泥沙侵蚀经验式经验系数不确定性对异重流数学模型的影响
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摘要
文章应用基于贝叶斯定理的Metropolis-Hastings随机采样方法,结合现有异重流泥沙侵蚀实验数据,获取了异重流侵蚀公式(见式1)中经验系数(如N_1、N_2、A_3)的大量样本(样本总数15万)。统计表明,当A3=4时,占总样本数95%的N_1N_2取值组合中,N_1和N_2最大值分别是拟合最优值(即概率最大的N_1N_2值)的2倍和3.5倍。将样本值输入经典的异重流层平均数学模型,模拟陡坡上异重流演化过程,统计发现,1)计算异重流厚度、速度、浓度区间范围随运动距离的增加逐渐增大;2)采用概率最大经验系数值可能低估异重流厚度、高估异重流速度和浓度。对比表明,模型计算结果对N_1N_2取值的敏感度要远大于对A3N2取值的敏感度。
Uncertainties of the empirical relations of sediment entrainment for turbidity currents were investigated using the method of Metropolis-Hastings sampling based on Bayesian theory.A total of 150 thousands sample values for two sets of empirical coefficients of N_1N_2 and A_3N_2 were obtained.The statistical analysis of these sample values suggest that the range of the sample values of N_1N_2 in the case of A3=4may be likely smallest,corresponding to minimum uncertainty.Inputting these sample values of N_1N_2 into a classical layer-averaged model,a total of 150 thousand sets of numerical solutions was obtained for turbidity current evolution over a steep slope.Further statistical analysis of these numerical solutions indicates that the range of the computed current thickness,velocity and concentration increases with distance.If the sample values of N_1N_2 with the highest frequency were used,the model may underestimate the current thickness,but over-predict the current velocity and concentration.It is also noted that the sensitivity of the numerical results to N_1-N_2 is larger than to those of A_3-N_2.
Uncertainties of the empirical relations of sediment entrainment for turbidity currents were investigated using the method of Metropolis-Hastings sampling based on Bayesian theory.A total of 150 thousands sample values for two sets of empirical coefficients of N_1N_2 and A_3N_2 were obtained.The statistical analysis of these sample values suggest that the range of the sample values of N_1N_2 in the case of A3=4may be likely smallest,corresponding to minimum uncertainty.Inputting these sample values of N_1N_2 into a classical layer-averaged model,a total of 150 thousand sets of numerical solutions was obtained for turbidity current evolution over a steep slope.Further statistical analysis of these numerical solutions indicates that the range of the computed current thickness,velocity and concentration increases with distance.If the sample values of N_1N_2 with the highest frequency were used,the model may underestimate the current thickness,but over-predict the current velocity and concentration.It is also noted that the sensitivity of the numerical results to N_1-N_2 is larger than to those of A_3-N_2.
引文
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[12]周磊,安瑞冬,谭升魁,等.水库异重流淤积成因分析及前锋运动规律[J].水利水电科技进展,2012,32(2):6-10.DOI:10.3880/j.issn.1006-7647.2012.02.002.Zhou L,An R D,Tan S K,et al.Study on Reservoir Sedimentation Caused by Turbidity Currents and Experimental study on Front Movement[J].Advance in Science and Technology of Water Resources,2012,32(2):6-10.DOI:10.3880/j.issn.1006-7647.2012.02.002.
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[14] Traer M M,Hilley G E,Fildani A,et al.The Sensitivity of Turbidity Currents to Mass and Momentum Exchanges between These Underflows and Their Surroundings[J].Journal of Geophysical Research Atmospheres,2012,117(F1009)DOI:10.1029/2011JF001990,2012.
[15] Garcia M.Entrainment of Bed Sediment into Suspension[J].Journal of Hydraulic Engineering,1991,117(4):414-435.DOI:https:∥doi.org/10.1061/(asce)0733-9429(1991)117:4(414).
[16] Parker G,Garcia M,Fukushima Y,et al.Experiments on Turbidity Currents over an Erodible bed[J].Journal of Hydraulic Research,1987,25(1):123-147.DOI:https:∥doi.org/10.1080/00221688709499292.
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[18] Hilley G E,Mynatt I,Pollard D D.Structural Geometry of Raplee Ridge Monocline and Thrust Fault Imaged Using Inverse Boundary Element Modeling and ALSM Data[J].Journal of Structural Geology,2010,32(1):45-58.DOI:https:∥doi.org/10.1016/j.jsg.2009.06.015.
[19] Wang Y,Cao Z.Probabilistic Characterization of Young’s Modulus of Soil Using Equivalent Samples[J].Engineering Geology,2013,159:106-118.DOI:https:∥doi.org/10.1016/j.enggeo.2013.03.017.
[20] Parker G,Fukushima Y,Pantin H M.Self-accelerating Turbidity Currents[J].Journal of Fluid Mechanics,1986,171(171):145-181.DOI:https:∥doi.org/10.1017/s0022112086001404.
[21] Hu P,Phtz T,He Z.Is It Appropriate to Model Turbidity Currents with the Three-equation Model?[J].Journal of Geophysical Research Earth Surface,2015,120(7):1153-1170.DOI:https:∥doi.org/10.1002/2015jf003474.
[22] Parker G.Conditions for the Ignition of Catastrophically Erosive Turbidity Currents[J].Marine Geology,1982,46:307-327.DOI:https:∥doi.org/10.1016/0025-3227(82)90086-x.
[23] Dietrich W E.Settling Velocity of Natural Particles[J].Water Resources Research,1982,18(6):1615-1626.DOI:https:∥doi.org/10.1029/wr018i006p0161.
[24] Glas M,Glock K,Tritthart M,et al.Hydrodynamic and Morphodynamic Sensitivity of a River’s Main Channel to Groyne Geometry[J].Journal of Hydraulic Research,2018:1-13.DOI:10.1080/00221686.2017.1405369.
[2] Hu P,Cao Z,Pender G,et al.Numerical Modelling of Turbidity Currents in the Xiaolangdi Reservoir,Yellow River,China[J].Journal of Hydrology,2012:s464-465(41):41-53.DOI:http:∥dx.doi.org/10.1016/j.jhydrol.2012.06.032.
[3]李九发,何青,徐海根.长江河口浮泥形成机理及变化过程[J].海洋与湖沼,2001,32(3):302-310.DOI:10.3321/j.issn:0029-814X.2001.03.011.Li J F,He Q,Xu H G.The Fluid Mud Transportation Processes in ChangJiang River Estuary[J].Oceanologia Et Limnologia Sinica,2001,32(3):302-310.DOI:10.3321/j.issn:0029-814X.2001.03.011.
[4] Hu P,Cao Z.Fully Coupled Mathematical Modeling of Turbidity Currents over Erodible Bed[J].Advances in Water Resources,2009,32(1):1-15.DOI:10.1016/j.advwatres.2008.07.018.
[5] Meiburg E,Kneller B.Turbidity Currents and Their Deposits[J].Annual Review of Fluid Mechanics,2010,42(1):135-156.DOI:10.1146/annurev-fluid-121108-145618.
[6]范家骅.浑水异重流水量掺混系数的研究[J].水利学报,2011,42(1):19-26.DOI:10.13243/j.cnki.slxb.2011.01.007.Fan J H.Studies on Water Entrainment Coefficient of Turbid Density Currents[J].Journal of Hydraulic Engineering,2011,42(1):19-26.DOI:10.13243/j.cnki.slxb.2011.01.007.
[7]严忠銮,安瑞冬,李嘉,等.浊度型清浑水交界面识别方法及其在水库异重流观测中的应用[J].水利水电科技进展,2013,33(6):71-75.DOI:10.3880/j.issn.1006-7647.2013.06.015.Yan Z L,An R D,Li J,et al.Turbid Interface Identification Method of Turbidity Currents and its Application in Field Obervation at Zipingpu Reservoir[J].Advances in Science and Technology of Water Resources,2013,33(6):71-75.DOI:10.3880/j.issn.1006-7647.2013.06.015.
[8]王远见,江恩慧.黄河下游河道洪峰增值机理和条件研究[C]∥中国水利学会2016学术年会,2016.Wang Y J,Jiang E H.Mechanism of Amplifications of Hyper-concentrated Flood and Criterion of Its Occurrence in the Lower Yellow River[C]∥2016Annual Academic Conference of China Water Conservancy Society.
[9]贺治国,林挺,赵亮,等.异重流在层结与非层结水体中沿斜坡运动的实验研究[J].中国科学:技术科学,2016,46(6):570-578.DOI:10.1360/N092015-00176.He Z G,Lin T,Zhao L,et al.Experiments on Gravity Currents Down a Ramp in Unstratified and Linearly Stratified Salt Water Environment[J].Scientia Sinica Technologica,2016,46(6):570-578.DOI:10.1360/N092015-00176.
[10]曾曾,李嘉,安瑞冬,等.低含沙量异重流运动规律及其对水温分布的影响[J].水动力学研究与进展,2016,31(3):346-354.DOI:10.16076/j.cnki.cjhd.2016.03.012.Zeng Z,Li J,An R D,et al.The Motion Law of the Density Current with Low Sediment Content and Influence on Water Temperature Distribution[J].Chinese Journal of Hydrodynamics,2016,31(3):346-354.DOI:10.16076/j.cnki.cjhd.2016.03.012.
[11]赵琴,李嘉,安瑞冬.水库浑水异重流的两相流模型适用性研究[J].水动力学研究与进展,2010,25(1):76-84.DOI:10.3969/j.issn.1000-4874.2010-01.011.Zhao Q,Li J,An R D.Two-phase Flow Models for Turbid Density Current in a Reservoir[J].Chinese Journal of Hydrodynamics,2010,25(1):76-84.DOI:10.3969/j.issn.1000-4874.2010-01.011.
[12]周磊,安瑞冬,谭升魁,等.水库异重流淤积成因分析及前锋运动规律[J].水利水电科技进展,2012,32(2):6-10.DOI:10.3880/j.issn.1006-7647.2012.02.002.Zhou L,An R D,Tan S K,et al.Study on Reservoir Sedimentation Caused by Turbidity Currents and Experimental study on Front Movement[J].Advance in Science and Technology of Water Resources,2012,32(2):6-10.DOI:10.3880/j.issn.1006-7647.2012.02.002.
[13]胡鹏,胡元园,贺治国,等.泥沙异重流与环境物质交换经验式对比[J].水科学进展,2017,28(2):257-264.DOI:10.14042/j.cnki.32.1309.2017.02.011.Hu P,Hu Y Y,He Z G,et al.Numerical Comparative Studies on the Performances of Empirical Relations of Mass Exchanges for Turbidity Currents[J].Advance in Water Science,2017,28(2):257-264.DOI:10.14042/j.cnki.32.1309.2017.02.011.
[14] Traer M M,Hilley G E,Fildani A,et al.The Sensitivity of Turbidity Currents to Mass and Momentum Exchanges between These Underflows and Their Surroundings[J].Journal of Geophysical Research Atmospheres,2012,117(F1009)DOI:10.1029/2011JF001990,2012.
[15] Garcia M.Entrainment of Bed Sediment into Suspension[J].Journal of Hydraulic Engineering,1991,117(4):414-435.DOI:https:∥doi.org/10.1061/(asce)0733-9429(1991)117:4(414).
[16] Parker G,Garcia M,Fukushima Y,et al.Experiments on Turbidity Currents over an Erodible bed[J].Journal of Hydraulic Research,1987,25(1):123-147.DOI:https:∥doi.org/10.1080/00221688709499292.
[17] Garcia M,Parker G.Experiments on the Entrainment of Sediment into Suspension by a Dense Bottom Current[J].Journal of Geophysical Research Atmospheres,1993,98(C3):4793-4807.DOI:https:∥doi.org/10.1029/92jc02404.
[18] Hilley G E,Mynatt I,Pollard D D.Structural Geometry of Raplee Ridge Monocline and Thrust Fault Imaged Using Inverse Boundary Element Modeling and ALSM Data[J].Journal of Structural Geology,2010,32(1):45-58.DOI:https:∥doi.org/10.1016/j.jsg.2009.06.015.
[19] Wang Y,Cao Z.Probabilistic Characterization of Young’s Modulus of Soil Using Equivalent Samples[J].Engineering Geology,2013,159:106-118.DOI:https:∥doi.org/10.1016/j.enggeo.2013.03.017.
[20] Parker G,Fukushima Y,Pantin H M.Self-accelerating Turbidity Currents[J].Journal of Fluid Mechanics,1986,171(171):145-181.DOI:https:∥doi.org/10.1017/s0022112086001404.
[21] Hu P,Phtz T,He Z.Is It Appropriate to Model Turbidity Currents with the Three-equation Model?[J].Journal of Geophysical Research Earth Surface,2015,120(7):1153-1170.DOI:https:∥doi.org/10.1002/2015jf003474.
[22] Parker G.Conditions for the Ignition of Catastrophically Erosive Turbidity Currents[J].Marine Geology,1982,46:307-327.DOI:https:∥doi.org/10.1016/0025-3227(82)90086-x.
[23] Dietrich W E.Settling Velocity of Natural Particles[J].Water Resources Research,1982,18(6):1615-1626.DOI:https:∥doi.org/10.1029/wr018i006p0161.
[24] Glas M,Glock K,Tritthart M,et al.Hydrodynamic and Morphodynamic Sensitivity of a River’s Main Channel to Groyne Geometry[J].Journal of Hydraulic Research,2018:1-13.DOI:10.1080/00221686.2017.1405369.