A velocity-variation-based formulation for bedload particle hops in rivers
A velocity-variation-based formulation for bedload particle hops in rivers
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DOI：
10.1017/jfm.2020.1126
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发表时间：
2021-02
影响因子：
3.7
通讯作者：
Zi Wu;Arvind Singh;E. Foufoula‐Georgiou;M. Guala;Xu-dong Fu;Guangqian Wang
中科院分区：
文献类型：
--
作者：
Zi Wu;Arvind Singh;E. Foufoula‐Georgiou;M. Guala;Xu-dong Fu;Guangqian Wang
摘要
推移质颗粒的跳跃被定义为颗粒从起始到停止的连续运动，它是河流中推移质泥沙输运最基本的过程之一。尽管最近分别针对短跳跃和长跳跃确定了两种输运模式，但仍然缺乏一种理论来解释进行短跳跃的颗粒的平均跳跃距离 - 运动时间比例关系，短跳跃在输运中占主导地位，可能占总跳跃事件的80%以上。在本文中，我们提出了一种基于速度变化的公式，其控制方程与溶质在剪切流中的泰勒弥散控制方程本质上相同。关键参数，即扩散系数，可以由跳跃距离和运动时间确定，这比颗粒加速度更容易测量且更准确。我们首次获得了一个对整个运动时间范围都有效的平均跳跃距离 - 运动时间关系的解析解，该解析解与实测数据吻合良好。关于运动时间，我们根据不同的标度指数确定了三种不同的模式：初始模式约为1.5，过渡模式约为5/3，它们定义了短跳跃，而泰勒弥散模式为1，定义了长跳跃。跳跃距离的相应分布通过解析得到并经过实验验证。我们还表明，爱因斯坦提出的常规使用的指数分布仅适用于长跳跃。通过将模拟加速度与测量值进行比较，进一步验证了本文提出的公式。
Abstract Bedload particle hops are defined as successive motions of a particle from start to stop, characterizing one of the most fundamental processes of bedload sediment transport in rivers. Although two transport regimes have been recently identified for short and long hops, respectively, there is still the lack of a theory explaining the mean hop distance–travel time scaling for particles performing short hops, which dominate the transport and may cover over 80 % of the total hop events. In this paper, we propose a velocity-variation-based formulation, the governing equation of which is intrinsically identical to that of Taylor dispersion for solute transport within shear flows. The key parameter, namely the diffusion coefficient, can be determined by hop distances and travel times, which are easier to measure and more accurate than particle accelerations. For the first time, we obtain an analytical solution for the mean hop distance–travel time relation valid for the entire range of travel times, which agrees well with the measured data. Regarding travel times, we identify three distinct regimes in terms of different scaling exponents: respectively, $\sim$1.5 for the initial regime and $\sim$5/3 for the transition regime, which define the short hops, and 1 for the Taylor dispersion regime defining long hops. The corresponding distribution of the hop distance is analytically obtained and experimentally verified. We also show that the conventionally used exponential distribution, as proposed by Einstein, is solely for long hops. Further validation of the present formulation is provided by comparing the simulated accelerations with measurements.