一维悬移质泥沙输移方程及其滞后和离散效应
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摘要
一维悬移质泥沙输移方程的研究中,对与床面交换项相关的研究较多,而对沙峰滞后于水流的效应、是否存在纵向离散效应等问题关注较少。从立面二维悬移质连续性方程出发,推导了一维方程,发现对流项中含有纵向离散效应,并提出了一种对流项和纵向离散项的分解方法;最后用算例的计算结果说明本文提出的分解方法是合理的,并指出悬移质泥沙的对流速度滞后于水流的垂线平均流速,纵向离散效应不能用与紊动扩散相似的数学表达式描述。
In spite of plenty of studies have focused on sediment exchange between river bed and water flow in the one-dimensional transport equation of suspended sediment,inadequate attention has been paid on the hysteresis effect of sediment behind flow. An interesting question is raised that whether there is longitudinal dispersion in suspended sediment transport. This paper deduces a one-dimensional equation from the vertical twodimensional equation by depth averaging. It shows that the longitudinal dispersion does exist,and is implicitly included within the conventionally recognized convective term. A decomposition method for separating the longitudinal dispersion term from the convective one is further proposed. Examples are given to demonstrate the reasonability of the decomposition method. It is also found that the convective velocity of suspended sediment lags behind the depth-averaged water velocity. Instead of a normal distribution,a skewed longitudinal distribution of suspended sediment concentration is obtained in this paper,which highlights that the approximation of longitudinal dispersion by a form similar to the turbulent diffusion term will lead to non-negligible distortion.
In spite of plenty of studies have focused on sediment exchange between river bed and water flow in the one-dimensional transport equation of suspended sediment,inadequate attention has been paid on the hysteresis effect of sediment behind flow. An interesting question is raised that whether there is longitudinal dispersion in suspended sediment transport. This paper deduces a one-dimensional equation from the vertical twodimensional equation by depth averaging. It shows that the longitudinal dispersion does exist,and is implicitly included within the conventionally recognized convective term. A decomposition method for separating the longitudinal dispersion term from the convective one is further proposed. Examples are given to demonstrate the reasonability of the decomposition method. It is also found that the convective velocity of suspended sediment lags behind the depth-averaged water velocity. Instead of a normal distribution,a skewed longitudinal distribution of suspended sediment concentration is obtained in this paper,which highlights that the approximation of longitudinal dispersion by a form similar to the turbulent diffusion term will lead to non-negligible distortion.
引文
[1]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.
[2]韩其为.水库不平衡输沙的初步研究[C]//水库泥沙报告汇编,1973.
[3]Lin B N,Huang J,Li X.Unsteady transport of suspended load at small concentration[J].Journal of Hydraulic Engineering,1983,109(1):86-98.
[4]Lin B N,Shen H.Two-D flow with sediment by characteristics method[J].Journal of Hydraulic Engineering,1984,110(5):616-625.
[5]Zhou J J,Lin B N.One-dimensional mathematical model for suspended sediment by lateral integration[J].Journal of Hydraulic Engineering,1998,124(7):712-717.
[6]Armanini A,Di Silvio G.A one-dimensional model for transport of sediment mixture in non-equilibrium condition[J].Journal of Hydraulic Research,1988,26(3):275-292.
[7]Van Rijn Leo C.Mathematical modeling of suspended sediment in non-uniform flows[J].Journal of Hydraulic Engineering,1986,112(6):433-455.
[8]Falconer R A,Owens P H.Numerical modeling of suspended sediment fluxes in estuarine waters[J].Estuarine,Coastal and Shelf Science,1990,31:745-762.
[9]韩其为,陈绪坚.恢复饱和系数的理论计算方法[J].泥沙研究,2008(6):8-16.
[10]Ahn J,Yang C T.Determination of recovery factor for simulation of non-equilibrium sedimentation in reservoir[J].International Journal of Sediment Research,2015,30(2):68-73.
[11]Owens P H.Mathematical modelling of sediment transport in estuaries[D].University of Birmingham,1987.
[12]Wu W M,Altinakar M,Wang S S Y.Depth-averaged analysis of hysteresis between flow and sediment transport under unsteady conditions[J].International Journal of Sediment Research,2006,21(2):101-112.
[13]Wu W M.Computational river dynamics[M].Taylor&Francis,2007.
[14]Taylor G.Dispersion of soluble matter in solvent flowing slowly through a tube[J].Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences,1953,219:186-203.
[15]Elder J W.The dispersion of marked fluid in turbulent shear flow[J].Journal of Fluid Mechanics,1959,5(4):544-560.
[16]Fischer H B,List E J,Koh R C.Mixing in Inland and Coastal Waters[M].Academic Press,Dublin,1979.
[2]韩其为.水库不平衡输沙的初步研究[C]//水库泥沙报告汇编,1973.
[3]Lin B N,Huang J,Li X.Unsteady transport of suspended load at small concentration[J].Journal of Hydraulic Engineering,1983,109(1):86-98.
[4]Lin B N,Shen H.Two-D flow with sediment by characteristics method[J].Journal of Hydraulic Engineering,1984,110(5):616-625.
[5]Zhou J J,Lin B N.One-dimensional mathematical model for suspended sediment by lateral integration[J].Journal of Hydraulic Engineering,1998,124(7):712-717.
[6]Armanini A,Di Silvio G.A one-dimensional model for transport of sediment mixture in non-equilibrium condition[J].Journal of Hydraulic Research,1988,26(3):275-292.
[7]Van Rijn Leo C.Mathematical modeling of suspended sediment in non-uniform flows[J].Journal of Hydraulic Engineering,1986,112(6):433-455.
[8]Falconer R A,Owens P H.Numerical modeling of suspended sediment fluxes in estuarine waters[J].Estuarine,Coastal and Shelf Science,1990,31:745-762.
[9]韩其为,陈绪坚.恢复饱和系数的理论计算方法[J].泥沙研究,2008(6):8-16.
[10]Ahn J,Yang C T.Determination of recovery factor for simulation of non-equilibrium sedimentation in reservoir[J].International Journal of Sediment Research,2015,30(2):68-73.
[11]Owens P H.Mathematical modelling of sediment transport in estuaries[D].University of Birmingham,1987.
[12]Wu W M,Altinakar M,Wang S S Y.Depth-averaged analysis of hysteresis between flow and sediment transport under unsteady conditions[J].International Journal of Sediment Research,2006,21(2):101-112.
[13]Wu W M.Computational river dynamics[M].Taylor&Francis,2007.
[14]Taylor G.Dispersion of soluble matter in solvent flowing slowly through a tube[J].Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences,1953,219:186-203.
[15]Elder J W.The dispersion of marked fluid in turbulent shear flow[J].Journal of Fluid Mechanics,1959,5(4):544-560.
[16]Fischer H B,List E J,Koh R C.Mixing in Inland and Coastal Waters[M].Academic Press,Dublin,1979.