河道床面形态分形量化方法比较研究

Comparison of Fractal Dimension Calculation Methods for Channel Bedforms

河道床面形态是河流动力学及河床演变学的基本问题,它与冲积河流的流动结构、水流阻力及泥沙输运等方面有密切联系.河道床面形态是水流、泥沙相互作用的结果,其平面或空间结构具有不规则性,而微观粗糙结构具有自相似性,因此,可采用分形几何学中的分形维数来进行量化,这更能反映粗糙结构的内禀特性.目前粗糙表面分形维数的计算方法有投影覆盖法及其改进方法、立方体覆盖法及其改进方法、小岛法、分形交集公式法以及分数布朗表面的统计性质法等,分析了确定河道床面形态分形维数的可行方法,讨论了不同方法的计算精度,提出改进立方体覆盖法更适于计算各向异性粗糙床面的分形维数,为从微观角度开展河床演变、水流阻力及航道治理等问题的分形研究奠定了基础.

Research on channel bedforms is one of the basic topics of river dynamics and fluvial process studies, since it was closely associated with the problems such as turbulent structure, flow resistance and sediment transportation in alluvial rivers. As a result of motion water flow interacting with sediment, channel bedforms have irregular plane or space structures and self-similar microstructures, which were better analyzed by fractal method to reflect the intrinsic rough characteristics. In this study, several existing fractal dimension calculation methods were analyzed qualitatively and compared quantitatively, along with the disscusion of their applicabilies and computational accuracies. The following methods are included in this paper: Projective Covering Method and its improved method, Cubic Covering Method and its improved method, Slit Island Method, Fractal Intersection Formula Method and Fractional Brownian Surface's Statistic Property Method. Finally, it is suggested that the Improved Cubic Covering Method is suitable for calculating fractal dimension of rough anisotropic channel bedforms, which can provide references for future microfractal studies on fluvial process, flow resistance and waterway regulations.