交汇河道水动力特性和污染物掺混规律研究综述
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摘要
水流交汇广泛存在于天然河流中,通过交汇口作为节点连接大小河流形成水系乃至河网。交汇河道不同于单一河道,其交汇口上游壅水下游回流,存在分离区、最大流速区、压缩区等,具有独特的水流特性和污染物输移规律。从不同的角度对交汇河道进行了分类,强调了交汇河道的水动力特性和污染物输移特性研究的重要意义。从原型观测和模型试验、数值模拟和理论分析方面分析评述了交汇口水动力特性和污染物输移规律的研究现状和研究成果,讨论了研究现状存在的问题并对该领域的研究方向进行了展望。
The crossing and converging of currents is widespread among natural rivers, and the confluence is the joint that connects rivers into river system or even river network. Unlike the single channel, the confluent channel has unique water flow characteristics and pollutant transport pattern. In the upstream and downstream of the intersection, backwater and backflow phenomenon are normally found that flow separation zone, maximum velocity area and compression zone are defined. This paper classified the confluent channels from different angles and pointed out the importance of researches on the hydrodynamic characteristics and pollutant transport pattern. The research situation and achievement of hydrodynamic characteristics and pollutant transport pattern was analyzed in terms of prototype observation and model test, numerical simulation and theoretical analysis. At last, the existing problems of current researches were discussed, and the outlook of future research direction was made.
The crossing and converging of currents is widespread among natural rivers, and the confluence is the joint that connects rivers into river system or even river network. Unlike the single channel, the confluent channel has unique water flow characteristics and pollutant transport pattern. In the upstream and downstream of the intersection, backwater and backflow phenomenon are normally found that flow separation zone, maximum velocity area and compression zone are defined. This paper classified the confluent channels from different angles and pointed out the importance of researches on the hydrodynamic characteristics and pollutant transport pattern. The research situation and achievement of hydrodynamic characteristics and pollutant transport pattern was analyzed in terms of prototype observation and model test, numerical simulation and theoretical analysis. At last, the existing problems of current researches were discussed, and the outlook of future research direction was made.
引文
[1] BEST J L. Sediment transport and bed morphology at river channel confluences[J]. Sedimentology, 1988(35):481-498.
[2]兰波. 山区河流交汇河口的综合特性分析 [J]. 重庆交通学院学报, 1998,17(4):91-96.
[3]TAYLOR E H. Flow Characteristics at Rectangular Open-Channel Junctions[J]. Transactions of the American Society of Civil Engineers, 1944,109(1):893-902.
[4]BEST J L, REID I. Separation Zone at Open‐Channel Junctions[J]. Journal of Hydraulic Engineering, 1984,110(11):1588-1594.
[5]BEST J L. Flow dynamics at river channel confluences:implications for sediment transport and bed morphology[J]. Special Publications, 1987,39:27-35.
[6]ROY A G, BEST J L. Mixing-layer distortion at the confluence of channels of different depth[J]. Nature, 1991,350(6317):411-413.
[7]BIRON P, BEST J L, ROY A G. Effects of bed discordance on flow dynamics at open channel confluences[J]. Journal of Hydraulic Engineering, 1996,12(122):676-682.
[8]HSU C, WU F, LEE W. Flow at 90° degrees equal-width open-channel junction[J]. Journal of Hydraulic Engineering, 1998,124(2):186-191.
[9]HSU C C, LEE W J, CHENG C H. Subcritical open-channel junction flow[J]. Journal of Hydraulic Engineering, 1998,124(8):847-855.
[10]WEBER B L J, SCHUMATE E D, MAWER N. Experiments on flow at a 90° open-channel junction[J]. Journal of Hydraulic Engineering, 2001,5(127):340-350.
[11]MIGNOT E, VINKOVIC I, DOPPLER D, et al. Mixing layer in open-channel junction flows[J]. Environmental Fluid Mechanics, 2014,14(5):1027-1041.
[12]BISWAL S K, MOHAPATRA P, MURALIDHAR K. Hydraulics of combining flow in a right-angled compound open channel junction[J]. Sadhana, 2016,41(1):97-110.
[13]罗保平. 汇流河段干支流分界线的实验研究[J]. 水运工程, 1994(11):13-16.
[14]周华君, 王绍成. 长江嘉陵江交汇口水力特征研究[J]. 水运工程, 1994(12):24-29.
[15]兰波, 汪勇. 干支流交汇水面形态特征分析[J]. 重庆交通学院学报, 1997(4):111-116.
[16]茅泽育, 张磊, 陈嘉范, 等. 数字粒子图像处理技术及其在明渠交汇试验研究中流速测量的应用[J]. 水利学报, 2003,34(6):65-71.
[17]茅泽育, 赵升伟, 张磊, 等. 明渠交汇口三维水力特性试验研究[J]. 水利学报, 2004,35(2):1-7.
[18]茅泽育, 赵升伟, 罗异, 等. 明渠交汇口水流分离区研究[J]. 水科学进展, 2005,16(1):8-13.
[19]王协康, 王宪业, 卢伟真, 等. 明渠水流交汇区流动特征试验研究[J]. 四川大学学报(工程科学版), 2006(2):1-5.
[20]刘同宦, 郭炜, 王协康, 等. 人汇角为30°时交汇区水流结构试验研究[J]. 长江科学院院报, 2007,24(4):75-78.
[21]刘同宦, 郭炜, 詹磊. 90°支流入汇区域时均流速分布特征试验研究[J]. 水科学进展, 2009(4):485-489.
[22]钟博刚. 直角明渠交汇区水流特性的水槽试验研究[D]. 西安:西安理工大学, 2013.
[23]海霞. 垂直入汇河段交汇区水流特性试验研究[D]. 西安:西安理工大学, 2014.
[24]YUAN S, TANG H, XIAO Y, et al. Turbulent flow structure at a 90-degree open channel confluence: Accounting for the distortion of the shear layer[J]. Journal of Hydro-environment Research, 2016,12:130-147.
[25]郭维东, 王晓刚, 曹继文, 等. “Y”型汇流口水流水力特性试验研究[J]. 水电能源科学, 2005,23(3):53-56.
[26]冯亚辉, 郭维东, 王晓刚. 明渠交汇水流的螺旋度分析[J]. 人民长江, 2007(1):119-121.
[27]吴迪, 郭维东, 刘卓也. 复式断面河道“Y”型交汇河口水流水力特性[J]. 水利水电科技进展, 2007,27(3):21-23.
[28]付中敏, 谷祖鹏, 郑惊涛, 等. 干支流汇合口水力特性的试验性研究[J]. 水运工程, 2013(4):46-51.
[29]贾猛. 曲线交汇条件下弯道水流水力特性试验研究[D]. 邯郸:河北工程大学, 2016.
[30]WANG K H, CLEVELAND T G, FITZGERALD S, et al. Hydrodynamic flow modeling at confluence of two streams[J]. Journal of Engineering Mechanics, 1996,122:994-1002.
[31]BABARUTSI S, CHU V H. Modeling transverse mixing layer in shallow open-channel flows[J]. Journal of Hydraulic Engineering, 1998,124(7):718-727.
[32]GHOSTINE R, VAZQUEZ J, TERFOUS A, et al. A comparative study of 1D and 2D approaches for simulating flows at right angled dividing junctions[J]. Applied Mathematics and Computation, 2013,219(10):5070-5082.
[33]KHAN A A, CADAVID R, WANG S S Y. Simulation of channel confluence and bifurcation using the CCHE2D model[J]. 2000,142(2):97-102.
[34]BRADBROOK K F, BIRON P M, LANE S N, et al. Investigation of controls on secondary circulation in a simple confluence geometry using a three-dimensional numerical model[J]. Hydrological Processes, 1998,12(8):1371 - 1396.
[35]BRADBROOK K F, LANE S N, RICHARDS K S, et al. Large Eddy Simulation of periodic flow characteristics at river channel confluences[J]. Journal of Hydraulic Research, 2010(1):207-215.
[36]HAN S, RAMAMURTHY A S, BIRON P M. Three-Dimensional Numerical Modeling of Mixing at River Confluences[J]. Journal of Hydraulic Engineering, 2004,130(3):243-253.
[37]KESSERWANI G, GHOSTINE R, VAZQUEZ J, et al. Simulation of subcritical flow at open-channel junction[J]. Advances in Water Resources, 2008,31(2):287-297.
[38]SONG C G, SEO I W, KIM Y D. Analysis of secondary current effect in the modeling of shallow flow in open channels[J]. Advances in Water Resources, 2012,41:29-48.
[39]SHAKIBAINIA A, TABATABAI M R M, ZARRATI A R. Three-dimensional numerical study of flow structure in channel confluences[J]. Canadian Journal of Civil Engineering, 2010,37(5):772-781.
[40]茅泽育, 罗昇, 赵升伟, 等. 等宽明渠交汇口水流一维数学模型[J]. 水利学报, 2004(8):26-32.
[41]赵升伟, 茅泽育, 罗昇, 等. 等宽明渠交汇水流数值计算[J]. 河海大学学报(自然科学版), 2005,33(5):494-499.
[42]冯镜洁, 李然, 王协康, 等. 河流交汇分离区特性研究[J]. 水动力学研究与进展, 2009,24(3):320-325.
[43]周晶. 明渠交汇水流三维数值模拟[D]. 广州:中山大学, 2010.
[44]刘盛赟, 康鹏, 李然, 等. 水流交汇区的水动力学特性数值模拟[J]. 水利水电科技进展, 2012(4):14-18.
[45]王凯. 不同汇流比时支流入汇角对水面线的影响[J]. 水利科技与经济, 2014(12):60-61.
[46]魏文礼, 邵世鹏, 刘玉玲. 不同交汇角度明渠交汇口三维水力特性的大涡模拟研究[J]. 应用力学学报, 2015,32(1):57-63.
[47]魏文礼, 张泽伟, 邵世鹏, 等. 明渠交汇口三维水力特性大涡模拟研究[J]. 武汉大学学报(工学版), 2016,49(2):173-179.
[48]冯亚辉, 郭维东. Y型明渠交汇水流数值计算[J]. 水利水运工程学报, 2006(4):34-40.
[49]郭维东, 梁岳, 冯亚辉, 等. Y型明渠交汇水流分离区的数值分析[J]. 水利水电科技进展, 2007,27(6):49-52.
[50]王晓刚, 严忠民. Y型汇流口壅水规律研究[J]. 河海大学学报(自然科学版), 2008(2):185-188.
[51]王晓刚, 严忠民, 张幸农. 河床高差对Y型汇流口螺旋流结构的影响[J]. 水科学进展, 2008(6):828-834.
[52]王晓刚, 严忠民, 王明才. 汇流比对“Y型”汇流口处螺旋流结构的影响[J]. 大连海事大学学报, 2008(4):79-83.
[53]杨泽一.干支流交汇口水力特性三维数值模拟研究[D]. 重庆:重庆交通大学, 2013.
[54]AZEVEDO I C, BORDALO A A, DUARTE P M. Influence of river discharge patterns on the hydrodynamics and potential contaminant dispersion in the Douro estuary (Portugal)[J]. Water Research, 2010,44(10):3133-3146.
[55]SCHEMEL L E, COX M H, RUNKEL R L, et al. Multiple injected and natural conservative tracers quantify mixing in a stream confluence affected by acid mine drainage near Silverton, Colorado[J]. Hydrological Processes, 2006,20(13):2727-2743.
[56]RIBEIRO M L, BOILLAT J L, SCHLEISS A J, et al. Experimental study on a widening tributary channel and its influence on the confluence morphology[J]. River Flow,2010(1):961-968.
[57]BINELLI A, COGNI D, PAROLINI M, et al. Multi-biomarker approach to investigate the state of contamination of the R. Lambro/R. Po confluence (Italy) by zebra mussel (Dreissena polymorpha)[J]. Chemosphere, 2010,79(5):518-528.
[58]郑庆华, 何悦强, 张银英, 等. 珠江口咸淡水交汇区营养盐的化学自净研究[J]. 热带海洋, 1995(2):68-75.
[59]张银英, 郑庆华, 何悦强, 等. 珠江口咸淡水交汇区水中CODMn,油类,砷自净规律的试验研究[J]. 热带海洋, 1995(3):67-74.
[60]洪益平. 交汇河段的紊流模型及在三峡库区水污染控制中的应用[D]. 北京:清华大学, 2000.
[61]茅泽育, 武蓉, 马吉明. 明渠交汇口水流及污染物输移数值计算[J]. 水利学报, 2003(8):43-48.
[62]刘雪兰. 重庆两江汇流流场及水质的数值模拟[D]. 重庆:重庆大学, 2005.
[63]周富春, 陈培帅, 刘国东. 两江汇流口污染混合区变化规律分析[J]. 水利水运工程学报, 2013(3):60-64.
[64]魏娟, 李然, 康鹏, 等. 水流交汇区污染物输移扩散特性[J]. 水科学进展, 2012(6):822-828.
[65]李娟, 冯民权, 刘淑文. 汾河入黄口水流特性与污染物扩散模拟[J]. 水土保持通报, 2014,34(6):189-192.
[66]韩龙喜, 陆东, 计红. 平原河网十字型汊口出入流断面污染物浓度响应关系研究[J]. 中山大学学报(自然科学版), 2011(1):123-128.
[67]袁航. 斜支入干型交汇河道污染物掺混规律及横向混合系数分布研究[D]. 南京:河海大学, 2016.
[68]LI C W, XIE J F. Numerical modeling of free surface flow over submerged and highly flexible vegetation[J]. Advances in Water Resources, 2011,34(4):468-477.
[69]BRAATEN P J, GUY C S. Relations between Physicochemical Factors and Abundance of Fishes in Tributary Confluences of the Lower Channelized Missouri River[J]. Transactions of the American Fisheries Society, 1999,128(6):1213-1221.
[70]FERNANDES C C, PODOS J, LUNDBERG J G. Amazonian ecology: tributaries enhance the diversity of electric fishes[J]. Science, 2004,305(5692):1960-1962.
[2]兰波. 山区河流交汇河口的综合特性分析 [J]. 重庆交通学院学报, 1998,17(4):91-96.
[3]TAYLOR E H. Flow Characteristics at Rectangular Open-Channel Junctions[J]. Transactions of the American Society of Civil Engineers, 1944,109(1):893-902.
[4]BEST J L, REID I. Separation Zone at Open‐Channel Junctions[J]. Journal of Hydraulic Engineering, 1984,110(11):1588-1594.
[5]BEST J L. Flow dynamics at river channel confluences:implications for sediment transport and bed morphology[J]. Special Publications, 1987,39:27-35.
[6]ROY A G, BEST J L. Mixing-layer distortion at the confluence of channels of different depth[J]. Nature, 1991,350(6317):411-413.
[7]BIRON P, BEST J L, ROY A G. Effects of bed discordance on flow dynamics at open channel confluences[J]. Journal of Hydraulic Engineering, 1996,12(122):676-682.
[8]HSU C, WU F, LEE W. Flow at 90° degrees equal-width open-channel junction[J]. Journal of Hydraulic Engineering, 1998,124(2):186-191.
[9]HSU C C, LEE W J, CHENG C H. Subcritical open-channel junction flow[J]. Journal of Hydraulic Engineering, 1998,124(8):847-855.
[10]WEBER B L J, SCHUMATE E D, MAWER N. Experiments on flow at a 90° open-channel junction[J]. Journal of Hydraulic Engineering, 2001,5(127):340-350.
[11]MIGNOT E, VINKOVIC I, DOPPLER D, et al. Mixing layer in open-channel junction flows[J]. Environmental Fluid Mechanics, 2014,14(5):1027-1041.
[12]BISWAL S K, MOHAPATRA P, MURALIDHAR K. Hydraulics of combining flow in a right-angled compound open channel junction[J]. Sadhana, 2016,41(1):97-110.
[13]罗保平. 汇流河段干支流分界线的实验研究[J]. 水运工程, 1994(11):13-16.
[14]周华君, 王绍成. 长江嘉陵江交汇口水力特征研究[J]. 水运工程, 1994(12):24-29.
[15]兰波, 汪勇. 干支流交汇水面形态特征分析[J]. 重庆交通学院学报, 1997(4):111-116.
[16]茅泽育, 张磊, 陈嘉范, 等. 数字粒子图像处理技术及其在明渠交汇试验研究中流速测量的应用[J]. 水利学报, 2003,34(6):65-71.
[17]茅泽育, 赵升伟, 张磊, 等. 明渠交汇口三维水力特性试验研究[J]. 水利学报, 2004,35(2):1-7.
[18]茅泽育, 赵升伟, 罗异, 等. 明渠交汇口水流分离区研究[J]. 水科学进展, 2005,16(1):8-13.
[19]王协康, 王宪业, 卢伟真, 等. 明渠水流交汇区流动特征试验研究[J]. 四川大学学报(工程科学版), 2006(2):1-5.
[20]刘同宦, 郭炜, 王协康, 等. 人汇角为30°时交汇区水流结构试验研究[J]. 长江科学院院报, 2007,24(4):75-78.
[21]刘同宦, 郭炜, 詹磊. 90°支流入汇区域时均流速分布特征试验研究[J]. 水科学进展, 2009(4):485-489.
[22]钟博刚. 直角明渠交汇区水流特性的水槽试验研究[D]. 西安:西安理工大学, 2013.
[23]海霞. 垂直入汇河段交汇区水流特性试验研究[D]. 西安:西安理工大学, 2014.
[24]YUAN S, TANG H, XIAO Y, et al. Turbulent flow structure at a 90-degree open channel confluence: Accounting for the distortion of the shear layer[J]. Journal of Hydro-environment Research, 2016,12:130-147.
[25]郭维东, 王晓刚, 曹继文, 等. “Y”型汇流口水流水力特性试验研究[J]. 水电能源科学, 2005,23(3):53-56.
[26]冯亚辉, 郭维东, 王晓刚. 明渠交汇水流的螺旋度分析[J]. 人民长江, 2007(1):119-121.
[27]吴迪, 郭维东, 刘卓也. 复式断面河道“Y”型交汇河口水流水力特性[J]. 水利水电科技进展, 2007,27(3):21-23.
[28]付中敏, 谷祖鹏, 郑惊涛, 等. 干支流汇合口水力特性的试验性研究[J]. 水运工程, 2013(4):46-51.
[29]贾猛. 曲线交汇条件下弯道水流水力特性试验研究[D]. 邯郸:河北工程大学, 2016.
[30]WANG K H, CLEVELAND T G, FITZGERALD S, et al. Hydrodynamic flow modeling at confluence of two streams[J]. Journal of Engineering Mechanics, 1996,122:994-1002.
[31]BABARUTSI S, CHU V H. Modeling transverse mixing layer in shallow open-channel flows[J]. Journal of Hydraulic Engineering, 1998,124(7):718-727.
[32]GHOSTINE R, VAZQUEZ J, TERFOUS A, et al. A comparative study of 1D and 2D approaches for simulating flows at right angled dividing junctions[J]. Applied Mathematics and Computation, 2013,219(10):5070-5082.
[33]KHAN A A, CADAVID R, WANG S S Y. Simulation of channel confluence and bifurcation using the CCHE2D model[J]. 2000,142(2):97-102.
[34]BRADBROOK K F, BIRON P M, LANE S N, et al. Investigation of controls on secondary circulation in a simple confluence geometry using a three-dimensional numerical model[J]. Hydrological Processes, 1998,12(8):1371 - 1396.
[35]BRADBROOK K F, LANE S N, RICHARDS K S, et al. Large Eddy Simulation of periodic flow characteristics at river channel confluences[J]. Journal of Hydraulic Research, 2010(1):207-215.
[36]HAN S, RAMAMURTHY A S, BIRON P M. Three-Dimensional Numerical Modeling of Mixing at River Confluences[J]. Journal of Hydraulic Engineering, 2004,130(3):243-253.
[37]KESSERWANI G, GHOSTINE R, VAZQUEZ J, et al. Simulation of subcritical flow at open-channel junction[J]. Advances in Water Resources, 2008,31(2):287-297.
[38]SONG C G, SEO I W, KIM Y D. Analysis of secondary current effect in the modeling of shallow flow in open channels[J]. Advances in Water Resources, 2012,41:29-48.
[39]SHAKIBAINIA A, TABATABAI M R M, ZARRATI A R. Three-dimensional numerical study of flow structure in channel confluences[J]. Canadian Journal of Civil Engineering, 2010,37(5):772-781.
[40]茅泽育, 罗昇, 赵升伟, 等. 等宽明渠交汇口水流一维数学模型[J]. 水利学报, 2004(8):26-32.
[41]赵升伟, 茅泽育, 罗昇, 等. 等宽明渠交汇水流数值计算[J]. 河海大学学报(自然科学版), 2005,33(5):494-499.
[42]冯镜洁, 李然, 王协康, 等. 河流交汇分离区特性研究[J]. 水动力学研究与进展, 2009,24(3):320-325.
[43]周晶. 明渠交汇水流三维数值模拟[D]. 广州:中山大学, 2010.
[44]刘盛赟, 康鹏, 李然, 等. 水流交汇区的水动力学特性数值模拟[J]. 水利水电科技进展, 2012(4):14-18.
[45]王凯. 不同汇流比时支流入汇角对水面线的影响[J]. 水利科技与经济, 2014(12):60-61.
[46]魏文礼, 邵世鹏, 刘玉玲. 不同交汇角度明渠交汇口三维水力特性的大涡模拟研究[J]. 应用力学学报, 2015,32(1):57-63.
[47]魏文礼, 张泽伟, 邵世鹏, 等. 明渠交汇口三维水力特性大涡模拟研究[J]. 武汉大学学报(工学版), 2016,49(2):173-179.
[48]冯亚辉, 郭维东. Y型明渠交汇水流数值计算[J]. 水利水运工程学报, 2006(4):34-40.
[49]郭维东, 梁岳, 冯亚辉, 等. Y型明渠交汇水流分离区的数值分析[J]. 水利水电科技进展, 2007,27(6):49-52.
[50]王晓刚, 严忠民. Y型汇流口壅水规律研究[J]. 河海大学学报(自然科学版), 2008(2):185-188.
[51]王晓刚, 严忠民, 张幸农. 河床高差对Y型汇流口螺旋流结构的影响[J]. 水科学进展, 2008(6):828-834.
[52]王晓刚, 严忠民, 王明才. 汇流比对“Y型”汇流口处螺旋流结构的影响[J]. 大连海事大学学报, 2008(4):79-83.
[53]杨泽一.干支流交汇口水力特性三维数值模拟研究[D]. 重庆:重庆交通大学, 2013.
[54]AZEVEDO I C, BORDALO A A, DUARTE P M. Influence of river discharge patterns on the hydrodynamics and potential contaminant dispersion in the Douro estuary (Portugal)[J]. Water Research, 2010,44(10):3133-3146.
[55]SCHEMEL L E, COX M H, RUNKEL R L, et al. Multiple injected and natural conservative tracers quantify mixing in a stream confluence affected by acid mine drainage near Silverton, Colorado[J]. Hydrological Processes, 2006,20(13):2727-2743.
[56]RIBEIRO M L, BOILLAT J L, SCHLEISS A J, et al. Experimental study on a widening tributary channel and its influence on the confluence morphology[J]. River Flow,2010(1):961-968.
[57]BINELLI A, COGNI D, PAROLINI M, et al. Multi-biomarker approach to investigate the state of contamination of the R. Lambro/R. Po confluence (Italy) by zebra mussel (Dreissena polymorpha)[J]. Chemosphere, 2010,79(5):518-528.
[58]郑庆华, 何悦强, 张银英, 等. 珠江口咸淡水交汇区营养盐的化学自净研究[J]. 热带海洋, 1995(2):68-75.
[59]张银英, 郑庆华, 何悦强, 等. 珠江口咸淡水交汇区水中CODMn,油类,砷自净规律的试验研究[J]. 热带海洋, 1995(3):67-74.
[60]洪益平. 交汇河段的紊流模型及在三峡库区水污染控制中的应用[D]. 北京:清华大学, 2000.
[61]茅泽育, 武蓉, 马吉明. 明渠交汇口水流及污染物输移数值计算[J]. 水利学报, 2003(8):43-48.
[62]刘雪兰. 重庆两江汇流流场及水质的数值模拟[D]. 重庆:重庆大学, 2005.
[63]周富春, 陈培帅, 刘国东. 两江汇流口污染混合区变化规律分析[J]. 水利水运工程学报, 2013(3):60-64.
[64]魏娟, 李然, 康鹏, 等. 水流交汇区污染物输移扩散特性[J]. 水科学进展, 2012(6):822-828.
[65]李娟, 冯民权, 刘淑文. 汾河入黄口水流特性与污染物扩散模拟[J]. 水土保持通报, 2014,34(6):189-192.
[66]韩龙喜, 陆东, 计红. 平原河网十字型汊口出入流断面污染物浓度响应关系研究[J]. 中山大学学报(自然科学版), 2011(1):123-128.
[67]袁航. 斜支入干型交汇河道污染物掺混规律及横向混合系数分布研究[D]. 南京:河海大学, 2016.
[68]LI C W, XIE J F. Numerical modeling of free surface flow over submerged and highly flexible vegetation[J]. Advances in Water Resources, 2011,34(4):468-477.
[69]BRAATEN P J, GUY C S. Relations between Physicochemical Factors and Abundance of Fishes in Tributary Confluences of the Lower Channelized Missouri River[J]. Transactions of the American Fisheries Society, 1999,128(6):1213-1221.
[70]FERNANDES C C, PODOS J, LUNDBERG J G. Amazonian ecology: tributaries enhance the diversity of electric fishes[J]. Science, 2004,305(5692):1960-1962.