弯曲河段床面粗糙高度的分形研究

Fractal study on roughness height of river bed in meander reach

根据水槽试验的结果,从河床表面物理形态特征入手,分析了粗糙高度ks与河床表面分形维数D的关系,并进一步分析了D与糙率系数n的关系。结果表明床面粗糙高度ks可通过床面三维起伏度r来表达,r与D之间遵循幂指数的增长关系,即ks与D之间定量函数关系式可通过幂指数函数表达。因此描述n与D之间的定量函数关系也可进一步建立起来。在忽略其他影响因素的条件下,床面形态分形维数D和水流条件R均会引起糙率系数n值的变化,两者作用效果相反。因此n值的变化趋势取决于两者之间的对比关系;同时公式中的两系数a、b的变化对n值的变化亦存在相反的作用,但系数b的影响远大于系数a的影响。

Based on flume experimental result,river bed form was studied quantitatively by fractal dimension D of river bed surface. Relationships between n and D were analyzed qualitatively. The function between k_s and D has been established based on the morphological characteristics of river bed surface,finally the formula of n depending on D is established by theoretical analysis. Results indicate that there is obvious positive correlation between n and D,but D is not the only factor,because n is also related with flow movement conditions.Three dimension fluctuation degree rcan represent k_s,a power exponent function can be used to depict the increasing relation between r and D,then the function between k_sand D also is depicted by power exponent function,therefore the formula of n depending on D is established by theoretical analysis. Form parameter D and flow movement parameter R are the main factors influencing n if the other factors can be neglected,but these factors have the opposite effect,so the trend of n depends on the contrast strength; meanwhile the coefficient a and b has the same impact as the D and R,but the effect of a is larger than that of b.