冲积河流泥沙输移幂律函数指数变化规律
|
摘要
冲积河流泥沙输移幂律函数关系与不平衡输沙理论是对河道不平衡输沙同一物理现象的不同描述,两者既有区别也有联系。比较研究发现:对于恒定均匀流不平衡输沙过程,当输沙位于近平衡态时两者含沙量导函数表达式具有一阶近似等价性,当输沙远离平衡态时前者含沙量导函数中隐含考虑有泥沙恢复饱和系数的变化。基于两者等价性,推导建立了幂律函数指数计算表达式,表明指数随泥沙沉速、单宽流量和沿程距离而变化,且随着输移距离的增大呈指数衰减。基于前者含沙量导函数表达式结构特点,分析建立了相应泥沙恢复饱和系数变化的计算表达式。综合以上成果,改进提出了一种变幂指数的泥沙输移幂律函数计算模型。对库里·阿雷克沉沙池沿程断面输沙指数及含沙量计算结果表明,不同距离过水断面输沙指数的变化规律是合理的,含沙量计算值与实测值变化趋势基本符合。
The empirical power law relationship model and non-equilibrium sediment transport theory are two different methods used to describe the suspended sediment transport in alluvial rivers. The mathematical comparison results show that,for steady uniform flow,the derivatives of sediment concentration of the two above mentioned methods are first order approximate when sediment transport state is near equilibrium condition,and the variation of the saturation recovery coefficient is considered in power law relationship when sediment transport state is far away from the equilibrium condition. Based on the equivalence property,the calculation formula of exponent in power law function is established,showing that the value of exponent varies with the saturation recovery coefficient,sediment fall velocity,unit width discharge and longitudinal distance. Based on the derivative of power law function for the structural features of sediment concentration,the calculation expression of saturation recovery coefficient which is far away from the equilibrium condition is extracted and expressed. Finally,a new power law relationship model with changing exponent is proposed and applied to the sand basin. The application result revealed that the computed suspended sediment concentration along the distance of the sand basin is in suitable agreement with the measured values.
The empirical power law relationship model and non-equilibrium sediment transport theory are two different methods used to describe the suspended sediment transport in alluvial rivers. The mathematical comparison results show that,for steady uniform flow,the derivatives of sediment concentration of the two above mentioned methods are first order approximate when sediment transport state is near equilibrium condition,and the variation of the saturation recovery coefficient is considered in power law relationship when sediment transport state is far away from the equilibrium condition. Based on the equivalence property,the calculation formula of exponent in power law function is established,showing that the value of exponent varies with the saturation recovery coefficient,sediment fall velocity,unit width discharge and longitudinal distance. Based on the derivative of power law function for the structural features of sediment concentration,the calculation expression of saturation recovery coefficient which is far away from the equilibrium condition is extracted and expressed. Finally,a new power law relationship model with changing exponent is proposed and applied to the sand basin. The application result revealed that the computed suspended sediment concentration along the distance of the sand basin is in suitable agreement with the measured values.
引文
[1]钱宁,张仁,李九发,等.黄河下游挟沙能力自动调整机理的初步探讨[J].地理学报,1981,36(2):143-155.(QIAN N,ZHANG R,LI J F,et al.A preliminary study on the mechanism of self-regulation of sediment transport capacity in the lower Huanghe(The Yellow River)[J].Acta Geographica Sinica,1981,36(2):143-155.(in Chinese))
[2]万兆惠,宋天成.一维泥沙数学模型在黄河下游应用的讨论[J].水科学进展,1993,4(2):120-126.(WAN Z H,SONG T C.A review of 1-D mathematical models used the Lower Yellow River[J].Advances in Water Science,1993,4(2):120-126.(in Chinese))
[3]胡春宏,王延贵,张燕菁,等.中国江河水沙变化趋势与主要影响因素[J].水科学进展,2010,21(4):524-532.(HU C H,WANG Y G,ZHANG Y J,et al.Variation tendency of runoff and sediment load in China major rivers and its causes[J].Advances in Water Science,2010,21(4):524-532.(in Chinese))
[4]姚文艺,冉大川,陈江南.黄河流域近期水沙变化及其趋势预测[J].水科学进展,2013,24(5):607-616.(YAO W Y,RAN D C,CHEN J N.Recent changes in runoff and sediment regimes and future projections in the Yellow River basin[J].Advances in Water Science,2013,24(5):607-616.(in Chinese))
[5]傅开道,黄河清,钟荣华,等.水库下游水沙变化与河床演变研究综述[J].地理学报,2011,66(9):1239-1250.(FU K D,HUANG H Q,ZHONG R H,et al.Reservoir-induced downstream change of water sediment and channel morphology:a literature review[J].Acta Geographica Sinica,2011,66(9):1239-1250.(in Chinese))
[6]吴保生,张原锋.黄河下游输沙量的沿程变化规律和计算方法[J].泥沙研究,2007(1):30-35.(WU B S,ZHANG Y F.Analysis on sediment transport in the Lower Yellow River[J].Journal of Sediment Research,2007(1):30-35.(in Chinese))
[7]刘月兰,张原锋.高村—陶城铺河段整治后河道形态变化及其对输沙的影响[J].人民黄河,1994(3):12-16.(LIU Y L,ZHANG Y F.Change of channel geometry and effect on sediment transport capacity after river regulation for Gaocun—Taochengpu reach of the lower Yellow River[J].Yellow River,1994(3):12-16.(in Chinese))
[8]吴保生,刘可晶,申红彬,等.黄河内蒙古河段输沙量与淤积量计算方法[J].水科学进展,2015,26(3):311-321.(WU B S,LIU K J,SHEN H B,et al.Calculation methods for sediment load and deposition volume in the Inner Mongolia reach of the Yellow River[J].Advances in Water Science,2015,26(3):311-321.(in Chinese))
[9]刘月兰,韩少发,吴知.黄河下游河道冲淤计算方法[J].泥沙研究,1987(3):30-42.(LIU Y L,HAN S F,WU Z.A method for calculating sediment erosion and deposition in the Lower Yellow River[J].Journal of Sediment Research,1987(3):30-42.(in Chinese))
[10]姚文艺,严忠民,李勇.黄河下游河道萎缩过程中输沙能力的调整[J].水利水电科技进展,2006,26(3):10-14.(YAO W Y,YAN Z M,LI Y.Adjustment of sediment capacity during channel shrinkage for lower Yellow River[J].Advances in Science and Technology of Water Resources,2006,26(3):10-14.(in Chinese))
[11]TA W Q,WANG H B,JIA X P.Suspended sediment transport response to upstream wash-load supply in the sand-bed reach of the upper Yellow River,China[J].Journal of Hydrology,2015,528:562-570.
[12]彭文昌,李永山.黄河内蒙古段异源水沙输移特性[J].中国沙漠,2016,36(3):805-813.(PENG W C,LI Y S.Transport characteristics of water and sediment from different sources in Inner Mongolian reach of the Yellow River[J].Journal of Desert Research,2016,36(3):805-813.(in Chinese))
[13]张艳艳,吴保生,傅旭东.黄河下游河道场次洪水输沙特性分析[J].水力发电学报,2002,31(3):70-76.(ZHANG Y Y,WU B S,FU X D.Characteristics of sediment transport by flood events in the lower Yellow River[J].Journal of Hydroelectric Engineering,2002,31(3):70-76.(in Chinese))
[14]傅旭东,姜立伟,吴保生,等.黄河下游河道场次洪水排沙比及其不确定性[J].中国科学:技术科学,2010,40(4):349-357.(FU X D,JIANG L W,WU B S,et al.Sediment delivery ratio and its uncertainties on flood event scale:quantification forthe lower Yellow River[J].Sci China:Tech Sci,2010,40(4):349-357.(in Chinese))
[15]申红彬.黄河上游内蒙古河段水沙变化与河道输沙冲淤演变的复杂响应[R].北京:清华大学,2013.(SHEN H B.Runoff and sediment variation and fluvial processes in the Inner Mongolian reach of Yellow River[R].Beijing:Tsinghua University,2013.(in Chinese))
[16]窦国仁.潮汐水流中的悬沙运动及冲淤计算[J].水利学报,1963(4):13-24.(DOU G R.Calculation of deposition and erosion due to suspended sediment movement in tidal flow[J].Journal of Hydraulic Engineering,1963(4):13-24.(in Chinese))
[17]韩其为.非均匀悬移质不平衡输沙的研究[J].科学通报,1979(17):804-808.(HAN Q W.A study of the non-equilibrium transportation of non-uniform suspended load[J].Chinese Science Bulletin,1979(17):804-808.(in Chinese))
[18]ZHOU J J.A new approach to the equation for non-equilibrium transport of suspended sediment[A]//Beijing:Proc.,7th Congress of ADP-IAHR,1990:266-272.
[19]赵明登,李义天.二维泥沙数学模型及工程应用问题探讨[J].泥沙研究,2002(1):66-70.(ZHAO M D,LI Y T.Study on two-dimensional sediment mathematical models and problems in Application[J].Journal of Sediment Research,2002(1):66-70.(in Chinese))
[20]韩其为.黄河下游输沙及冲淤的若干规律[J].泥沙研究,2004(3):1-13.(HAN Q W.Some rules of sediment transportation and deposition-scouring in the lower Yellow River[J].Journal of Sediment Research,2004(3):1-13.(in Chinese))
[21]DOBBINS W E.Effect of turbulence on sedimentation[J].Trans,ASCE,1944,109(1):629-656.
[22]张启舜.明渠水流泥沙扩散过程的研究及其应用[J].泥沙研究,1980(12):37-52.(ZHANG Q S.Diffusion process of sediment in open channel and its application[J].Journal of Sediment Research,1980(12):37-52.(in Chinese))
[23]韦直林.二度恒定均匀流中泥沙的淤积过程[J].武汉水利电力学院学报,1982(4):35-47.(WEI Z L.Settling process of sediment in two-dimensional steady uniform flow[J].Engineering Journal of Wuhan University,1982(4):35-47.(in Chinese))
[2]万兆惠,宋天成.一维泥沙数学模型在黄河下游应用的讨论[J].水科学进展,1993,4(2):120-126.(WAN Z H,SONG T C.A review of 1-D mathematical models used the Lower Yellow River[J].Advances in Water Science,1993,4(2):120-126.(in Chinese))
[3]胡春宏,王延贵,张燕菁,等.中国江河水沙变化趋势与主要影响因素[J].水科学进展,2010,21(4):524-532.(HU C H,WANG Y G,ZHANG Y J,et al.Variation tendency of runoff and sediment load in China major rivers and its causes[J].Advances in Water Science,2010,21(4):524-532.(in Chinese))
[4]姚文艺,冉大川,陈江南.黄河流域近期水沙变化及其趋势预测[J].水科学进展,2013,24(5):607-616.(YAO W Y,RAN D C,CHEN J N.Recent changes in runoff and sediment regimes and future projections in the Yellow River basin[J].Advances in Water Science,2013,24(5):607-616.(in Chinese))
[5]傅开道,黄河清,钟荣华,等.水库下游水沙变化与河床演变研究综述[J].地理学报,2011,66(9):1239-1250.(FU K D,HUANG H Q,ZHONG R H,et al.Reservoir-induced downstream change of water sediment and channel morphology:a literature review[J].Acta Geographica Sinica,2011,66(9):1239-1250.(in Chinese))
[6]吴保生,张原锋.黄河下游输沙量的沿程变化规律和计算方法[J].泥沙研究,2007(1):30-35.(WU B S,ZHANG Y F.Analysis on sediment transport in the Lower Yellow River[J].Journal of Sediment Research,2007(1):30-35.(in Chinese))
[7]刘月兰,张原锋.高村—陶城铺河段整治后河道形态变化及其对输沙的影响[J].人民黄河,1994(3):12-16.(LIU Y L,ZHANG Y F.Change of channel geometry and effect on sediment transport capacity after river regulation for Gaocun—Taochengpu reach of the lower Yellow River[J].Yellow River,1994(3):12-16.(in Chinese))
[8]吴保生,刘可晶,申红彬,等.黄河内蒙古河段输沙量与淤积量计算方法[J].水科学进展,2015,26(3):311-321.(WU B S,LIU K J,SHEN H B,et al.Calculation methods for sediment load and deposition volume in the Inner Mongolia reach of the Yellow River[J].Advances in Water Science,2015,26(3):311-321.(in Chinese))
[9]刘月兰,韩少发,吴知.黄河下游河道冲淤计算方法[J].泥沙研究,1987(3):30-42.(LIU Y L,HAN S F,WU Z.A method for calculating sediment erosion and deposition in the Lower Yellow River[J].Journal of Sediment Research,1987(3):30-42.(in Chinese))
[10]姚文艺,严忠民,李勇.黄河下游河道萎缩过程中输沙能力的调整[J].水利水电科技进展,2006,26(3):10-14.(YAO W Y,YAN Z M,LI Y.Adjustment of sediment capacity during channel shrinkage for lower Yellow River[J].Advances in Science and Technology of Water Resources,2006,26(3):10-14.(in Chinese))
[11]TA W Q,WANG H B,JIA X P.Suspended sediment transport response to upstream wash-load supply in the sand-bed reach of the upper Yellow River,China[J].Journal of Hydrology,2015,528:562-570.
[12]彭文昌,李永山.黄河内蒙古段异源水沙输移特性[J].中国沙漠,2016,36(3):805-813.(PENG W C,LI Y S.Transport characteristics of water and sediment from different sources in Inner Mongolian reach of the Yellow River[J].Journal of Desert Research,2016,36(3):805-813.(in Chinese))
[13]张艳艳,吴保生,傅旭东.黄河下游河道场次洪水输沙特性分析[J].水力发电学报,2002,31(3):70-76.(ZHANG Y Y,WU B S,FU X D.Characteristics of sediment transport by flood events in the lower Yellow River[J].Journal of Hydroelectric Engineering,2002,31(3):70-76.(in Chinese))
[14]傅旭东,姜立伟,吴保生,等.黄河下游河道场次洪水排沙比及其不确定性[J].中国科学:技术科学,2010,40(4):349-357.(FU X D,JIANG L W,WU B S,et al.Sediment delivery ratio and its uncertainties on flood event scale:quantification forthe lower Yellow River[J].Sci China:Tech Sci,2010,40(4):349-357.(in Chinese))
[15]申红彬.黄河上游内蒙古河段水沙变化与河道输沙冲淤演变的复杂响应[R].北京:清华大学,2013.(SHEN H B.Runoff and sediment variation and fluvial processes in the Inner Mongolian reach of Yellow River[R].Beijing:Tsinghua University,2013.(in Chinese))
[16]窦国仁.潮汐水流中的悬沙运动及冲淤计算[J].水利学报,1963(4):13-24.(DOU G R.Calculation of deposition and erosion due to suspended sediment movement in tidal flow[J].Journal of Hydraulic Engineering,1963(4):13-24.(in Chinese))
[17]韩其为.非均匀悬移质不平衡输沙的研究[J].科学通报,1979(17):804-808.(HAN Q W.A study of the non-equilibrium transportation of non-uniform suspended load[J].Chinese Science Bulletin,1979(17):804-808.(in Chinese))
[18]ZHOU J J.A new approach to the equation for non-equilibrium transport of suspended sediment[A]//Beijing:Proc.,7th Congress of ADP-IAHR,1990:266-272.
[19]赵明登,李义天.二维泥沙数学模型及工程应用问题探讨[J].泥沙研究,2002(1):66-70.(ZHAO M D,LI Y T.Study on two-dimensional sediment mathematical models and problems in Application[J].Journal of Sediment Research,2002(1):66-70.(in Chinese))
[20]韩其为.黄河下游输沙及冲淤的若干规律[J].泥沙研究,2004(3):1-13.(HAN Q W.Some rules of sediment transportation and deposition-scouring in the lower Yellow River[J].Journal of Sediment Research,2004(3):1-13.(in Chinese))
[21]DOBBINS W E.Effect of turbulence on sedimentation[J].Trans,ASCE,1944,109(1):629-656.
[22]张启舜.明渠水流泥沙扩散过程的研究及其应用[J].泥沙研究,1980(12):37-52.(ZHANG Q S.Diffusion process of sediment in open channel and its application[J].Journal of Sediment Research,1980(12):37-52.(in Chinese))
[23]韦直林.二度恒定均匀流中泥沙的淤积过程[J].武汉水利电力学院学报,1982(4):35-47.(WEI Z L.Settling process of sediment in two-dimensional steady uniform flow[J].Engineering Journal of Wuhan University,1982(4):35-47.(in Chinese))