552 / 2024-07-23 19:19:59

Experimental study on fractal characteristics and surface form resistance of riverbeds

Riverbed surface; evolution; resistance; fractal dimension

Subtheme 7: Sediment Regulation and Management > Topic 1: Sediments Transport Dynamics

Quantitative description of the surface morphology of movable riverbeds has received extensive research efforts in river dynamics, partly because it has intimate relationship with the calculation of bed from resistance. Meanwhile it also belongs to the research of complicate geometry morphology of fluvial landforms. The fractal theory has been successfully employed to solve many problems of surface morphology with fine and irregular structures in nature. The surface area-size method was employed to calculate the fractal dimension of movable riverbed surfaces in this research and its relations with both riverbed evolution and bed form resistance are analyzed through flume experiments and theoretical analyses. The results indicate that the fractal dimension D can reflect the dynamic processes of riverbed evolution including longitudinal deformation of the thalweg and transverse deformation of swales. The fluctuation degree λ_f, which can reflect the irregularity in both the longitudinal and transverse directions of a riverbed surface, is also analyzed, and it is found that the fluctuation degree increases with the fractal dimension. These imply that D can to some extent represent the roughness of riverbed surfaces and in turn influence the resistance. Based on the analysis, the equivalence roughness height of a movable riverbed is supposed to consist of two parts, with the former part being the fluctuation degree which is a linear function of D while the latter three times of d₉₀. The significant negative correlation between the non-dimensional resistance coefficient R^1/6/(ng^0.5) and relative roughness height (λ_f+3d₉₀)/R suggests the possible success of studying movable riverbed resistance employing the fractal dimension D according to the experimental results.

Quantitative description of the surface morphology of movable riverbeds has received extensive research efforts in river dynamics, partly because it has intimate relationship with the calculation of bed from resistance. Meanwhile it also belongs to the research of complicate geometry morphology of fluvial landforms. The fractal theory has been successfully employed to solve many problems of surface morphology with fine and irregular structures in nature. The surface area-size method was employed to calculate the fractal dimension of movable riverbed surfaces in this research and its relations with both riverbed evolution and bed form resistance are analyzed through flume experiments and theoretical analyses. The results indicate that the fractal dimension D can reflect the dynamic processes of riverbed evolution including longitudinal deformation of the thalweg and transverse deformation of swales. The fluctuation degree λ_f, which can reflect the irregularity in both the longitudinal and transverse directions of a riverbed surface, is also analyzed, and it is found that the fluctuation degree increases with the fractal dimension. These imply that D can to some extent represent the roughness of riverbed surfaces and in turn influence the resistance. Based on the analysis, the equivalence roughness height of a movable riverbed is supposed to consist of two parts, with the former part being the fluctuation degree which is a linear function of D while the latter three times of d₉₀. The significant negative correlation between the non-dimensional resistance coefficient R^1/6/(ng^0.5) and relative roughness height (λ_f+3d₉₀)/R suggests the possible success of studying movable riverbed resistance employing the fractal dimension D according to the experimental results.