基于分形理论的河床表面形态量化方法研究

Quantity Method of River Bed Surface Form Based on Fractal Theory

提出以河床表面分形维数从整体上量化河床形态,并依据表面积—尺度法原理,在对现有面分维计算方法的表面积估算、边界处理及无标度区判断等方面进行改进的基础上,给出了适用于具有不规则边界的表面分形维数计算方法,该方法对河床表面分维计算具有较好的适用性.将典型河段的年内冲淤变化、局部河势、河型与河床表面分形维数变化结合起来,说明了河床表面形态具有一定的分形特征,河床表面分形维数可随着河床的冲淤变化而改变,河床形态冲淤起伏愈剧烈,则河床表面分形维数愈大,其能定量反映河床形态的复杂程度,可用于河势量化分析、河型判别以及河道形态阻力计算等相关问题研究.

The river bed surface fractal dimension （BSD）is put forward to measure river bed. Based on improvements in some aspects of Surface area-Scale Method, such as, estimation of surface area, boundary treatment and judgment of non-scale range, the calculation method of surface fractal dimension with irregular boundary was obtained, and the new method had good applicability on the bed surface fractal dimension calculation. The fractal characteristics of river bed surface morphology were discussed by combination with river-pattern, river regime, river process and changes of BSD. The results showed that BSD could change with fiver process, the more severe bed form undulates, the greater BSD was. The BSD could reflect complexity of bed form quantitatively, which could be used to study some related problems, such as analysis of river regime, distinction of river pattern, calculation of river resistance and so on.