基于固液两相紊流理论的近岸悬移质泥沙运动数值研究
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摘要
建立在高水平数值模型基础上的悬移质泥沙运动研究不仅具有重要的理论意义,也具有重要的应用背景。随着近十几年随着两相流理论与数值方法的发展,加上计算机硬件能力的大幅度提升,应用两相流模型研究低浓度含沙水流问题已逐渐成为可能。本论文从稀疏两相流的双流体模型基本方程出发,借鉴气固两相紊流理论,建立了低含沙量问题的通用数学模型,同时构建了有效的数值计算方法,编写了相应的计算机程序。并在多种条件下对数值模型进行了验证。
论文应用建立的数学模型对单向流条件下的悬移质泥沙运动进行数值计算,并用已知的实验成果对数值模型进行了验证。研究了恒定流中泥沙浓度及扩散系数沿垂向的分布规律,并就泥沙沉降规律以及含沙水流紊动结构等问题进行了讨论,还探讨了两种常用的颗粒相紊流模型的优缺点及其适用范围。论文应用建立的数学模型也对边界层往复流条件下的悬移质泥沙运动进行数值计算。通过与实验结果的对比,分析了边界层水流运动结构的特征以及泥沙浓度分布的规律,探讨了往复流作用下各类相间作用力的时空变化规律及其对悬移质泥沙运动的影响。
论文还应用建立的数学模型对波浪作用下的悬移质泥沙运动进行了数值计算。研究了波浪作用下悬移质泥沙浓度的垂线分布规律,探讨了波浪作用下各类相间作用力的时空变化规律及其对悬移质泥沙运动的影响,采用基于颗粒轨道模型模拟了单颗粒泥沙对于紊动作用以外的相间作用力的反应。还就波浪作用下的输沙率进行了初步的探讨。
Development of advanced numerical models for sediment-laden flows is of current significance because improvement of our understanding on sediment transport phenomena in coastal environment has been pushed for decades to meet the requirement from engineers who are in charge of planning, design, or construction of coastal and harbor facilities. With the enhancement of two-phase flow models and advances in numerical methods, it is now possible to apply numerical models to study sediment transport problems with low concentration. This thesis is based on newly derived governing equations of sediment-laden flows. Relevant numerical method is also proposed. The numerical model is extensively verified.
Suspended sediment transport under unidirectional flow condition is investigated. Vertical distributions of the sediment concentration and the diffusion coefficient are carefully discussed. The effectiveness of two turbulence models, i.e., Ap model and k p model, is also studied. Suspended sediment motion in the boundary layer under oscillatory flow condition is also studied. The characteristics of the turbulent flow and its resulted sediment transport in the boundary layer are demonstrated. Variation of the various inter-phase forces in the time and space are examined.
To consider sediment transport under wave motion, numerical methods are established so as to represent wave-making and wave absorbing, and to trace the free surface, under two-phase flow conditions. The numerical model is then used to compute the vertical distribution of the averaged sediment concentration within a wave period. Variation of the various inter-phase forces in the time and space are shown. Sediment transport rate under waves is also briefly discussed.
论文应用建立的数学模型对单向流条件下的悬移质泥沙运动进行数值计算,并用已知的实验成果对数值模型进行了验证。研究了恒定流中泥沙浓度及扩散系数沿垂向的分布规律,并就泥沙沉降规律以及含沙水流紊动结构等问题进行了讨论,还探讨了两种常用的颗粒相紊流模型的优缺点及其适用范围。论文应用建立的数学模型也对边界层往复流条件下的悬移质泥沙运动进行数值计算。通过与实验结果的对比,分析了边界层水流运动结构的特征以及泥沙浓度分布的规律,探讨了往复流作用下各类相间作用力的时空变化规律及其对悬移质泥沙运动的影响。
论文还应用建立的数学模型对波浪作用下的悬移质泥沙运动进行了数值计算。研究了波浪作用下悬移质泥沙浓度的垂线分布规律,探讨了波浪作用下各类相间作用力的时空变化规律及其对悬移质泥沙运动的影响,采用基于颗粒轨道模型模拟了单颗粒泥沙对于紊动作用以外的相间作用力的反应。还就波浪作用下的输沙率进行了初步的探讨。
Development of advanced numerical models for sediment-laden flows is of current significance because improvement of our understanding on sediment transport phenomena in coastal environment has been pushed for decades to meet the requirement from engineers who are in charge of planning, design, or construction of coastal and harbor facilities. With the enhancement of two-phase flow models and advances in numerical methods, it is now possible to apply numerical models to study sediment transport problems with low concentration. This thesis is based on newly derived governing equations of sediment-laden flows. Relevant numerical method is also proposed. The numerical model is extensively verified.
Suspended sediment transport under unidirectional flow condition is investigated. Vertical distributions of the sediment concentration and the diffusion coefficient are carefully discussed. The effectiveness of two turbulence models, i.e., Ap model and k p model, is also studied. Suspended sediment motion in the boundary layer under oscillatory flow condition is also studied. The characteristics of the turbulent flow and its resulted sediment transport in the boundary layer are demonstrated. Variation of the various inter-phase forces in the time and space are examined.
To consider sediment transport under wave motion, numerical methods are established so as to represent wave-making and wave absorbing, and to trace the free surface, under two-phase flow conditions. The numerical model is then used to compute the vertical distribution of the averaged sediment concentration within a wave period. Variation of the various inter-phase forces in the time and space are shown. Sediment transport rate under waves is also briefly discussed.
引文
[1] 严恺, 梁其荀. 海岸工程. 北京: 海洋出版社, 2002:211-212.
[2] 朱志夏. 一维水流泥沙数学模型理论及应用[硕士学位论文]. 天津: 天津大学建筑工程学院, 1995.
[3] O’Brien M P. Review of the theory of turbulent flow and its relation to sediment transport. Trans Amer Geophys Union, 1933.
[4] Dobbins W E. Effect of turbulence on sedimentation. Trans ASCE, 1943, 109:660-666.
[5] 窦国仁. 潮汐水流中的悬沙运动及其淤积计算. 水利学报, 1963, 4:11-20.
[6] Han Q W. A study of the non-equilibrium transportation of non-uniform suspended load. Chinese Sci Bull, 1979, 17(7):804-808.
[7] Lin B N, Huan J Q, Li X Q. Unsteady transport of suspended load at small concentrations. J Hydr Engrg, ASCE, 1983, 109(91):86-98.
[8] Zhou J J, Lin B N. One-dimensional mathematical model for suspended sediment by lateral integration. J Hydr Engrg, ASCE, 1998, 124(7):712-717.
[9] Fang H W, Wang G Q. Three-dimensional mathematical model of suspended- sediment transport. J Hydr Engrg, ASCE, 2000, 126(8):578-592.
[10] 钱宁, 万兆蕙. 泥沙运动力学. 北京: 科学出版社, 2003.
[11] Bangold R A. Motion of waves in shallow water, Interaction between waves and sand bottom. Proc Royal Society London, A187, 1946:1-15.
[12] Rance P J, Warren N F. The threshold movement of coarse material in oscillatory flow. Proc 11th Coastal Eng Conf ASCE, 1968:487-491.
[13] Madsen U S, Grant W D. Sediment Transport in the Coastal Environment. Coastal Engrg, 1976:1-28.
[14] 赵子丹. 波浪作用下的泥沙起动. 海洋通报, 1983, 2:75-79.
[15] 周益人. 波浪作用下的泥沙起动. 水利水运科学研究, 1998, 12:338-346.
[16] 窦国仁, 窦希萍, 李提来. 波浪作用下泥沙的起动规律. 中国科学 E 辑, 2001, 12: 566-573.
[17] Horikawa K, Watanabe A, Katori S. Sediment transport under sheet flow conditions. Coastal Engineering Proc 18th Int Con, 1982:1335-1352.
[18] Ribberink J, Al-Salem A. Time dependent sediment transport phenomena in oscillatory boundary layer flow under sheet flow conditions. Technical Report H840, 1992, 20, Part IV, Delft Hydraulics.
[19] 窦国仁, 董风舞. 潮流和波浪的挟沙能力. 科学通报, 1995, 3:443-446.
[20] 刘峰, 李义天. 新的水流挟沙力计算公式. 长江科学院院报, 1997, 3:16-20.
[21] 曹祖德, 李蓓, 孔令双. 波流共存时的水体挟沙力. 水道港口, 2001, 12:151-155.
[22] 倪晋仁, 王光谦, 张红武. 固液两相流基本理论及其最新应用. 北京: 科学出版社, 1991.
[23] 倪晋仁, 惠遇甲. 悬移质浓度垂线分布的各种理论及其间关系. 水利水运科学研究, 1988, 1:83-95.
[24] 李付军, 谈广鸣, 陈立. 挟沙水流紊动结构研究现状及进展. 水动力学研究与进展 A辑, 1999, 9:265-272.
[25] 张瑞瑾. 论重力理论兼论悬移质运动过程. 水利学报, 1963, 3:11-23.
[26] Pai S I. Two-phase flows. Braunschweig: Vieweg-Verlag, 1977.
[27] Ishii M. Thermo-Fluid Dynamics Theory of Two-Phase Flow. Paris: Eyrolles, 1975.
[28] Drew D A. Average Field Equations for two-phase Media. Stu Appl Math, 1971, 50: 133-166.
[29] Drew D A. Averaged equations for two-phase flows. Stu Appl Math, 1971, 50:205-231.
[30] Drew D A. Mathematical modeling of two-phase flow. Ann Rev Fluid Mech, 1983, 15: 261-291.
[31] Drumheller D S, Bedford A. A thermomechanical theory for reacting immiscible mixtures. Arch Rational Mech Anal, 1980, 73:257-284.
[32] Johnson G, Massoudi M, Rajagopal K R. Flow of a fluid-solid mixture between flat plates. Chemical Engineering Science, 1991, 46(7):1713-1723.
[33] 刘大有. 二相流体动力学. 北京: 高等教育出版社, 1993.
[34] 蔡树棠, 范正翘, 陈越南. 两相流基本方程. 应用数学和力学, 1986, 7(6):477-485.
[35] 陈天翔. 多相流体力学的场方程及其平均. 力学进展, 1986, 16(4):482-494.
[36] 刘大有. 再论二相流基本方程—关于固相碰撞应力的讨论. 中国科学 A 辑, 1998, 1:72-79.
[37] 刘大有. 建立两相流方程的动力论方法. 力学学报, 1987, 5:213-221.
[38] 刘大有. 关于二相流、多相流、多流体模型和非牛顿流等概念的探讨. 力学进展, 1994, 1:66-74.
[39] 刘大有. 研究多相介质运动的意义、内容和方法. 力学与实践, 1995, 6:1-10.
[40] 傅旭东. 固液两相流动理学模型研究[博士论文]. 北京: 清华大学水利水电工程系, 2001.
[41] Melville W K, Bray K N C. A model of the two-phase turbulent jet. Int J Heat Mass Transfer, 1979, 22:647-656.
[42] Picart A, Berlemont A , Gouesbet G. Modelling and predicting turbulence fields and the dispersion of discrete particles transported by turbulent flows. Int J Multiphase Flow, 1986, 12:237-261.
[43] Elghobashi S E, Abou-Arab T W.A two-equation turbulence model for two-phase flows. Phys Fluids, 1983, 26(4):931-938.
[44] Chen C P, Wood P E. A turbulence closure model for dilute gas-particle flows. The Canadian Journal of Chemical Engineering, 1985, 63:349-360.
[45] Viollet P L, Simonin O. Modelling dispersed two-phase flows: Closure, Validation and software development. Appl Mech Rev, 1994, 47(6), part2:80-84.
[46] Besnard D C, Harlow F H. Turbulence in multiphase flow. Int J Multiphase Flow, 1988, 14(6):679-699.
[47] Cao J, Ahmadi G. Gas-particle two-phase turbulent flow in a vertical duct. Int J Multiphase Flow, 1995, 21(6):1203-1228.
[48] Hinze J O. Turbulence. NewYork: McGraw-Hill, 1975.
[49] Choi Y D, Chung M K. Analysis of turbulent gas-solid suspension flow in a pipe. Journal of Fluids Engineering, 1983, 105:329-334.
[50] Rizk M A, Elghobashi S E. A two-equation turbulence model for dispersed dilute confined two-phase flow. Int J Multiphase Flow, 1989, 15:119-133.
[51] 周力行. 湍流气粒两相流动和燃烧的理论与数值模拟. 北京: 科学出版社, 1994.
[52] Rouse H. Modern Conceptions of the Mechanics of Turbulence. Trans ASCE, 1937, 102:463-543.
[53] Lane E W, Kalinske A A. Engineering Calculation of Suspended Sediment. Trans Amer Geophys Union, 1941:603-607.
[54] 邵学军, 夏震寰. 悬浮颗粒紊动扩散系数的随机分析. 水利学报, 1990, 10:32-40.
[55] 曹志先, 张效先, 习和忠. 基于湍流猝发的明渠流悬沙浓度分布. 水利学报, 1997, 2: 52-57.
[56] 刘大有. 从二相流方程出发研究平衡输沙—扩散理论和泥沙扩散系数的讨论. 水利学报, 1995, 4:62-67.
[57] 刘大有. 现有泥沙理论的不足和改进—扩散模型和费克定律适用性的讨论. 泥沙研究, 1996, 3:39-45.
[58] 白玉川, 杨建民, 黄本胜. 二维水沙数学模型在复杂河道治理中的应用. 水利学报, 2203, 9:25-30.
[59] 余明辉, 吴腾, 杨国录. 剖面二维水沙数学模型及其初步应用. 水力发电学报, 2006, 8:66-69.
[60] 夏云峰. 感潮河道三维水流泥沙数值模拟研究与应用[博士学位论文]. 江苏: 河海大学交通与海洋工程学院, 2002.
[61] 黄国鲜. 弯曲和分叉河道水沙输运及其演变的三维数值模拟研究[博士学位论文]. 北京: 清华大学水利水电工程系, 2006.
[62] 周新民. 水沙两相流湍流模式及其应用[博士学位论文]. 四川: 四川大学水利水电学院, 2001.
[63] 白玉川, 蒋昌波, 罗纪生, 赵子丹. 振荡流底层拟序结构及其与泥沙相互作用研究. 力学进展, 2003, 8:347-356.
[64] Jonsson I G. Measurement in the turbulent wave boundary layer. Proc 10th Congr. IHAR, London, 1963, 1:85-92.
[65] Hino M, Kashiwanayagi M, Nakayama A, Hara T. Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow. J Fluid Mech, 1983, 131:363-400.
[66] Sleath J F A. Turbulent oscillatory flow over rough beds. J fluid Mech, 1987, 182: 369-409.
[67] Jensen B L, Sumer B M, Fredsoe J. Turbulent oscillatory boundary layers at high Reynolds numbers. J Fluid Mech, 1989, 206:265-297.
[68] Jonsson I G. Wave boundary layers and friction factors. Proc 10th Conf Coastal Eng ASCE, Tokyo, 1966:127-148.
[69] Kajiura K. A model for the bottom boundary layer in water waves. J Fluid Mech, 1968, 182:369-409.
[70] Bakker W T. Sand concentration in an oscillatory flow. Proc 14th Conf Coastal Eng Copenhagen, 1974:1129-1148.
[71] Johns B. The form of the velocity profile in a turbulent shear wave boundary. J Geophys Res, 1975, 80:5109-5112.
[72] Myrhaug D. On a theoretical model of rough turbulent wave boundary layers. Ocean Eng, 1982, 9(6):547-565.
[73] Thowbridge J H, Madsen O S. Turbulent wave boundary layers: 1.model formation and first order solution. Geophys Res, 1984, 89(C5):7989-7997.
[74] Thowbridge J H, Madsen O S. Turbulent wave boundary layers:1.Second order theory and mass transport. Geophys Res, 1984, 89(C5):7999-8007.
[75] Hagatun K, Eidsvik K J. Oscillating turbulent boundary layers with suspended sediment. J Geophys Res, 1986, 91(C11):13045-13055.
[76] Justesen P. Prediction of turbulent oscillatory flaw over rough beds. Coastal Eng, 1988, 12:257-284.
[77] Justesen P. A note on turbulence calculations in the wave boundary layer. J Hydr Res, 1991, 29(5):699-711.
[78] 赵子丹, 蒋昌波, 白玉川. 振荡流底部边界层运动的数值研究. 天津大学学报, 2001, 5: 568-572.
[79] Ahmad Sana, Hitoshi Tanaka, Hiroto Yamaji, Ikuo Kawamura. Hydrodynamic behavior of asymmetric oscillatory boundary layers at low Reynolds numbers. J Hydr Eng, 2006, 132 (10):1086-1096.
[80] Sleath J F A. Measurements of bed load in oscillatory flow. Journal of the Waterway, Port, Coastal and Ocean Division, 1978, 104(4):291-307.
[81] Staub C, Jonsson L G, Svendsen L A. Variation of suspended sediment in oscillatory flow. Coastal Engineering Proc 19th Int Conf, 1984:2310-2321.
[82] Nielsen P. Suspended sediment concentrations under waves. Coastal Engng, 1986, 10: 22-31.
[83] Ahilan R V, Sleath J F A. Sediment transport in oscillatory flow over flat beds. J hydr Div ASCE, 1987, 113:308-322.
[84] Makoto I. Field observation and numerical calculation of suspended sediment concentration in the surf zone. Coastal Engineering in Japan, 1988, 30(2):75-881.
[85] Savioli J, Justesen P. Sediment in oscillatory flows over a plane bed. J Hydr Res, 1997, 35(2):177-189.
[86] Davies A G, Li Z. Modelling sediment transport beneath regular symmetrical and asymmetrical waves above a plane bed. Continental Shelf Res,1997, 5:555-582.
[87] 蒋昌波, 白玉川, 赵子丹, 张红武. 振荡流底层悬沙运动的数值模拟. 水科学进展, 2003, 2:136-142.
[88] Emily A, Robert L. Sediment Transport over Ripples in Oscillatory Flow. J Hydr Eng, 2006, 132 (2):180-193.
[89] Asano T. Two-phase flow model on oscillatory sheet-flow. Pro 22th Inter Conf on Coastal Eng, 1990:2372-2384.
[90] Li L, Sawamto M. Multi-phase model on sediment transport in sheet flow regime under oscillatory flow. Coastal Eng In Japan. 1995, 38(2):157-178.
[91] Ono M, Deguchi I, Sawaragi T. Numerical modeling of sediment transport for various mode. Pro 25th Int Conf on Coastal Eng, 1996:2372-2384.
[92] Dong P, Zhang K. Two-phase flow modeling of sediment motions in oscillatory sheet flow. Coastal Eng, 1999, 36:87-109.
[93] Hsu T W, Chang H, Hsieh C. A two-phase flow model of wave-induced sheet flow. J Hydraulic Res, 2003, 41(3):299-310.
[94] Longo S. Two-phase flow modeling of sediment motion in sheet-flows above plane beds. J Hydraulic Eng, ASCE, 2005, 131(5):366-379.
[95] 王尚毅. 波浪作用下含沙量的垂向分布. 中国科学 A 辑, 1984, 12:1151-1160.
[96] Van Rijn L C. Principles of sediment transport in rivers, estuaries and coastal seas. Amsterdam: Aqua Publications, 1993.
[97] Williams J J, Bell P S, etc. Observed and predicted vertical suspended sediment concentration profiles and bedforms in oscillatory flow. J Coastal Research, 2000, 16(3):698-708.
[98] Kos’yan R D. Vertical distribution of suspended sediment concentrations of seawards of the breaking zone. Coastal Eng, 1985, 9:171-187.
[99] Nielsen P, Teakle I A. Turbulent diffusion of momentum and suspended particles: A finite mixing length theory. Phys Fluids, 2004, 7:2342-2348.
[100] 严冰. 波浪及波流共同作用下悬移质浓度垂线分布的研究[硕士学位论文]. 天津: 天津大学建筑工程学院, 2004.
[101] 严冰, 张庆河. 波浪作用下悬沙浓度垂线分布的研究. 泥沙研究, 2006, 10(5):63-68.
[102] 王建峰. 波流共同作用下悬沙浓度垂向分布的研究[硕士学位论文]. 天津: 天津大学建筑工程学院, 2004.
[103] Durst F, Milojevic D, Schonung B. Eulerian and lagrangian predictions of particulate two-phase flows: a numerical study. Appl Math Mo delling, 1984, 8:101-115.
[104] Soo S L. Fluid Dynamics of Multiphase Systems. Blaisdell, Waltham, l967.
[105] Buyevich Yu A, Shchelchkova I N. Flow of dense suspensions. Progr Aerospace Sci, 1978, 188:121-150.
[106] Smoot L D, Smith P J. Coal Combustion and Gasification. Plenum Press. 1985.
[107] Lee S L, Durst F. On the motion of particles in turbulent duct flows. Int J Multiphase Flow, 1982, 8:125-146.
[108] 米尔恩-汤姆森. 理论流体力学. 李裕立, 晏名文 译. 北京: 机械工业出版社, 1984.
[109] 怀特. 粘性流体动力学. 魏中磊, 甄思淼 译. 北京: 机械工业出版社, 1982.
[110] Schiller L, Nauman A. A drag coefficient correlation. VDI Zeits, 1933, 77:318-320.
[111] 岑可法, 樊建人. 工程气固多相流动的理论及计算. 杭州: 浙江大学出版社, 1990.
[112] Ishii M, Zuber N. Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows. AIChE J, 1979, 25(5):843-855.
[113] Ihme F, Schmidt-Traub H, Brauer H. Theoretical studies on. mass transfer at and flow past spheres. Chem Ing Tech, 1972, 44(5):306-313.
[114] 窦国仁. 紊流力学. 下册. 北京: 高等教育出版社, 1987.
[115] Odar F. Verification of the proposed equation of the forces on a sphere accelerating in a viscous fluid. J Fluid Mech, 1966, 25(3):591-592.
[116] Ahamadi G, Gordschemidt V W. Motion of particles in a turbulent fluid the Basset history term. J Appl mech, 1971, 38:561-563.
[117] Tsuji Y ,etal. Experiment measurement of Magnus forces on a rotating shere at low Peynolds. J. Fluid of Eng, 1985, 107(4):484-488.
[118] Saffman P G. The lift on a small sphere in slow shear flow. J Fluid Mech, 1965, 22: 385-400.
[119] Saffman P G. Corrigendum to “The Lift on a Small Sphere in a Slow Shear Flow”. J Fluid Mech, 1968, 31:624.
[120] Mei R. An approximate expression for the shear lifts force of a spherical particle at finite Reyolds number. Int J Multiphase Flow, 1992, 18(1):145-148.
[121] 李绍林. 两相悬浮体剪切流的理论和实验. 北京: 科学出版社, 1985.
[122] Tam C K W. The drag on a cloud of spherical particles in low Reynolds number flow. J Fluid Mech, 1969, l38:537-546.
[123] Zuber N. On the dispersed two-phase flow in the laminar flow region. Chen Eng Scien, 1964, 19(4):897-917.
[124] Murray J D. Some basic aspects of one-dimensional incompressible particle-fluid two-phase flows. Astronaut Acta, 1967, 13:417-430.
[125] 黄社华, 李炜, 程良骏. 任意流场中稀疏颗粒运动方程及其性质. 应用数学和力学, 2000, 3:265-276.
[126] Van Doormaal J P, Raithby G D. Enhancement of the SIMPLE method for predicting incompressible fluid flow. Number Heat Transfer, 1984, 7:147-163.
[127] Patankar S V. Numerical Heat Transfer and Fluid Flow. New York: Hemispher, 1980.
[128] 陶文铨. 数值传热学. 2 版. 西安: 西安交通大学出版社, 2001.
[129] 陶文铨. 计算传热学的近代进展. 北京: 科学出版社, 2000.
[130] Hayase T, Humphrey J A C, Greif R.A. Consistently Formulated QUICK Scheme for fast and Stable Convergence Using Finite-Volume Iterative Calculation Procedures. J Compu. Phys, 1992, 98:108-118.
[131] Demirdzic I, Gosman A D, Issa R I, Peric M A. Calculation procedure for turbulent flow in complex geometries. Comput Fluids, 1987, 15(3):251-273.
[132] 徐士良. Fortran 常用算法程序集. 2 版. 北京: 清华大学出版社, 1995.
[133] Stone H L. Iterative solution of implicit approximation of multidimensional partial differential equations. SIAM J on Numerical Analysis, 1968, 5:530-558.
[134] Alfrink B, van Rijn L C. Two-equation turbulent model for flow in trench. J Hydr Eng, 1983, 109(3):941-958.
[135] Launder B E, Spalding D B. The Numerical Computation of Turbulent Flows. Comp Meth Appl Mech Engr, 1974, 2:269-289.
[136] 韩其为, 何明民. 论非均匀悬移质二维不平衡输沙方程及其边界条件. 水利学报, 1997, 1:1-10.
[137] Coleman N L. Effects of suspended sediment on the open-channel velocity distribution. Water Resources Res, 1986, 22(10):1377-1384.
[138] van Rijn L C. Entrainment of fine sediment particles; development of concentration profiles in a steady, uniform flow without initial sediment load. Rep. No. M1531, Part II, Delft Hydraulic Laboratory, Delft, The Netherlands, 1981.
[139] Shields A. Anwedung der aehnlichkeitmechanik und der turbulenzforschuang aufdie geschiebebewegung, Mitt Preuses, Versuchanst. Wasserbau schiffbau, 1936, 26.
[140] 李丹勋. 悬移质颗粒运动特性的研究[博士学位论文]. 北京: 清华大学水利水电工程系, 1999.
[141] Wang Z B, Ribberringk J S. The validity of a depth-integrated model for suspended sediment transport. Journal of Hydraulic Research, 1986, 24 (1):53-63.
[142] Van Rijn L C. Mathematical modeling of morphological processes in the case of suspended sediment transport[PhD dissertation]. Delft Univ Netherlands, 1987.
[143] 陆永军. 三维紊流泥沙数学模型及其应用[博士后研究报告]. 南京: 南京水利科学院, 2002.
[144] 刘建军. 明渠水流含沙量沿垂线分布研究. 泥沙研究, 1996, 6(2):105-108.
[145] 谈广鸣,夏军强, 郑邦民. 挟沙水流紊动扩散系数的研究. 水利学报, 1998, 12:23-27.
[146] 周家俞. 抉沙水流泥沙颗粒悬浮规律的试验研究[硕士学位论文]. 武汉: 武汉大学水利水电学院, 2005.
[147] Andreas Muller. Turbulence Measurements over a Movable Bed with Sediment Transport by Laser-Anemometry. International Association for Hydraulic Research. 1963.
[148] 王兴奎. 悬移质泥沙运动及其对水流结构的影响[博士学位论文]. 北京: 清华大学水利水电工程系, 1985.
[149] 春宏, 惠遇甲. 明渠挟沙水流运动的力学和统计规律. 北京:科学出版社, 1995.
[150] 林鹏, 陈立. 低含沙水流紊动结构的实验研究. 水动力学研究与进展, 2003, 3:209-216.
[151] Rubey W W. Settling velocities of gravel, sand and silt particles. Am J Sci, 1993, 25(148):325-338.
[152] Cheng N. Discussion on “A fall-velocity equation by Ahrens (2000)”, J of Waterway, Port, Coastal and Ocean Eng, ASCE, 2001, 127(4):250-251.
[153] Chang H K, Liou J C. Disscussion on “A fall-velocity equation by Ahrens (2000)”, J of Waterway, Port, Coastal and Shelf Science, 2001, 46:733-742.
[154] Van Rijin L C. Sediment transport,part II: suspended load transport. J Hydraulic eng, ASCE, 1984, 110(11):1613-1641.
[155] 费祥俊. 黄河中下游含沙水流粘度的计算模型. 泥沙研究, 1991, 2:1-13.
[156] Fredsφ e J, Deigaard R. Mechanics of coastal sediment transport. World Scientific Publishing Co Pte Ltd, 1994.
[157] Engelund F, Fredsφ e J. A sediment transport model for straight alluvial channels. Nordic Hydrology, 1976, 7:293-306.
[158] Zyserman J A, Fredsφ e J. Data Analysis of Bed Concentration of Suspended Sediment. Journal of Hydraulic Engineering, ASCE 1994, 120(9):1021-1042.
[159] Justesen P, Fredsφ e J, Deigaard R. The bottleneck problem for turbulence in relation to suspended sediment in the surf zone. Proc 20th Int Conf Coastal Eng, 1986:1225-1239.
[160] Ohyama T, Kiota W, Tada A. Applicability of numerical models to nonlinear dispersive waves. Coastal Engineering, 1995, 24(3-4):297-313.
[161] Bullock G N, Murton G J. Performance of a Wedge Type Absorbing Wave Maker. J Waterway, Port, Coastal, and Ocean Engineering, 1989, 115(1):1-17.
[162] 王永学. 无反射造波数值波浪水槽. 水动力学研究与进展 A 辑, 1994, 2:205-213.
[163] Baker G, Meiron D, Orszag S. Generalized vortex methods for free-surface flow problems. J Fluid Mech, 1982, 123:477-501.
[164] Zhou Xiaoquan, Cao Shuyou. Periodic Boundary Condition in Simulation of Turbulent Flow. Journal of Hydrodynamics, Ser B, 2002, 14(3):111-116.
[165] Thorne P D, Williams J J. Suspended sediments under waves measured in a large scale flume facility. J Geophys Res, 2002, 107(C8):1-16.
[166] Graaff J Van de. Sediment concentration due to wave action[PhD dissertation]. Delf University of Technology, 1988.
[167] Longuet-Higgins M S. Mass Transport in Water Waves. Phil Trans, Royal Soc London, Ser A, 1953, 245:535-581.
[2] 朱志夏. 一维水流泥沙数学模型理论及应用[硕士学位论文]. 天津: 天津大学建筑工程学院, 1995.
[3] O’Brien M P. Review of the theory of turbulent flow and its relation to sediment transport. Trans Amer Geophys Union, 1933.
[4] Dobbins W E. Effect of turbulence on sedimentation. Trans ASCE, 1943, 109:660-666.
[5] 窦国仁. 潮汐水流中的悬沙运动及其淤积计算. 水利学报, 1963, 4:11-20.
[6] Han Q W. A study of the non-equilibrium transportation of non-uniform suspended load. Chinese Sci Bull, 1979, 17(7):804-808.
[7] Lin B N, Huan J Q, Li X Q. Unsteady transport of suspended load at small concentrations. J Hydr Engrg, ASCE, 1983, 109(91):86-98.
[8] Zhou J J, Lin B N. One-dimensional mathematical model for suspended sediment by lateral integration. J Hydr Engrg, ASCE, 1998, 124(7):712-717.
[9] Fang H W, Wang G Q. Three-dimensional mathematical model of suspended- sediment transport. J Hydr Engrg, ASCE, 2000, 126(8):578-592.
[10] 钱宁, 万兆蕙. 泥沙运动力学. 北京: 科学出版社, 2003.
[11] Bangold R A. Motion of waves in shallow water, Interaction between waves and sand bottom. Proc Royal Society London, A187, 1946:1-15.
[12] Rance P J, Warren N F. The threshold movement of coarse material in oscillatory flow. Proc 11th Coastal Eng Conf ASCE, 1968:487-491.
[13] Madsen U S, Grant W D. Sediment Transport in the Coastal Environment. Coastal Engrg, 1976:1-28.
[14] 赵子丹. 波浪作用下的泥沙起动. 海洋通报, 1983, 2:75-79.
[15] 周益人. 波浪作用下的泥沙起动. 水利水运科学研究, 1998, 12:338-346.
[16] 窦国仁, 窦希萍, 李提来. 波浪作用下泥沙的起动规律. 中国科学 E 辑, 2001, 12: 566-573.
[17] Horikawa K, Watanabe A, Katori S. Sediment transport under sheet flow conditions. Coastal Engineering Proc 18th Int Con, 1982:1335-1352.
[18] Ribberink J, Al-Salem A. Time dependent sediment transport phenomena in oscillatory boundary layer flow under sheet flow conditions. Technical Report H840, 1992, 20, Part IV, Delft Hydraulics.
[19] 窦国仁, 董风舞. 潮流和波浪的挟沙能力. 科学通报, 1995, 3:443-446.
[20] 刘峰, 李义天. 新的水流挟沙力计算公式. 长江科学院院报, 1997, 3:16-20.
[21] 曹祖德, 李蓓, 孔令双. 波流共存时的水体挟沙力. 水道港口, 2001, 12:151-155.
[22] 倪晋仁, 王光谦, 张红武. 固液两相流基本理论及其最新应用. 北京: 科学出版社, 1991.
[23] 倪晋仁, 惠遇甲. 悬移质浓度垂线分布的各种理论及其间关系. 水利水运科学研究, 1988, 1:83-95.
[24] 李付军, 谈广鸣, 陈立. 挟沙水流紊动结构研究现状及进展. 水动力学研究与进展 A辑, 1999, 9:265-272.
[25] 张瑞瑾. 论重力理论兼论悬移质运动过程. 水利学报, 1963, 3:11-23.
[26] Pai S I. Two-phase flows. Braunschweig: Vieweg-Verlag, 1977.
[27] Ishii M. Thermo-Fluid Dynamics Theory of Two-Phase Flow. Paris: Eyrolles, 1975.
[28] Drew D A. Average Field Equations for two-phase Media. Stu Appl Math, 1971, 50: 133-166.
[29] Drew D A. Averaged equations for two-phase flows. Stu Appl Math, 1971, 50:205-231.
[30] Drew D A. Mathematical modeling of two-phase flow. Ann Rev Fluid Mech, 1983, 15: 261-291.
[31] Drumheller D S, Bedford A. A thermomechanical theory for reacting immiscible mixtures. Arch Rational Mech Anal, 1980, 73:257-284.
[32] Johnson G, Massoudi M, Rajagopal K R. Flow of a fluid-solid mixture between flat plates. Chemical Engineering Science, 1991, 46(7):1713-1723.
[33] 刘大有. 二相流体动力学. 北京: 高等教育出版社, 1993.
[34] 蔡树棠, 范正翘, 陈越南. 两相流基本方程. 应用数学和力学, 1986, 7(6):477-485.
[35] 陈天翔. 多相流体力学的场方程及其平均. 力学进展, 1986, 16(4):482-494.
[36] 刘大有. 再论二相流基本方程—关于固相碰撞应力的讨论. 中国科学 A 辑, 1998, 1:72-79.
[37] 刘大有. 建立两相流方程的动力论方法. 力学学报, 1987, 5:213-221.
[38] 刘大有. 关于二相流、多相流、多流体模型和非牛顿流等概念的探讨. 力学进展, 1994, 1:66-74.
[39] 刘大有. 研究多相介质运动的意义、内容和方法. 力学与实践, 1995, 6:1-10.
[40] 傅旭东. 固液两相流动理学模型研究[博士论文]. 北京: 清华大学水利水电工程系, 2001.
[41] Melville W K, Bray K N C. A model of the two-phase turbulent jet. Int J Heat Mass Transfer, 1979, 22:647-656.
[42] Picart A, Berlemont A , Gouesbet G. Modelling and predicting turbulence fields and the dispersion of discrete particles transported by turbulent flows. Int J Multiphase Flow, 1986, 12:237-261.
[43] Elghobashi S E, Abou-Arab T W.A two-equation turbulence model for two-phase flows. Phys Fluids, 1983, 26(4):931-938.
[44] Chen C P, Wood P E. A turbulence closure model for dilute gas-particle flows. The Canadian Journal of Chemical Engineering, 1985, 63:349-360.
[45] Viollet P L, Simonin O. Modelling dispersed two-phase flows: Closure, Validation and software development. Appl Mech Rev, 1994, 47(6), part2:80-84.
[46] Besnard D C, Harlow F H. Turbulence in multiphase flow. Int J Multiphase Flow, 1988, 14(6):679-699.
[47] Cao J, Ahmadi G. Gas-particle two-phase turbulent flow in a vertical duct. Int J Multiphase Flow, 1995, 21(6):1203-1228.
[48] Hinze J O. Turbulence. NewYork: McGraw-Hill, 1975.
[49] Choi Y D, Chung M K. Analysis of turbulent gas-solid suspension flow in a pipe. Journal of Fluids Engineering, 1983, 105:329-334.
[50] Rizk M A, Elghobashi S E. A two-equation turbulence model for dispersed dilute confined two-phase flow. Int J Multiphase Flow, 1989, 15:119-133.
[51] 周力行. 湍流气粒两相流动和燃烧的理论与数值模拟. 北京: 科学出版社, 1994.
[52] Rouse H. Modern Conceptions of the Mechanics of Turbulence. Trans ASCE, 1937, 102:463-543.
[53] Lane E W, Kalinske A A. Engineering Calculation of Suspended Sediment. Trans Amer Geophys Union, 1941:603-607.
[54] 邵学军, 夏震寰. 悬浮颗粒紊动扩散系数的随机分析. 水利学报, 1990, 10:32-40.
[55] 曹志先, 张效先, 习和忠. 基于湍流猝发的明渠流悬沙浓度分布. 水利学报, 1997, 2: 52-57.
[56] 刘大有. 从二相流方程出发研究平衡输沙—扩散理论和泥沙扩散系数的讨论. 水利学报, 1995, 4:62-67.
[57] 刘大有. 现有泥沙理论的不足和改进—扩散模型和费克定律适用性的讨论. 泥沙研究, 1996, 3:39-45.
[58] 白玉川, 杨建民, 黄本胜. 二维水沙数学模型在复杂河道治理中的应用. 水利学报, 2203, 9:25-30.
[59] 余明辉, 吴腾, 杨国录. 剖面二维水沙数学模型及其初步应用. 水力发电学报, 2006, 8:66-69.
[60] 夏云峰. 感潮河道三维水流泥沙数值模拟研究与应用[博士学位论文]. 江苏: 河海大学交通与海洋工程学院, 2002.
[61] 黄国鲜. 弯曲和分叉河道水沙输运及其演变的三维数值模拟研究[博士学位论文]. 北京: 清华大学水利水电工程系, 2006.
[62] 周新民. 水沙两相流湍流模式及其应用[博士学位论文]. 四川: 四川大学水利水电学院, 2001.
[63] 白玉川, 蒋昌波, 罗纪生, 赵子丹. 振荡流底层拟序结构及其与泥沙相互作用研究. 力学进展, 2003, 8:347-356.
[64] Jonsson I G. Measurement in the turbulent wave boundary layer. Proc 10th Congr. IHAR, London, 1963, 1:85-92.
[65] Hino M, Kashiwanayagi M, Nakayama A, Hara T. Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow. J Fluid Mech, 1983, 131:363-400.
[66] Sleath J F A. Turbulent oscillatory flow over rough beds. J fluid Mech, 1987, 182: 369-409.
[67] Jensen B L, Sumer B M, Fredsoe J. Turbulent oscillatory boundary layers at high Reynolds numbers. J Fluid Mech, 1989, 206:265-297.
[68] Jonsson I G. Wave boundary layers and friction factors. Proc 10th Conf Coastal Eng ASCE, Tokyo, 1966:127-148.
[69] Kajiura K. A model for the bottom boundary layer in water waves. J Fluid Mech, 1968, 182:369-409.
[70] Bakker W T. Sand concentration in an oscillatory flow. Proc 14th Conf Coastal Eng Copenhagen, 1974:1129-1148.
[71] Johns B. The form of the velocity profile in a turbulent shear wave boundary. J Geophys Res, 1975, 80:5109-5112.
[72] Myrhaug D. On a theoretical model of rough turbulent wave boundary layers. Ocean Eng, 1982, 9(6):547-565.
[73] Thowbridge J H, Madsen O S. Turbulent wave boundary layers: 1.model formation and first order solution. Geophys Res, 1984, 89(C5):7989-7997.
[74] Thowbridge J H, Madsen O S. Turbulent wave boundary layers:1.Second order theory and mass transport. Geophys Res, 1984, 89(C5):7999-8007.
[75] Hagatun K, Eidsvik K J. Oscillating turbulent boundary layers with suspended sediment. J Geophys Res, 1986, 91(C11):13045-13055.
[76] Justesen P. Prediction of turbulent oscillatory flaw over rough beds. Coastal Eng, 1988, 12:257-284.
[77] Justesen P. A note on turbulence calculations in the wave boundary layer. J Hydr Res, 1991, 29(5):699-711.
[78] 赵子丹, 蒋昌波, 白玉川. 振荡流底部边界层运动的数值研究. 天津大学学报, 2001, 5: 568-572.
[79] Ahmad Sana, Hitoshi Tanaka, Hiroto Yamaji, Ikuo Kawamura. Hydrodynamic behavior of asymmetric oscillatory boundary layers at low Reynolds numbers. J Hydr Eng, 2006, 132 (10):1086-1096.
[80] Sleath J F A. Measurements of bed load in oscillatory flow. Journal of the Waterway, Port, Coastal and Ocean Division, 1978, 104(4):291-307.
[81] Staub C, Jonsson L G, Svendsen L A. Variation of suspended sediment in oscillatory flow. Coastal Engineering Proc 19th Int Conf, 1984:2310-2321.
[82] Nielsen P. Suspended sediment concentrations under waves. Coastal Engng, 1986, 10: 22-31.
[83] Ahilan R V, Sleath J F A. Sediment transport in oscillatory flow over flat beds. J hydr Div ASCE, 1987, 113:308-322.
[84] Makoto I. Field observation and numerical calculation of suspended sediment concentration in the surf zone. Coastal Engineering in Japan, 1988, 30(2):75-881.
[85] Savioli J, Justesen P. Sediment in oscillatory flows over a plane bed. J Hydr Res, 1997, 35(2):177-189.
[86] Davies A G, Li Z. Modelling sediment transport beneath regular symmetrical and asymmetrical waves above a plane bed. Continental Shelf Res,1997, 5:555-582.
[87] 蒋昌波, 白玉川, 赵子丹, 张红武. 振荡流底层悬沙运动的数值模拟. 水科学进展, 2003, 2:136-142.
[88] Emily A, Robert L. Sediment Transport over Ripples in Oscillatory Flow. J Hydr Eng, 2006, 132 (2):180-193.
[89] Asano T. Two-phase flow model on oscillatory sheet-flow. Pro 22th Inter Conf on Coastal Eng, 1990:2372-2384.
[90] Li L, Sawamto M. Multi-phase model on sediment transport in sheet flow regime under oscillatory flow. Coastal Eng In Japan. 1995, 38(2):157-178.
[91] Ono M, Deguchi I, Sawaragi T. Numerical modeling of sediment transport for various mode. Pro 25th Int Conf on Coastal Eng, 1996:2372-2384.
[92] Dong P, Zhang K. Two-phase flow modeling of sediment motions in oscillatory sheet flow. Coastal Eng, 1999, 36:87-109.
[93] Hsu T W, Chang H, Hsieh C. A two-phase flow model of wave-induced sheet flow. J Hydraulic Res, 2003, 41(3):299-310.
[94] Longo S. Two-phase flow modeling of sediment motion in sheet-flows above plane beds. J Hydraulic Eng, ASCE, 2005, 131(5):366-379.
[95] 王尚毅. 波浪作用下含沙量的垂向分布. 中国科学 A 辑, 1984, 12:1151-1160.
[96] Van Rijn L C. Principles of sediment transport in rivers, estuaries and coastal seas. Amsterdam: Aqua Publications, 1993.
[97] Williams J J, Bell P S, etc. Observed and predicted vertical suspended sediment concentration profiles and bedforms in oscillatory flow. J Coastal Research, 2000, 16(3):698-708.
[98] Kos’yan R D. Vertical distribution of suspended sediment concentrations of seawards of the breaking zone. Coastal Eng, 1985, 9:171-187.
[99] Nielsen P, Teakle I A. Turbulent diffusion of momentum and suspended particles: A finite mixing length theory. Phys Fluids, 2004, 7:2342-2348.
[100] 严冰. 波浪及波流共同作用下悬移质浓度垂线分布的研究[硕士学位论文]. 天津: 天津大学建筑工程学院, 2004.
[101] 严冰, 张庆河. 波浪作用下悬沙浓度垂线分布的研究. 泥沙研究, 2006, 10(5):63-68.
[102] 王建峰. 波流共同作用下悬沙浓度垂向分布的研究[硕士学位论文]. 天津: 天津大学建筑工程学院, 2004.
[103] Durst F, Milojevic D, Schonung B. Eulerian and lagrangian predictions of particulate two-phase flows: a numerical study. Appl Math Mo delling, 1984, 8:101-115.
[104] Soo S L. Fluid Dynamics of Multiphase Systems. Blaisdell, Waltham, l967.
[105] Buyevich Yu A, Shchelchkova I N. Flow of dense suspensions. Progr Aerospace Sci, 1978, 188:121-150.
[106] Smoot L D, Smith P J. Coal Combustion and Gasification. Plenum Press. 1985.
[107] Lee S L, Durst F. On the motion of particles in turbulent duct flows. Int J Multiphase Flow, 1982, 8:125-146.
[108] 米尔恩-汤姆森. 理论流体力学. 李裕立, 晏名文 译. 北京: 机械工业出版社, 1984.
[109] 怀特. 粘性流体动力学. 魏中磊, 甄思淼 译. 北京: 机械工业出版社, 1982.
[110] Schiller L, Nauman A. A drag coefficient correlation. VDI Zeits, 1933, 77:318-320.
[111] 岑可法, 樊建人. 工程气固多相流动的理论及计算. 杭州: 浙江大学出版社, 1990.
[112] Ishii M, Zuber N. Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows. AIChE J, 1979, 25(5):843-855.
[113] Ihme F, Schmidt-Traub H, Brauer H. Theoretical studies on. mass transfer at and flow past spheres. Chem Ing Tech, 1972, 44(5):306-313.
[114] 窦国仁. 紊流力学. 下册. 北京: 高等教育出版社, 1987.
[115] Odar F. Verification of the proposed equation of the forces on a sphere accelerating in a viscous fluid. J Fluid Mech, 1966, 25(3):591-592.
[116] Ahamadi G, Gordschemidt V W. Motion of particles in a turbulent fluid the Basset history term. J Appl mech, 1971, 38:561-563.
[117] Tsuji Y ,etal. Experiment measurement of Magnus forces on a rotating shere at low Peynolds. J. Fluid of Eng, 1985, 107(4):484-488.
[118] Saffman P G. The lift on a small sphere in slow shear flow. J Fluid Mech, 1965, 22: 385-400.
[119] Saffman P G. Corrigendum to “The Lift on a Small Sphere in a Slow Shear Flow”. J Fluid Mech, 1968, 31:624.
[120] Mei R. An approximate expression for the shear lifts force of a spherical particle at finite Reyolds number. Int J Multiphase Flow, 1992, 18(1):145-148.
[121] 李绍林. 两相悬浮体剪切流的理论和实验. 北京: 科学出版社, 1985.
[122] Tam C K W. The drag on a cloud of spherical particles in low Reynolds number flow. J Fluid Mech, 1969, l38:537-546.
[123] Zuber N. On the dispersed two-phase flow in the laminar flow region. Chen Eng Scien, 1964, 19(4):897-917.
[124] Murray J D. Some basic aspects of one-dimensional incompressible particle-fluid two-phase flows. Astronaut Acta, 1967, 13:417-430.
[125] 黄社华, 李炜, 程良骏. 任意流场中稀疏颗粒运动方程及其性质. 应用数学和力学, 2000, 3:265-276.
[126] Van Doormaal J P, Raithby G D. Enhancement of the SIMPLE method for predicting incompressible fluid flow. Number Heat Transfer, 1984, 7:147-163.
[127] Patankar S V. Numerical Heat Transfer and Fluid Flow. New York: Hemispher, 1980.
[128] 陶文铨. 数值传热学. 2 版. 西安: 西安交通大学出版社, 2001.
[129] 陶文铨. 计算传热学的近代进展. 北京: 科学出版社, 2000.
[130] Hayase T, Humphrey J A C, Greif R.A. Consistently Formulated QUICK Scheme for fast and Stable Convergence Using Finite-Volume Iterative Calculation Procedures. J Compu. Phys, 1992, 98:108-118.
[131] Demirdzic I, Gosman A D, Issa R I, Peric M A. Calculation procedure for turbulent flow in complex geometries. Comput Fluids, 1987, 15(3):251-273.
[132] 徐士良. Fortran 常用算法程序集. 2 版. 北京: 清华大学出版社, 1995.
[133] Stone H L. Iterative solution of implicit approximation of multidimensional partial differential equations. SIAM J on Numerical Analysis, 1968, 5:530-558.
[134] Alfrink B, van Rijn L C. Two-equation turbulent model for flow in trench. J Hydr Eng, 1983, 109(3):941-958.
[135] Launder B E, Spalding D B. The Numerical Computation of Turbulent Flows. Comp Meth Appl Mech Engr, 1974, 2:269-289.
[136] 韩其为, 何明民. 论非均匀悬移质二维不平衡输沙方程及其边界条件. 水利学报, 1997, 1:1-10.
[137] Coleman N L. Effects of suspended sediment on the open-channel velocity distribution. Water Resources Res, 1986, 22(10):1377-1384.
[138] van Rijn L C. Entrainment of fine sediment particles; development of concentration profiles in a steady, uniform flow without initial sediment load. Rep. No. M1531, Part II, Delft Hydraulic Laboratory, Delft, The Netherlands, 1981.
[139] Shields A. Anwedung der aehnlichkeitmechanik und der turbulenzforschuang aufdie geschiebebewegung, Mitt Preuses, Versuchanst. Wasserbau schiffbau, 1936, 26.
[140] 李丹勋. 悬移质颗粒运动特性的研究[博士学位论文]. 北京: 清华大学水利水电工程系, 1999.
[141] Wang Z B, Ribberringk J S. The validity of a depth-integrated model for suspended sediment transport. Journal of Hydraulic Research, 1986, 24 (1):53-63.
[142] Van Rijn L C. Mathematical modeling of morphological processes in the case of suspended sediment transport[PhD dissertation]. Delft Univ Netherlands, 1987.
[143] 陆永军. 三维紊流泥沙数学模型及其应用[博士后研究报告]. 南京: 南京水利科学院, 2002.
[144] 刘建军. 明渠水流含沙量沿垂线分布研究. 泥沙研究, 1996, 6(2):105-108.
[145] 谈广鸣,夏军强, 郑邦民. 挟沙水流紊动扩散系数的研究. 水利学报, 1998, 12:23-27.
[146] 周家俞. 抉沙水流泥沙颗粒悬浮规律的试验研究[硕士学位论文]. 武汉: 武汉大学水利水电学院, 2005.
[147] Andreas Muller. Turbulence Measurements over a Movable Bed with Sediment Transport by Laser-Anemometry. International Association for Hydraulic Research. 1963.
[148] 王兴奎. 悬移质泥沙运动及其对水流结构的影响[博士学位论文]. 北京: 清华大学水利水电工程系, 1985.
[149] 春宏, 惠遇甲. 明渠挟沙水流运动的力学和统计规律. 北京:科学出版社, 1995.
[150] 林鹏, 陈立. 低含沙水流紊动结构的实验研究. 水动力学研究与进展, 2003, 3:209-216.
[151] Rubey W W. Settling velocities of gravel, sand and silt particles. Am J Sci, 1993, 25(148):325-338.
[152] Cheng N. Discussion on “A fall-velocity equation by Ahrens (2000)”, J of Waterway, Port, Coastal and Ocean Eng, ASCE, 2001, 127(4):250-251.
[153] Chang H K, Liou J C. Disscussion on “A fall-velocity equation by Ahrens (2000)”, J of Waterway, Port, Coastal and Shelf Science, 2001, 46:733-742.
[154] Van Rijin L C. Sediment transport,part II: suspended load transport. J Hydraulic eng, ASCE, 1984, 110(11):1613-1641.
[155] 费祥俊. 黄河中下游含沙水流粘度的计算模型. 泥沙研究, 1991, 2:1-13.
[156] Fredsφ e J, Deigaard R. Mechanics of coastal sediment transport. World Scientific Publishing Co Pte Ltd, 1994.
[157] Engelund F, Fredsφ e J. A sediment transport model for straight alluvial channels. Nordic Hydrology, 1976, 7:293-306.
[158] Zyserman J A, Fredsφ e J. Data Analysis of Bed Concentration of Suspended Sediment. Journal of Hydraulic Engineering, ASCE 1994, 120(9):1021-1042.
[159] Justesen P, Fredsφ e J, Deigaard R. The bottleneck problem for turbulence in relation to suspended sediment in the surf zone. Proc 20th Int Conf Coastal Eng, 1986:1225-1239.
[160] Ohyama T, Kiota W, Tada A. Applicability of numerical models to nonlinear dispersive waves. Coastal Engineering, 1995, 24(3-4):297-313.
[161] Bullock G N, Murton G J. Performance of a Wedge Type Absorbing Wave Maker. J Waterway, Port, Coastal, and Ocean Engineering, 1989, 115(1):1-17.
[162] 王永学. 无反射造波数值波浪水槽. 水动力学研究与进展 A 辑, 1994, 2:205-213.
[163] Baker G, Meiron D, Orszag S. Generalized vortex methods for free-surface flow problems. J Fluid Mech, 1982, 123:477-501.
[164] Zhou Xiaoquan, Cao Shuyou. Periodic Boundary Condition in Simulation of Turbulent Flow. Journal of Hydrodynamics, Ser B, 2002, 14(3):111-116.
[165] Thorne P D, Williams J J. Suspended sediments under waves measured in a large scale flume facility. J Geophys Res, 2002, 107(C8):1-16.
[166] Graaff J Van de. Sediment concentration due to wave action[PhD dissertation]. Delf University of Technology, 1988.
[167] Longuet-Higgins M S. Mass Transport in Water Waves. Phil Trans, Royal Soc London, Ser A, 1953, 245:535-581.