泥沙颗粒运动规律及非线性分析
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摘要
河流中泥沙运动的研究是河流问题的核心内容，而单个泥沙颗粒的运动分析是研究泥沙群体行为的基础。因此，对单个泥沙颗粒的研究具有重要的理论研究意义和实际工程意义。
本文分析了水流泥沙的两相流模型，总结了混沌的研究现状及在水流泥沙颗粒研究方面的应用。通过研究稀疏颗粒相对流体运动时所受到的各种作用力，建立了任意流场中稀疏泥沙颗粒运动方程一般形式。
应用非线性动力学方法研究了单颗粒泥沙在紊动水流中周期运动的稳定性，推导了定常周期解的稳定条件，解释了泥沙在紊动水流中存在的跳跃现象。结果表明：在较小紊动激励幅值的作用下，某一粒径颗粒位移运动幅值可以发生从小到大的跳跃。在某些条件下，泥沙颗粒粒径和水流紊动频率的较小变化同样可以造成泥沙颗粒运动幅值的突变。
用随机Melnikov均方准则研究了随机紊动水流中单颗粒泥沙运动的混沌参数域，用路径积分法求解了单颗粒泥沙随机运动的概率密度函数。研究表明，单颗粒泥沙混沌参数域的大小与水流激励参数密切相关，周期水流激励的幅值、白噪声强度越大，泥沙运动的随机混沌参数域也越大。
考虑近床面水流结构和泥沙颗粒排列方式的双重影响，采用滚动模式建立了非均匀沙的起动流速公式，通过试验资料验证的结果表明，公式的计算值与实验资料符合较好；从水流动力、粘性泥沙的组成及结构分析了影响粘性细泥沙起动的因素，系统分析总结了粘性细泥沙起动研究现状，并对今后的研究提出展望。
从泥沙颗粒垂向运动的动力学角度分析，得到了影响泥沙浓度垂线分布有关因素的关系式。研究表明，随着摩阻流速的增大，浓度曲线愈来愈陡，即浓度分布逐渐均匀。且随着颗粒直径、密度和摩阻流速的增大，浓度拐点越来越高。
The study on the laws of flow and sediment transport was the core content ofrivers, and the analysis of single sediment particle motion was the foundation ofsediment microscopic properties. Therefore, the research of a single sediment particlewas important and significance both in theory and practical engineering.
Two phase flow model of flow and sediment was analyzed in this paper, then thestatus of research on chaos and its application of sediment were summarized. Theforces on rigid particles moving in relation to fluid having been studied, a generalform of equation for discrete particles motion in arbitrary flow field is obtained.
The stability for single sediment particle in turbulent flows was studied by thenonlinear dynamic methods, the stable conditions for the periodic stationary rollmotion were ascertained, and the jump phenomena are explained analytically. It isfound that the amplitude of particle motion could have mutations, even under asmaller flow turbulence frequency. Under some conditions, the small changes ofsediment particle size or the flow turbulence frequency could also cause the mutationof movement amplitude.
Considering bottom flow structure and the random position of non-uniformSediment on the bed, formulas for calculating the incipient velocity of non-uniformsediment was established by using the rolling model. The results show that thevalidity of the formula was verified by experiment data. The factors effecting theincipient motion of cohesive fine sediment were analyzed in the view ofhydrodynamic conditions, cohesive sediment composition and structure, the researchstatus of incipient motion of cohesive sediment was summarized systematically, andfurther research methods were discussed.
Expression of related factors infecting the vertical distribution of sedimentconcentration was obtained through the dynamics analysis of sediment verticalmovement.The results show that with the increase of the friction velocity, theconcentration curve increasingly steep, that the concentration well distributed.And with the increases of particle diameter, density and friction velocity，concentrationsof inflection point became higher.
本文分析了水流泥沙的两相流模型，总结了混沌的研究现状及在水流泥沙颗粒研究方面的应用。通过研究稀疏颗粒相对流体运动时所受到的各种作用力，建立了任意流场中稀疏泥沙颗粒运动方程一般形式。
应用非线性动力学方法研究了单颗粒泥沙在紊动水流中周期运动的稳定性，推导了定常周期解的稳定条件，解释了泥沙在紊动水流中存在的跳跃现象。结果表明：在较小紊动激励幅值的作用下，某一粒径颗粒位移运动幅值可以发生从小到大的跳跃。在某些条件下，泥沙颗粒粒径和水流紊动频率的较小变化同样可以造成泥沙颗粒运动幅值的突变。
用随机Melnikov均方准则研究了随机紊动水流中单颗粒泥沙运动的混沌参数域，用路径积分法求解了单颗粒泥沙随机运动的概率密度函数。研究表明，单颗粒泥沙混沌参数域的大小与水流激励参数密切相关，周期水流激励的幅值、白噪声强度越大，泥沙运动的随机混沌参数域也越大。
考虑近床面水流结构和泥沙颗粒排列方式的双重影响，采用滚动模式建立了非均匀沙的起动流速公式，通过试验资料验证的结果表明，公式的计算值与实验资料符合较好；从水流动力、粘性泥沙的组成及结构分析了影响粘性细泥沙起动的因素，系统分析总结了粘性细泥沙起动研究现状，并对今后的研究提出展望。
从泥沙颗粒垂向运动的动力学角度分析，得到了影响泥沙浓度垂线分布有关因素的关系式。研究表明，随着摩阻流速的增大，浓度曲线愈来愈陡，即浓度分布逐渐均匀。且随着颗粒直径、密度和摩阻流速的增大，浓度拐点越来越高。
The study on the laws of flow and sediment transport was the core content ofrivers, and the analysis of single sediment particle motion was the foundation ofsediment microscopic properties. Therefore, the research of a single sediment particlewas important and significance both in theory and practical engineering.
Two phase flow model of flow and sediment was analyzed in this paper, then thestatus of research on chaos and its application of sediment were summarized. Theforces on rigid particles moving in relation to fluid having been studied, a generalform of equation for discrete particles motion in arbitrary flow field is obtained.
The stability for single sediment particle in turbulent flows was studied by thenonlinear dynamic methods, the stable conditions for the periodic stationary rollmotion were ascertained, and the jump phenomena are explained analytically. It isfound that the amplitude of particle motion could have mutations, even under asmaller flow turbulence frequency. Under some conditions, the small changes ofsediment particle size or the flow turbulence frequency could also cause the mutationof movement amplitude.
Considering bottom flow structure and the random position of non-uniformSediment on the bed, formulas for calculating the incipient velocity of non-uniformsediment was established by using the rolling model. The results show that thevalidity of the formula was verified by experiment data. The factors effecting theincipient motion of cohesive fine sediment were analyzed in the view ofhydrodynamic conditions, cohesive sediment composition and structure, the researchstatus of incipient motion of cohesive sediment was summarized systematically, andfurther research methods were discussed.
Expression of related factors infecting the vertical distribution of sedimentconcentration was obtained through the dynamics analysis of sediment verticalmovement.The results show that with the increase of the friction velocity, theconcentration curve increasingly steep, that the concentration well distributed.And with the increases of particle diameter, density and friction velocity，concentrationsof inflection point became higher.
引文
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