Statistical Analysis of Bed Load Transport over an Armored Bed Layer with Cluster Microforms
Abstract
:1. Introduction
2. Theoretical Backgrounds
3. Experimental Techniques and Methodology
3.1. Experimental Setup
3.2. Image Processing
4. Experimental Results
4.1. MSD Growth and Particle Diffusion Regimes
4.2. Particle Number Activity
4.3. Particle Velocity
4.4. Particle Step Length and Rest Period
5. Discussion
5.1. Comparison with Previous Experiments
5.2. Particle Diffusion Regime and Particle Motion Statistics
5.3. Limitations of the Present Study
6. Conclusions
- The scaling growth of the MSD with time showed that the particle diffusion regimes in this experiment varied at different time scales: the particle diffusion regime was superdiffusive at small time scales (T < 50 s), but became subdiffusive at larger time scales.
- The particle number activity followed a negative binomial distribution, which is consistent with the theoretical solution derived in Ancey et al. [22] by accounting for the collective entrainment processes. The power-law tails in the probability distributions of both the streamwise and transverse particle velocities indicated a significant amount of fast-travelling particles, whereas the negative tail in the streamwise particle velocity distribution indicated a noticeable amount of grains occasionally moved in the upstream direction, which has rarely been considered in previous experiments. This may be explained by the particle clusters over dual impact on bed load transport exerted by the armored bed layers: some particles are accelerated in the preferential paths between particle clusters, while others were obstructed by the clusters to produce negative streamwise particle velocities. The distributions of the transverse particle velocity, the step length and the rest period all displayed heavy tails that were well described by the α-stable and M-L distributions. Nonetheless, the effect of the armored bed layer with cluster microforms on the distributions of these parameters needs to be confirmed with more experimental data.
- The particle transport regime may be scale-dependent, i.e., the transport process may exhibit different diffusion regimes on different timescales. Meanwhile, the shapes of the distribution tails of the bed load motion parameters varied as observation time scale increases. We propose that the heavy tails in the distributions of the bed load motion parameters were associated with small time scales and may average out over longer observation periods. Nonetheless, the time scales associated with the transition of particle diffusion regimes and those with the changes in the statistical characteristics of bed load particle motions were different. Further investigation is needed in unraveling their connections.
Author Contributions
Funding
Conflicts of Interest
References
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Size Group | Median Size (mm) | Size Range (mm) | Weight Fraction (%) |
---|---|---|---|
1 | 0.45 | 0.25–0.8 | 10 |
2 | 1.0 | 0.6–1.25 | 15 |
3 | 3.0 | 1.0–5.0 | 25 |
4 | 7.0 | 5.0–10.0 | 25 |
5 | 17.0 | 15.0–20.0 | 25 |
Q (L/s) | H (cm) | Fr | Re | Θ | U* (m/s) |
---|---|---|---|---|---|
130 | 16.1 | 0.64 | 9.8 × 104 | 0.13 | 0.08 |
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Zhu, Z.; Zhang, S.; Chen, D. Statistical Analysis of Bed Load Transport over an Armored Bed Layer with Cluster Microforms. Water 2019, 11, 2082. https://doi.org/10.3390/w11102082
Zhu Z, Zhang S, Chen D. Statistical Analysis of Bed Load Transport over an Armored Bed Layer with Cluster Microforms. Water. 2019; 11(10):2082. https://doi.org/10.3390/w11102082
Chicago/Turabian StyleZhu, Zhenhui, Shiyan Zhang, and Dong Chen. 2019. "Statistical Analysis of Bed Load Transport over an Armored Bed Layer with Cluster Microforms" Water 11, no. 10: 2082. https://doi.org/10.3390/w11102082