Fractal Characteristics Of Channel Bedform Resistance

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.