河道形态阻力分形特征研究
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摘要
河道阻力直接决定着河流的泄流、输沙等能力,是水力学与河流动力学研究的基本问题,也是江河治理设计的关键参数,河道阻力问题研究具有重要的理论意义和广阔的应用前景。本文采用理论分析、数值计算和水槽试验相结合的方法,开展了河道形态阻力的分形特征研究,取得了如下主要成果:
(1)河道床面形态具有自相似特征,可视为分形。采用分形理论中的一维和二维RMD模型,实现了在给定平面区域上生成不同分形维数、粗糙程度及分辨率的河道剖面轮廓及床面形态,模拟结果凸显了精细的微观粗糙结构。
(2)基于少量的数据资料,应用一元分形插值理论和二元分形插值理论分别实现了河道剖面轮廓及床面形态的分形重构,较好地克服了规则欧氏几何粗糙度测量中的尺度相关性和数据有限性问题。
(3)从定性与定量角度对剖面轮廓及粗糙表面分形维数的各种计算方法进行了系统分析比较,提出分别采用结构函数法和改进立方体覆盖法来计算河道剖面轮廓及床面形态的分形维数。
(4)对爱因斯坦法、姜国干法、洛特尔法以及加权平均法等综合阻力分割方法进行了分析讨论与验证比较,提出爱因斯坦法总体最优。
(5)探讨了糙率尺寸法及暴露度分析法在床面粗糙度表征中存在的问题,提出采用分形理论来研究具有自相似精细结构的床面粗糙度,确立了床面粗糙度分形表征函数的基本结构形式。
(6)建立了沙粒当量粗糙度k_(s1)与沙粒阻力系数n_b '及f_b'的分形关系式,式中引入的剖面轮廓分形维数D,可综合反映床沙粒径级配及随机排列所形成的粗糙形态,对公式的验证、分析与讨论表明,公式结构较为合理,计算精度令人满意。
(7)通过引入充分体现三维沙波床面特征(如平面沙波多寡、几何形态及分布状况等)的分形维数D,建立了沙波当量粗糙度k_(s2) /Δ及沙波阻力系数f_b"的分形关系式,导得了k_(s2) /Δ与f_b"之间的关系,讨论了f_b"随k_(s2) /Δ的变化规律。
(8)对曼宁公式存在的量纲不和谐及影响因素不明确两大缺陷进行了尝试性改进,初步建立了量纲和谐且经分形细化的曼宁公式。
Channel resistance is one of the basic topics of hydraulics and river dynamics, which determines the river’s capability of flood discharge and sediment transportation,it is a key parameter in the river improvement designs. Studies of channel resistance have an important theoretical meaning and wide application prospects. In this dissertation, a fractal research of bedform resistance is carried out based on the comprehensive approaches of theoretical analysis, numeric calculation and flume experiment. The main results can be summarized as follows:
(1) Channel bedforms which have self-similar characteristics can be regarded as fractals. Both the channel bed profiles and rough bedforms with different fractal dimensions, roughness and resolutions are generated respectively by using one-dimensional and two-dimensional RMD model in fractal theory, and the simulating results fully showed the fine microscopic rough structures.
(2) On the basis of limit measured data, the channel bed profiles and rough bedforms are reproduced accurately by using the unary and bivariate fractal interpolation methods, which well resolved the problems of scale correlation and information limitation existing in the regular Euclidean geometry model.
(3) A number of fractal dimension computing methods for the bed profiles and rough surfaces are analysed and compared systematically in terms of qualitative and quantitative point, and presented that calculating the fractal dimension of channel bed profiles and rough bedforms with the Structure Function Method and the Improved Cubic Covering Method respectively.
(4) Total resistance splitting methods such as Einstein Method, Jiang Guo-gan Method, Lotter Method and Weighted Averages Method are discussed and validated by the testing data. Comparatively, Einstein Method is optimal on the whole.
(5) Due to the limitations of Roughness-Size Method and Exposure-Degree Method, the fractal theory is suggested to be a better roughness description method, and the fractal function expression is obtained.
(6) The fractal relationships between sand grain roughness k_(s1) and grain resistance coefficient n_b ' and f_b' are developed, where the channel bed profile’s fractal dimension D which comprehensively reflected the rough characteristics formed by sediment with different sizes and random arrangements is introduced. Various kinds of experimental data are employed to validate the above relations, which indicates that the formulas are reasonable and the calculation accuracy are satisfactory.
(7) By introducing the channel bedform’s fractal dimension D , which fully reflected the three-dimensional bedform configurations, the fractal formulas of bedform roughness k_(s2) /Δand bedform resistance coefficient f b" are established respectively. Additionally, the relations of k_(s2) /Δand f_b" are derived, and their variationtrends are discussed.
(8) A trial improvement work to the Manning formula’s defects of dimensionally nonhomogeneous and influence factors ambiguous is conducted, and the dimensionally homogeneous and fractal refined Manning formula is preliminary achieved.
(1)河道床面形态具有自相似特征,可视为分形。采用分形理论中的一维和二维RMD模型,实现了在给定平面区域上生成不同分形维数、粗糙程度及分辨率的河道剖面轮廓及床面形态,模拟结果凸显了精细的微观粗糙结构。
(2)基于少量的数据资料,应用一元分形插值理论和二元分形插值理论分别实现了河道剖面轮廓及床面形态的分形重构,较好地克服了规则欧氏几何粗糙度测量中的尺度相关性和数据有限性问题。
(3)从定性与定量角度对剖面轮廓及粗糙表面分形维数的各种计算方法进行了系统分析比较,提出分别采用结构函数法和改进立方体覆盖法来计算河道剖面轮廓及床面形态的分形维数。
(4)对爱因斯坦法、姜国干法、洛特尔法以及加权平均法等综合阻力分割方法进行了分析讨论与验证比较,提出爱因斯坦法总体最优。
(5)探讨了糙率尺寸法及暴露度分析法在床面粗糙度表征中存在的问题,提出采用分形理论来研究具有自相似精细结构的床面粗糙度,确立了床面粗糙度分形表征函数的基本结构形式。
(6)建立了沙粒当量粗糙度k_(s1)与沙粒阻力系数n_b '及f_b'的分形关系式,式中引入的剖面轮廓分形维数D,可综合反映床沙粒径级配及随机排列所形成的粗糙形态,对公式的验证、分析与讨论表明,公式结构较为合理,计算精度令人满意。
(7)通过引入充分体现三维沙波床面特征(如平面沙波多寡、几何形态及分布状况等)的分形维数D,建立了沙波当量粗糙度k_(s2) /Δ及沙波阻力系数f_b"的分形关系式,导得了k_(s2) /Δ与f_b"之间的关系,讨论了f_b"随k_(s2) /Δ的变化规律。
(8)对曼宁公式存在的量纲不和谐及影响因素不明确两大缺陷进行了尝试性改进,初步建立了量纲和谐且经分形细化的曼宁公式。
Channel resistance is one of the basic topics of hydraulics and river dynamics, which determines the river’s capability of flood discharge and sediment transportation,it is a key parameter in the river improvement designs. Studies of channel resistance have an important theoretical meaning and wide application prospects. In this dissertation, a fractal research of bedform resistance is carried out based on the comprehensive approaches of theoretical analysis, numeric calculation and flume experiment. The main results can be summarized as follows:
(1) Channel bedforms which have self-similar characteristics can be regarded as fractals. Both the channel bed profiles and rough bedforms with different fractal dimensions, roughness and resolutions are generated respectively by using one-dimensional and two-dimensional RMD model in fractal theory, and the simulating results fully showed the fine microscopic rough structures.
(2) On the basis of limit measured data, the channel bed profiles and rough bedforms are reproduced accurately by using the unary and bivariate fractal interpolation methods, which well resolved the problems of scale correlation and information limitation existing in the regular Euclidean geometry model.
(3) A number of fractal dimension computing methods for the bed profiles and rough surfaces are analysed and compared systematically in terms of qualitative and quantitative point, and presented that calculating the fractal dimension of channel bed profiles and rough bedforms with the Structure Function Method and the Improved Cubic Covering Method respectively.
(4) Total resistance splitting methods such as Einstein Method, Jiang Guo-gan Method, Lotter Method and Weighted Averages Method are discussed and validated by the testing data. Comparatively, Einstein Method is optimal on the whole.
(5) Due to the limitations of Roughness-Size Method and Exposure-Degree Method, the fractal theory is suggested to be a better roughness description method, and the fractal function expression is obtained.
(6) The fractal relationships between sand grain roughness k_(s1) and grain resistance coefficient n_b ' and f_b' are developed, where the channel bed profile’s fractal dimension D which comprehensively reflected the rough characteristics formed by sediment with different sizes and random arrangements is introduced. Various kinds of experimental data are employed to validate the above relations, which indicates that the formulas are reasonable and the calculation accuracy are satisfactory.
(7) By introducing the channel bedform’s fractal dimension D , which fully reflected the three-dimensional bedform configurations, the fractal formulas of bedform roughness k_(s2) /Δand bedform resistance coefficient f b" are established respectively. Additionally, the relations of k_(s2) /Δand f_b" are derived, and their variationtrends are discussed.
(8) A trial improvement work to the Manning formula’s defects of dimensionally nonhomogeneous and influence factors ambiguous is conducted, and the dimensionally homogeneous and fractal refined Manning formula is preliminary achieved.
引文
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