Application of Hausdorff fractal derivative to the determination of the vertical sediment concentration distribution
Application of Hausdorff fractal derivative to the determination of the vertical sediment concentration distribution
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DOI：
10.1016/j.ijsrc.2022.07.007
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发表时间：
2022-11-08
影响因子：
3.6
通讯作者：
Zheng, Chunmiao
中科院分区：
文献类型：
--
作者：
Sun, Hongguang;Nie, Shiqian;Zheng, Chunmiao
在定常挟沙水流中，悬沙浓度分布常采用Rouse公式及其变形公式计算，其中扩散通量假定为Fickian。湍流，然而，具有分形特性，导致非菲克扩散通量的泥沙颗粒。为了表征非Fickian动力学的悬浮泥沙，目前的研究提出了一个基于Hausdorff分形导数的对流-弥散方程（HADE）模型，其中的Fickian扩散通量在Rouse模型中被替换为分形导数重新缩放使用恒定的扩散率。设计了Hausdorff分形导数的阶数来表征多重分形湍流结构对泥沙扩散的影响。应用结果表明，HADE模型的解析解用指数函数表示，能较准确地描述不同粒径悬沙浓度垂线分布。这种改进很好地捕捉到了湍流中垂直泥沙浓度的非指数衰减。实测含沙量剖面的进一步分析表明，Hausdorff分形阶数随Rouse参数而降低，Rouse参数描述了湍流的更强影响和较小颗粒的更均匀的含沙量剖面。模型比较还表明，HADE模型提供了更好的性能，在描述泥沙浓度剖面比改进的劳斯公式和标准的分数阶导数对流-弥散方程（FADE），无论是低估或高估的泥沙颗粒的垂直位移，可能是由于相干湍流结构。(c)2022年国际侵蚀和沉积研究和培训中心/世界沉积和侵蚀研究协会。Elsevier B. V.出版，保留所有权利。
The Rouse formula and its variants have been widely used to calculate the steady-state vertical con-centration distribution for suspended sediment in steady sediment-laden flows, where the diffusive flux is assumed to be Fickian. Turbulent flow, however, exhibits fractal properties, leading to non-Fickian diffusive flux for sediment particles. To characterize non-Fickian dynamics of suspended sediment, the current study proposes a Hausdorff fractal derivative based advection-dispersion equation (HADE) model, where the Fickian diffusive flux in the Rouse model is replaced by a fractal derivative re-scaled using a constant diffusivity. The order of the Hausdorff fractal derivative is designed to characterize the influence of the multi-fractal turbulence structure on sediment diffusion. Applications show that the HADE model, with the analytical solution expressed using a stretched exponential function, can accu-rately describe the observed vertical concentration profiles for suspended sediment with different sizes. This improvement well captures the non-exponential decay of the vertical sediment concentration in turbulent flow. Further analyses of measured sediment concentration profiles reveal that the Hausdorff fractal order decreases with the Rouse parameter, which describes the stronger impact of turbulent flow and a more uniform sediment concentration profile for smaller particles. Model comparisons also show that the HADE model provides better performance in describing the sediment concentration profiles than the improved Rouse formula and the standard fractional derivative advection-dispersion equation (FADE), which either under-or over-estimates vertical displacement of sediment particles, likely due to coherent turbulent structures.(c) 2022 International Research and Training Centre on Erosion and Sedimentation/the World Association for Sedimentation and Erosion Research. Published by Elsevier B.V. All rights reserved.