.
[2]孙昭华,李义天,李明等.长江中游宜昌-沙市段河床冲淤与枯水位变化[J].水利水运工程学报,2007(4)：14-20.
[3]李义天,葛华,孙昭华.葛洲坝下游局部卡口对宜昌枯水水位影响的初步分析[J].应用基础与工程科学学报,2007,15(4)：435-444.
[4]孙昭华,李义天,葛华等.三峡下游沙卵石河段纵剖面形态对枯水位影响[J].泥沙研究,2007(3)：9-16.
[5]葛华,李义天,朱玲玲等.三峡蓄水初期宜昌枯水位稳定机理初步分析[J].四川大学学报(工程科学版),2009,41(1)：47-53.
[6]王兴奎,邵学军,王光谦等.河流动力学[M].北京：科学出版社,2004.
[7]黄颖,李义天.维持通航建筑物口门水深的护底加糙措施研究[J].水利学报,Feb.2005,No.2：141-154.
[8]长江科学院.三峡水库下游宜昌至大通河段冲淤一维数模计算分析[A].长江三峡工程泥沙问题研究(第七卷)[C].北京：知识产权出版社,2002,211-310.
[9]李华国.枢纽下游水位降落问题探讨[J].水道港口,2006,27(4)：217-222.
[2]张瑞瑾.河流泥沙动力学[M].北京：中国水利水电出版社,1989.6.
[3]陈立,明宗富.河流动力学[M].武汉：武汉大学出版社,2001.
[4]王兴奎,邵学军,王光谦,等.河流动力学[M].北京：科学出版社,2004.
[5]钱宁,万兆惠.泥沙运动力学[M].北京：科学出版社,1983.182-415.
[6]天津水运工程科学研究所,清华大学.葛洲坝枢纽下游水位变化对船闸与航道影响及对策研究[A].国务院三峡工程建设委员会办公室泥沙课题专家组,中国长江三峡工程开发总公司三峡工程泥沙专家组.长江三峡工程泥沙问题研究(1996.2000第六卷长江三峡工程坝下游泥沙问题(一))[C].北京：知识出版社,2002,1-34.
[7]李云中.长江宜昌河段低水位变化研究[J].中国三峡建设,2002(5)：12-14.
[8]孙昭华,李义天,李明,等.长江中游宜昌-沙市段河床冲淤与枯水位变化[J].水利水运工程学报,2007(4)：14-20.
[9]李义天,葛华,孙昭华.葛洲坝下游局部卡口对宜昌枯水水位影响的初步分析[J].应用基础与工程科学学报,2007,]5(4)：435-444.
[10]孙昭华,李义天,葛华,等.三峡下游沙卵石河段纵剖面形态对枯水位影响[J].泥沙研究,2007(3)：9-16.
[11]葛华,李义天,朱玲玲,等.三峡蓄水初期宜昌枯水位稳定机理初步分析[J].四川大学学报(工程科学版),2009,41(1)：47-53.
[12]王光谦,张红武,夏军强,著.游荡型河流演变及模拟[M].北京：科学出版社,2005.
[13]孙赞盈,曲少军,苏运启,等.描述黄河中下游河道横断面形态的新指标[J].山地学报,2004,22(2)：161-164.
[14]蔡大富,曾庆云,段文忠.长江荆江河段河弯平面形态变化规律研究[J].水道港口,2006,27(2)：84-88.
[15]Brice.G.C. Channel Patterns and terraces of the Loup River in Nebraska, U.S.Geol.Survey, 1964,422.
[16]谢鉴衡,主编.河床演变及整治[M].北京：中国水利水电出版社,1997.
[17]中国水利学会泥沙专业委员会,主编.泥沙手册[M].北京：中国环境科学出版社,1989.
[]8]张俊勇.河流再造床河型变化过程与结果的初步研究[D].武汉：武汉大学博士论文,2006.
[19]倪晋仁,王随继.论顺直河流[J].水利学报,2000,(12)：14-20.
[20]赵晓马.顺直冲积型河道河相关系和稳定指标研究[D].重庆：重庆交通大学硕士论文,2009.
[21]刘金,陈立,周银军,等.三峡蓄水后宜昌河段河床演变分析[J].水运工程,2009.11(434)：116-120.
[22]吴娱,陈立,桂波,等.汉江兴隆至新泗港河段河道演变及浅滩碍航机理分析[J].水运工程,2008(4)：76-79.
[23]长江航道规划设计研究院,长江重庆航运工程勘察设计院.长江三峡工程航道泥沙原型观测2006-2007年度分析报告[R].2007.10.
[24]韩其为,杨克诚.三峡水库建成后下荆江河型变化趋势的研究[J].泥沙研究,2000(3)：1-11.
[25]长江水利委员会水文局.2007年度三峡工程坝下游宜昌至湖口河段冲淤及河床组成变化分析[R].2008.4
[26]覃莲超,余明辉,谈广鸣,等.河湾水流动力轴线变化与切滩撇弯关系研究[J].水动力学研究与进展A辑.2009,24(1)：29-35.
[27]韩其为,何明民.三峡水库建成后长江中下游河道演变的趋势[J].长江科学院院报,1997(1)：12-16
[28]潘庆燊.长江中下游河道演变趋势及对策[J].人民长江,1997(5)：22-25.
[29]许炯心.汉江丹江口下游游荡段河岸侵蚀及其在河床调整中的意义[J].科学通报,1998,40(8)：1689-1693.
[30]许炯心.汉江丹江口水库下游河床调整过程中的复杂响应[J].科学通报,1989(6).
[31]冯源.年内交替型分汊河道冲刷调整规律与机理的初步研究[D].武汉大学博士论文,2009.5
[32]陈立,鲍倩,何娟,吴娱.枢纽下游近坝段不同类型河段的再造床过程及其对航道条件的影响[J].水运工程,2008(7)：109-115.
[33]何娟,陈立,周银军,等.河床边界条件改变对强约束型分汊河道冲刷调整的影响[J].水运工程,2009.5(428)：92-97.
[34]何娟,陈立,关洪林.水库下游不同约束条件分汊河道冲刷调整规律研究[J].长江科学 院院报,2009,26(5)：5-8.
[35]龚国元.汉江丹江口水库下游河床演变[J].地理研究,1982,1(1)：69-78.
[36]夏军强,吴保生,王艳平.近期黄河下游河床调整过程及特点[J].水科学进展,2008,19(3)：301-308.
[37]贾锐敏.从丹江口、葛洲坝水库下游河床冲刷看三峡工程下游河床演变对航道的影响[J].1996,(3)：1-13
[38]许炯心.黄河下游游荡河段清水冲刷时期河床调整的复杂响应现象[J].水科学进展,2001,12(3)：291-299.
[39]张敏.黄河下游河道横断面形态演变特点及调整规律探讨[D].太原理工大学硕士论文,2006.
[40]陆中臣,陈劭锋,陈浩.黄河下游游荡段河道平面形态与河势变化趋势预测[J].地理学报,2000,55(6)：729-736.
[41]H W Shen, Henry M. F. and Cesar M.Bed Form Resistances in open Channel Flows[J]. Journal of Hydraulic Engineering,1990,116(6):799-815.
[42]Yalin M.S. Mechanics of Sediment Transport.Oxford:Pergamon Press,1972,1-223.
[43]Brownlie W R. Flow depth in sand-bed channels[J]. Journal of the Hydraulics Division,1983,109 (7):959-990.
[44]Lovera F and Kennedy J F. Friction factors for flat-bed flows in sand channels[J]. Journal of the Hydraulics Division,1969,95 (4):1227-1234.
[45]Alam AMZ and Kennedy J F. Friction factors for flow in sand bed channels[J]. Journal of the Hydraulics Division,1969,95 (6):1973-1992.
[46]Vanoni V. A., and Hwang L. S. (1967). Relation between bed forms and friction in streams[J]. Journal of the Hydraulics Division,1967,93 (3):121-144.
[47]郭俊克,惠遇甲.沙垄阻力的理论分析与试验研究[J].水动力学研究与进展A辑,1990,6(1)：1-12.
[48]Shu-Qing Yang and Soon-Keat Tan. Flow Resistance over Mobile Bed in an Open-Channel Flow[J]. Journal of the Hydraulic Engineering,2008,134 (7):937-947.
[49]乐培九,李献忠.沙波阻力问题的研究[J].水道港口,1989,(1)：1-7.
[50]喻国良,敖汝庄,郑丙辉,等.冲积河床的河床阻力[J].水利学报,1999,30(4)：1-8.
[51]George A. G. Form Resistance in Gravel Channels with Mobile Beds[J]. Journal of the
Hydraulic Engineering,1989,115 (3):340-355.
[52]Wang S Q, White W R. Alluvial resistance in transition regime[J]. Journal of the Hydraulic Engineering,1993,119 (6):725-741.
[53]赵连白,袁美琦.床面形态与河床阻力关系[J].水道港口.1999年6月第2期：19-24.
[54]黄才安,顾春锋.动床沙粒阻力计算的研究[J].水力发电学报.2008,27(1)：74-78.
[55]黄才安,严恺.动床阻力的研究进展及发展趋势[J].泥沙研究,2002(4)：76-81.
[56]王士强.冲积河渠床面阻力试验研究[J].水利学报,1990,21(12)：18-29.
[57]F Karim.Bed Configuration and Hydraulic Resistance in Alluvial-Channel Flows[J].Journal of Hydraulic Engineering,1995,121 (1):15-25.
[58]White, W.R., Paris, E., and Bettess R. The Frictional Characteristics of Alluvial Streams:A New Approach.Proc.Inst.Civ.En.grs,1980,69 (2):737-700.
[59]Simons D. B., and Richardson, E. V. Forms of bed roughness in alluvial channels[J]. Trans. Am. Soc. Civ. Eng.,1963,128 (1):284-323.
[60]H Afzalimehr and F Anctil. Estimation of gravel-bed river flow resistance[J]. Journal of Hydraulic Engineering,1998,124(10):1054-1058.
[61]苏启东,韩慧卿,王学金.黄河山东段复式河槽动床阻力分布特性[J].水文,1999(6)：48-50.
[62]秦荣昱,刘淑杰,王崇浩.黄河下游河道阻力与输沙特性的研究[J].泥沙研究,1995(4)：10-18.
[63]黄才安,赵晓冬,龚敏飞.基于水流功率理论的动床阻力计算方法[J].扬州大学学报(自然科学版),20047(4)：71-74.
[64]黄才安,周济人,张瑾,等.均匀沙床面动床阻力计算的人工神经网络模型[J].水利学报,2009,40(11)：1351-1356.
[65]Van Rijn, L.C.Equivalent. Roughness of Alluvial Bed[J].Journal of the Hydraulics Division, 1982,108 (10):1215-1218.
[66]James P B.Algorithm for resistance to flow and transport in sand-bed channels[J]. Journal of Hydraulic Engineering,1995,121 (8):578-590.
[67]Raudkivi A. J. Ripples on stream bed[J].Journal of Hydraulic Engineering,1997,123 (1): 58-64.
[68]Scott Wright and Gary Parker.Flow Resistance and Suspended Load in Sand-Bed Rivers:Simplified Stratification Model[J]. Journal of Hydraulic Engineering,2004,130(8): 796-805.
[69]Richard D. Hey.Bar Form Resistance in Gravel-Bed Rivers[J]. Journal of Hydraulic Engineering,1988,114(12):1498-1508.
[70]Hayashi T.Resistance to Flow in Alluvial Channels[C].In:Proceedings of the Fourth International Symposium on River Sedimentation, Beijing, China,1989:514-521.
[7]]赵连军,张红武.黄河下游河道摩阻特性的研究[J].人民黄河,1997,19(9)：17-20.
[72]周国栋,刘琼轶,王桂仙,等.床沙组成对水流阻力的影响[J].水动力学研究与进展A辑,2003,18(5)：576-583.
[73]V. Ferro and G. Giordano. Experimental Study of Flow Resistance in Gravel-Bed Rivers[J]. Journal of Hydraulic Engineering,1991,117(10):1239-1246.
[74]Song T., Chiew Y.M.,and Chin C.O. Effect of Bed-Load Movement on Flow Friction Factor[J]. Journal of Hydraulic Engineering,1998,124(2):165-175.
[75]周志德.中细沙平整动床的阻力[J].水利学报,1983,(5)：58-64.
[76]Smith J.D.,and McLean S.R. Spatially Averaged Flow over a Wavy Surface[J].Journal of Geophysical Research,1977,82(12):1735-1746.
[77]Wiberg P.L.,and Rubin D.M.Bed Roughness Produced by Saltating Sediment[J]. Journal of Geophysical Research,1989,94(4):5011-5016.
[78]D.A.Lyn. Resistance in Flat-Bed Sediment-Laden Flows[J]. Journal of Hydraulic Engineering,1991,117(1):94-114.
[79]Arora A.K,Rangaraju K.G,and Garde R.J.Resistance to Flow and Velocity Distribution in Rigid Boundary Channels Carrying Sediment-Laden Flow[J].Water Resources Research, 1986,22(6):943-951.
[80]Kereselidze N.B.,and Kutavaia V.I.Experimental Research on Kinematics of Flows withHigh Suspended Solid Concentration[J].Journal of Hydraulic Research,1995,33(1):65-75.
[81]Parker G.,and Coleman N.L.Simple Model of Sediment-Laden Flows[J].Journal of Hydraulic Engineering,1986,112(5):356-375.
[82]Chanson H. Drag Reduction in Open Channel Flow by Aeration and Suspended Load[J].Journal of Hydraulic Research,1994,32(1):87-101.
[83]Liu Q.Q.,Chen L,and Liu D.Effects of Existance of Sediment Particles on EnergyLoss of the
Sediment-Laden Flow[J].International Journal of Sediment Research,1996,11 (3):18-24.
[84]金忠青,韩龙喜,张健.复杂河网的水力计算及参数反问题[J].水动力学研究与进展A辑,1998,13(3)：280-285.
[85]郑邦民,齐鄂荣.天然河道非恒定流条件下阻力系数变化规律的研究[J].水动力学研究与进展A辑,1990,5(3)：49-59.
[86]董文军,杨则.一维圣维南方程的反问题研究与计算方法[J].水利学报,2002(9)：61-65.
[87]姜志群,王佩兰.河道洪水演进有限差分模型糙率系数的率定[J].水文,1996(6)：56-58.
[88]杨永德,刘炳衡.糙率变化过程的推算模型与长江三峡糙率探讨[J].人民长江,1991(22)12： 9-15.
[89]Fread, D. L. and Smith, G. F., Calibration Technique for 1-D Unsteady Flow Models, Journal of the Hydraulics Division[J].1978,104 (7):1027-1043.
[90]韩龙喜,朱羿,蒋莉华.山区型河道一维水力数值模拟糙率确定方法[J].水文,2002,22(6)：16-18.
[91]李义天,赵明登,曹志芳.河道平面二维水沙数学模型[M].北京：中国水利水电出版社,2001：24-27.
[92]要 威,李义天.游荡型河道阻力沿河宽分布的研究[J].四川大学学报：工程科学版,2007,39(1)：38-43.
[93]刘 臣,平克军.河道二维数值模拟糙率横向分布研究[J].水道港口,2008,29(2)：113-118.
[94]吴伟明.天然河流平面二维动床阻力问题研究[J].武汉水利电力大学学报,1996,9(3)：7-12.
[95]倪晋仁,马蔼乃,著.河流动力地貌学[M].北京：北京大学出版社,1998.
[96]邵学军,王兴奎,编著.河流动力学概论[M].北京：清华大学出版社,2005.
[97]余文畴.长江中下游长河段阻力系数分析[J].人民长江,1995,26(4)：8-14.
[98]秦荣昱,王崇浩,刘淑杰,刘峡.峡谷河道综合糙率变化规律的预报[J].泥沙研究,1995.3：59-69.
[99]沈玉吕,龚国元,编著.河流地貌学概论[M].北京：科学出版社,1986.
[100]Howard H. Chang.Variation of Flow Resistance Through Curved Channels[J]. Journal of Hydraulic Engineering,1984,112(10):1772-1782.
[101]叶青超,陆中臣,杨毅芬,等著.黄河下游河流地貌[M].北京：科学出版社,1990.
[102]V.A.范诺尼,候乐如.冲积河流河床形态和输沙率计算动态介绍.水利水电科技进展,1983(1)：151-182.
[103]P. Y. Julien, G. J. Klaassen, W. B. M. Ten Brinke and A. W. E. Wilbers.Case Study:Bed Resistance of Rhine River during 1998 Flood[J].Journal of Hydraulic Engineering,2002, 128(12):1042-1050.
[]04] 许炯心.基于对Leopold-Wolman关系修正的河床河型判别[J].地理学报2004,59(3)：462-467.
[105]Mandelbrot B B.The Fractal Geometry of Nature.San Francisco[M].Freeman,1982
[106]Mandelbrot B B.How long is the coast of Britain[J].Science,1967,155:636-638.
[107]谢和平,张永平,宋晓秋著.分形几何——数学基础与应用[M].重庆：重庆大学出版社,1991.
[108]Hastings H M and Sugihara G. Fractals:a user's guide for the natural sciences.Oxford University Press, Oxford, England,1993
[109]张济忠.分形[M].北京：清华大学出版社,1995,111-140.
[110]孙霞,吴自勤,黄畇编著.分形原理及应用[M].合肥：中国科学技术大学出版社,2003.
[111]Noordwijk MV, Purnomosidhi P, Van NM, et al. Root architecture in relation to tree-soil-crop interactions and shoot pruning in agroforestry. Agroforestry Systems,1995, 30:1-2,161-173
[112]邹明清.分形理论的若干应用[D].武汉：华中科技大学,2007：5-15.
[113]常福宣.分形理论在水文水资源研究中的应用[D].成都：四川大学,2001.
[114]孙霞,吴自勤.规则表面形貌的分形和多重分形描述.物理学报,2001,50(11)：2126-2131.
[115]张少文,王文圣,丁 晶,等.分形理论在水文水资源中的应用[J].水科学进展,2005,16(1)： 141-146.
[116]Gupta VK, Waymire E. Multiscaling properties of spatial rainfall and river flow distributions [J]. J Geophys Res,1990,95 (3):1999-2009.
[117]Samuele G. D., Massimo V., Leonardo P.. Estimated generalized dimensions of river networks[J]. Journal of Hydrology,2006,322:181-191.
[118]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,1992,15(7)：
516-519.
[119]Vincent D., Marc S. Topography of large-scale watersheds:fractal texture and global drift.Application to the Mississippi basin. Earth and Planetary Letters,1996,143:257-267.
[120]王倩,邹欣庆,朱大奎.基于GIS技术的秦淮河流域水系分维研究[J].水科学进展,2002,11 (6)： 751-756.
[121]张宏才,汤国安.基于GIS的河网分形研究[J].西北大学学报(自然科学版),2006,36(4)：659-662.
[122]崔灵周,肖学年,李占斌.基于GIS的流域地貌形态分形盒维数测定方法研究[J].水土保持通报,2004,24(2)：38-40.
[123]Nikota V I. Fractal sturctures of river plan forms[J].Water Resour. Res.,1991,27(6): 1327-1333.
[124]Nikora V I, Sapozhnikov V B, Noever D A-Fractal geometry of individual river channels and its computer simulation[J].Water Resour Res,1993,29 (10):3561-3568.
[125]Nikora V I, SapozhnikovVB. River network fractal geometry and its computer simulation[J].Water Resour Res,1993,29 (10):3569-3575.
[126]Sapozhnikov V B, Foufpula-Georgou E. Self-affinity in braided rivers[J]-Water Resour Res,1996,32 (5):1429-1439.
[127]冯平,冯焱.河流形态特征的分维计算方法[J].地理学报,1997,7(4)：324-330.
[128]白玉川,黄涛,许栋.蜿蜒河流平面形态的几何分形及统计分析[J].天津大学学报,2008,41(9)：1052-1056.
[129]朱嘉伟,赵云章等黄河下游河道地貌分形分维特征研究[J].测绘科学,2005,30(5)：28-30.
[130]Robert.A. Statistical properties of sediment bed profiles in alluvial channels [J]. Math. Geol.,1988,20:205-225.
[131]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)： 154-162.
[132]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[J].水科学进展,2002,13(3)：368-376.
[133]周银军,陈立,刘欣桐,等.河床表面分形特征及其分形维数计算方法研究[J].华东师范大学学报(自然科学版),2009,3：170-178.
[134]Tokinaga S, MoriyasuH, Miyazaki A, et al. Forecasting of time serieswith fractal geometry by using scale transformations and parameter esti-mations obtained by the wavelet transform[J].Electronics and Communications in Japan, Part 3,1997,80(9):2054-2062.
[135]刘德平.分形理论在水文过程形态特征分析中的应用[J]·水利学报,1998(2)：20-25.
[]36] 丁 晶,刘国东.日径流过程分维估计[J]·四川水力发电,1999,18(4)：74-76.
[137]冯 平,王仁超.水文干旱的时间分形特征探讨[J]·水利水电技术,1997,28(11)：48-51.
[138]冯利华,许晓路.金衢盆地旱涝统计特征初步分析[J]·水科学进展,1999,10(1)：84-88.
[139]方崇惠,郭生练,段亚辉,等.应用分形理论划分洪水分期的两种新途径[J].科学通报,2009,54(1])：1613-1617.
[140]张之湘,惠仕兵,沈焕荣,等.宽级配卵石推移质输移随机过程的分维研究[J].泥沙研究,2000(4)：60-64.
[141]杨清书,傅家谟,罗章仁.西北江三角洲来水来沙的非线性分形特征[J].泥沙研究,2002(6)：15-18.
[142]P.J. Shang, Santi K..Fractal nature of time series in the sediment transport phenomenon[J].Chaos, Solitons and Fractals,2005,26:997-1007.
[143]钟 亮,许光祥.分形理论在紊流与泥沙研究中的应用现状[J].重庆交通大学学报(自然科学版),2008,27(5)：806-811.
[144]FujisakaH, MoriH.Amaximum principle fordetermining the intermittency exponent of fully developed steady turbulence[J]. ProgTheorphys,1979,62 (8):54-60.
[145]Tabelling P. Sudden increase of the fractal dimension in a hydrodynamic system[J]. Phys Rev,1985,31 (5):3460-3462.
[146]Sreenivasan K R, Meneveau C.The fractal facets of turbulence[J].FluidMech,1986, 173 (3):357-386.
[147]Prasad T, MurayamaM, Tanida Y. Fractal analysis of turbulent premixed flame surface[J]. Experiment in Fluids,1997,245 (10):61-71.
[148]Ali R. K., Ali N. Z., Emdad H., et al. Fractal-Markovian scaling of turbulent bursting process in open channel flow[J].Chaos, Solitons and Fractals,2005,25 (2) 307-318
[149]D. Queiros-Conde, F. Foucher, C. Mounaim-Rousselle, et al. A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall[J].Physica A, 2008,387 (27):6712-6724.
[150]黄真理,李玉梁,余常昭.紊动射流的分维测量[J].科学通报,1994,39(6)：567-570.
[151]汤一波,金忠青.脉动压力的紊流分形特征[J].水科学进展,1998,9(4)：361-365.
[152]王玲玲,金忠青.分形理论及其在紊流研究中的应用[J].河海大学学报,1997,25(1)：1-5.
[153]李玉梁,田晓东,梁东方.二维半岛紊动尾流的分维量测与分析[J].水力发电学报,2004,23(4)：60-64.
[154]杨铁笙,张正红.泥沙淤积物颗粒排列结构的分形模式研究[J].应用基础与工程科学学报,1994,2(2、3)：152-156.
[155]李洪,李嘉,李克锋,等.泥沙的分形表面和分形吸附模型[J].水利学报,2003,34(3)： 14-18.
[156]王毅力,芦家娟,周岩梅,等.沉积物颗粒表面分形特征的研究[J].环境科学学报,2005，25(4)：457-463.
[157]方红卫,陈明洪,陈志和.泥沙颗粒污染前后表面孔隙力学特征分析[J].中国科学G 辑,2008,38(6)：714-720.
[158]李泳,陈晓清,胡凯衡,等.泥石流颗粒组成的分形特征[J].地理学报,2005,60(3)：495-502.
[159]陶高梁, 张季如.表征孔隙及颗粒体积与尺度分布的两类岩土体分形模型[J]_科学通报,2009,54(6)：838-846
[160]James.P.H., Luis.E. V..Fractal analysis of the roughness and size distribution of granular materials[J].Engineering Geology,1997,48 (4):231-244.
[161]武生智,魏春玲,马崇武,等.沙粒粗糙度和粒径分布的分形特性.兰州大学学报(自然科学版),1999,35(1)：53-56.
[162]王协康,方铎,姚令侃.非均匀沙床面粗糙度的分形特征[J].水利学报,1999,30(7)：70-74.
[163]姚令侃,方铎.非均匀沙自组织临界性及其应用研究[J].水利学报,1997,28(3)：26-32.
[164]王协康,方铎,曹叔尤.宽级配卵石泥沙颗粒特性的分维值及其应用[J].长江科学
院院报,1999,16(5)：9-12.
[1]何娟,陈立,关洪林.水库下游不同约束条件分汊河道冲刷调整规律研究[J].长江科学院院报,2009,26(5)：5-8.
[2]冯源.年内交替型分汊河道冲刷调整规律与机理的初步研究[D].武汉大学博士论文,2009.5
[3]张炯,陈立,何娟,等.三峡水库蓄水后宜都水道演变及航道变化[J].水运工程,2006(8)： 83-86.
[4]熊治平,邓良爱.关洲、芦家河水道演变的几点认识[J].水运工程.1996(11)：27-29.
[5]罗优,陈立,周银军.三峡蓄水后芦家河河段演变分析.水运工程,2009.12(435)：154-158.
[1]王兴奎,邵学军,王光谦,等编著.河流动力学[M].北京：科学出版社,2004.
[2]Mandelbrot B B.The Fractal Geometry of Nature [M].New York:W.H.Freeman,1992.
[3]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.
[4]余文畴,卢金友,编著.长江河道演变与治理[M].北京：中国水利水电出版社,2005.
[5]崔灵周,肖学年,李占斌.基于GIS的流域地貌形态分形盒维数测定方法研究[J].水土保持通报,2004,24(2)：38-40.
[6]Andreas C.W.Baas. Chaos,fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments[J]. Geomorphology.2002,200 (48):309-328.
[7]周宏伟,谢和平,KWASNIEWSKI M A.粗糙表面分维计算的立方体覆盖法[J].摩擦学学报,2000,20(6)：455-459.
[8]沈中原,李占斌,李鹏,等.流域地貌形态特征多重分形算法研究[J].水科学进展,2009,20(3)： 385-391
[9]王强.GIS在河道冲淤及河床演变分析中的应用[D].武汉：武汉大学,2004.5-13.
[10]兰宇.数字河流的河槽演变空间分析方法[D].南京：河海大学,2007.12-13.
[11]王建,白世彪,陈哗编著Surfer8地理信息制图[M].北京：中国地图出版社,2004.1-8.
[12]陆志波,陆雍森Surfer 8.0在环境评价和规划中的应用[J].同济大学学报(自然科学版).2005,33(2)：191-195.
[13]张强,施雅风,姜彤,等.长江中游马口——田家镇河段40年来河道演变[J].地理学报,2007,62(1)：62-71.
[14]何娟,陈立,黄荣敏,王鑫.DWG图形文件直接生成DEM的方法和实现[J].计算机应用研究.2007,(24)5：295-297.
[15]谢和平,等著.分形几何——数学基础与应用[M].重庆：重庆大学出版社,1991.
[16]Xie H, Wang J A, Stein E. Direct fractal measurement and multifractal properties of fracture surface[J].Physics Letters A,1998,242:41-50.
[17]张亚衡,周宏伟,谢和平.粗糙表面分形维数估算的改进立方体覆盖法[J].岩石力学与工程学报,2005,24(17)：3192-3196.
[18]周银军,陈立,刘欣桐,等.河床表面分形特征及其分形维数计算方法研究[J].华东师范大学学报(自然科学版),2009,3：170-178.
[19]Russ. J. C. Fractal Surfaces [M]. Plenum Prcss.1994.
[20]陈立,冯源,何娟,等.武桥水道水动力特性与汉阳边滩演变[J].武汉大学学报(工学版),2008,41(5)
[21]刘金,陈立,周银军,等.三峡蓄水后宜昌河段河床演变分析[J].水运工程,2009.11(434)：116-120.
[1]钱宁,张仁,周志德.河床演变学[M],北京：科学出版社,1987
[2]冯源.年内交替型分汊河道冲刷调整规律与机理的初步研究[D].武汉：武汉大学博士论文,2009.5
[1]冯源.年内交替型分汉河道冲刷调整规律与机理的初步研究[D].武汉：武汉大学博士论文,2009.5
[2]王兴奎,邵学军,王光谦,等编著.河流动力学[M].北京：科学出版社,2004.
[3]倪晋仁,马蔼乃,著.河流动力地貌学[M].北京：北京大学出版社,1998.
[4]沈玉昌,龚国元,编著.河流地貌学概论[M].北京：科学出版社,1986.
[5]叶青超,陆中臣,杨毅芬,等著.黄河下游河流地貌[M].北京：科学出版社,1990.
[6]许炯心.砂质河床与砾石河床的河型判别研究[J].水利学报,2002,(10)：14-20.
[7]许炯心.基于对Leoplod-Wolman关系修正的河床河型判别.地理学报[J].2004,59(3)：462-467.
[1]陈立,明宗富.河流动力学[M].武汉：武汉大学出版社,2001.
[1]Howard H.Chang.River morphology and thresholds [J]. Journal of Hydraulic Engineering, 1985, 111(3):503-519.
[2]孙昭华,李义天,李明等.长江中游宜昌-沙市段河床冲淤与枯水位变化[J].水利水运工程学报,2007(4)：14-20.
[3]李义天,葛华,孙昭华.葛洲坝下游局部卡口对宜昌枯水水位影响的初步分析[J].应用基础与工程科学学报,2007,15(4)：435-444.
[4]孙昭华,李义天,葛华等.三峡下游沙卵石河段纵剖面形态对枯水位影响[J].泥沙研究,2007(3)：9-16.
[5]葛华,李义天,朱玲玲等.三峡蓄水初期宜昌枯水位稳定机理初步分析[J].四川大学学报(工程科学版),2009,41(1)：47-53.
[6]王兴奎,邵学军,王光谦等.河流动力学[M].北京：科学出版社,2004.
[7]黄颖,李义天.维持通航建筑物口门水深的护底加糙措施研究[J].水利学报,Feb.2005,No.2：141-154.
[8]长江科学院.三峡水库下游宜昌至大通河段冲淤一维数模计算分析[A].长江三峡工程泥沙问题研究(第七卷)[C].北京：知识产权出版社,2002,211-310.
[9]李华国.枢纽下游水位降落问题探讨[J].水道港口,2006,27(4)：217-222.