Theoretical analysis for bedload particle deposition and hop statistics

推移质 热扩散率 机械 统计物理学 粒子(生态学) 沉积(地质) 物理 统计 地质学 数学 泥沙输移 热力学 古生物学 海洋学 沉积物
作者
Zi Wu,Weiquan Jiang,Li Zeng,Xudong Fu
出处
期刊:Journal of Fluid Mechanics [Cambridge University Press]
卷期号:954 被引量:28
标识
DOI:10.1017/jfm.2022.959
摘要

Understanding the statistics of bedload particle motions is of great importance. To model the hop events which are defined as trajectories of particles moving successively from the start to the end of their motions, recently, Wu et al. ( Water Resour. Res. , vol. 56, 2020, p. e2019WR025116) have successfully performed individual-based simulations according to the Fokker–Planck equation for particle velocities. However, analytical solutions are still not available due to (i) difficulties in treating the velocity-dependent diffusivity, and (ii) a knowledge gap in incorporating the termination of particle motions for the equation. To tackle the above-mentioned challenges, we first specify a Robin boundary condition representing the deposition of particles. Second, for analytical solutions of hop statistics, a variable transformation is devised to deal with the velocity-dependent diffusivity. The original bedload transport problem is thus found to be governed by the classic equation for the solute transport in tube flows with a constant diffusivity after the transformation. Finally, through solving the spatial and temporal moments of the governing equation, we investigate the influence of the deposition rate on three key characteristics of particle hops. Importantly, we have related the deposition rate to the mean travel times and hop distances, enabling a direct determination of this physical parameter based on measured particle motion statistics. The analytical solutions are validated by experimental observations with different bedload particle diameters and transport conditions. Based on the limited experimental datasets, the deposition frequency is shown to decrease as the shear stress increases when the flow rate is not small.
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