沙波阻力分形表征的定床试验研究

Immovable Bed Experiment Study on the Resistance of Sand Wave Characterized by Fractal Dimension

针对沙波床面形态具有自相似性的特点,将分形几何方法引入沙波阻力问题研究,提出采用分形维数描述沙波床面的三维特征,并应用改进立方体覆盖法计算分形维数值.床面阻力根据爱因斯坦综合阻力分割方法计算,并按摩阻作用可加性原理划分为沙粒阻力与沙波阻力.在试验基础上,引入沙波几何尺度参数和平面分布参数,建立了沙波阻力系数的表达式.对公式的验证、分析和比较表明,本文公式可定量地综合体现沙波床面的三维特征对沙波阻力的影响,在某种意义上是对现有结果的改进.

Considering the self-similar features of channel bed configurations（ CBC）, fractal geometry method was applied to bed form resistance study to use fractal dimension to describe the 3D characteristics of CBC. The value of fractal dimension was calculated with improved-cubiccovering-method. The total bed resistance was determined according to the Einstein＇ s method by divided it into sand grain resistance and bed form resistance with the additive principle. With the heuristic hints of physical experimental results, the parameters, such as the sand waves geometric scale and plane distribution, were introduced, and the fractal formula of bed form resistance coefficient was finally developed. The investigated results showed that the formula develop in this paper could be both quantitatively and comprehensively reflect how the bed form resistance was infulenced by the 3D characteristics of CBC, which can be regarded as an improvement on the existing results to some extent.