河床形态冲淤调整的分形度量

Fractal Measurement of River Bed Erosion and Deposition

将河流动力学与数学中的分形理论相结合,以河床冲淤较为剧烈的三峡坝下游典型分汊河段为例,分析了河床表面分形维数(BSD)的变化及其与相应河段平面、纵剖面、横断面冲淤调整特点的关系。结果表明:BSD具有时空变异性,一方面不同类型河段BSD是不同的,其可在一定程度上反映河型,甚至河型亚类的差异;另一方面同一河段BSD随河床冲淤进程亦发生相应变化,其与河床形态调整存在着必然联系。同时,BSD值与典型剖面形态的复杂程度呈正相关性,可从整体上描述河床表面形态冲淤起伏的剧烈程度。BSD作为河床表面形态冲淤起伏程度的定量工具,其在河流动力学领域中的河势量化分析、河型判别及河道形态阻力计算等方面将具有一定的参考价值。

Fractal theory is associated with river dynamics to study the method of quantifying riverbed surface form and its physical significance.Typical bifurcate reaches with severe riverbed erosion and deposition in downstream Three Gorges Dam are taken as the example to analyze the BSD（bed surface fractal dimension） variation and its relation with the erosion-deposition adjustment of the corresponding surface,longitudinal section,and cross-section of each reach.BSD can be used to reflect the nonlinear feature of the bed form variation across time and space,which is different for different reaches on the one hand,and changes along with the riverbed erosion-deposition adjustment on the other.It can also be used to describe the extent of the bed form adjustment as BSD value is positively correlated with the complexity of typical cross-section bed form.As a method of quantifying riverbed surface adjustment,BSD will be valuable for the quantitative analysis of river regime,the discrimination of river pattern,and the prediction of bed resistance tendency.