# Using a PIV Measurement System to Study the Occurrence of Bursting in the Flow Over a Movable Scour Hole Downstream of a Groundsill

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

^{3}. The image velocimetry was then adopted to analyze the moving trajectories of the black particles projected on the soft light paper.

^{2}/s (M1), q2 = 0.0283 m

^{2}/s (M2), and q3 = 0.0475 m

^{2}/s (M3), respectively, and had mild slopes. The other types of cases were S1, S2, and S3 with the same unit discharge corresponding to the return periods of 10, 20, and 100 years, respectively, to calculate when S = 0.015. The bed slope was based on the average bed slope of the middle and lower reaches of this river in Taiwan. The slopes were selected as S = 1% and S = 1.5% in order to fully explore changes in the discharge with space and time for both mild and steep slopes. Lastly, the particle size referred to the riverbed of Lung-En auxiliary weir at a scale of 1:50. A medium value of particle size D

_{50}= 2.7 mm was adopted. Detailed information is shown in Table 1.

## 3. Results and Discussion

#### 3.1. The Phenomenon of Bursting and It’s Occurrence Frequency

_{t}). In order to verify the accuracy of the PIV measurement system, a preliminary test in a fully developed scouring zone to examine PIV measurement was implemented [18]. The results indicated that the PIV-measured profiles revealed good agreement with the curves presented by Nezu and Rodi [19], except that the region was very close to the water surface and had some noises. This may have been affected by lights from the outdoors. However, as our research focused on the flow field near the riverbed, the errors near the water surface could be ignored; case M2, which had a medium flow depth (H = 0.025 m), was selected for detailed observation in this study. The CCD camera recorded images of the scouring evolution of the downstream groundsill. The process of the evolution of scour holes can be divided into four phases: an initial phase, a development phase, a stabilization phase, and an equilibrium phase [11]. Lu et al. [18] conducted experiments to compare previous studies [31,32,33,34]. They indicated the turbidity of the flow was extremely high for the first 15 min, a very high scouring rate occurred during the first hour, and the scouring phenomenon almost reached equilibrium after 5 h. Thus, an initial phase of scouring within 15 min, a developing phase within 1 h, a stabilization phase of 5 h, and an equilibrium phase after 5 h was defined in this study. Figure 2 shows images of the non-equilibrium scouring process (T = 15 min). When the scour hole was in the developing stage, bursting occurred. At the beginning of the experiment, the scour hole was relatively small, and the nappe flow easily impacted the bed during the flow plume, so the scouring was rapid. The sediment was lifted within the water to form suspended solids that were directly transported away from the scour hole, as shown in Figure 2b. Moreover, as former bursting stopped until the next bursting occurred, the water flow in the scour hole was separated because of the impact on the bed by flow, which also served as a counter flow; see Figure 2c. In the initial stage of the development of the scour hole, bursting was found to be more frequent, and the duration of the occurrence of a single bursting event was shorter.

#### 3.2. Analysis of the Characteristics of Bursting on the Flow Fields

_{t}= ρu‘v’) was obtained based on a Shields diagram where the critical shear stress (τ

_{c}) = 2.1 N/cm

^{2}when D

_{50}= 2.7 mm. In this study, M2 was used as the representative group to calculate the dimensionless mean absolute Reynolds shear stress (τ

_{D}$=\left|\overline{{\tau}_{t}}\right|/{U}_{*}^{2}$) at the lowest point along the x direction at every 0.06 m for a comparison of the occurrence or non-occurrence of bursting, as shown in Figure 7. As can be clearly seen in Figure 7a, at T = 15 min, the dimensionless mean absolute Reynolds stress (τ

_{D}) significantly increased when the high-speed flow nappe approached the bed at the section of the scour hole (X = 0.06 m). When it flowed into the scour hole (X = 0.12 m), it could be found that the value of τ

_{D}was greater than 2 with the occurrence of bursting, and it was even higher with the non-occurrence due to the impingement of the high-speed flow nappe toward the channel bed near the entrance region. When T = 1 h, as shown in Figure 7b, when the scour hole developed, the range of bursting continued to increase. Therefore, after X = 0.18 m, the dimensionless mean absolute Reynolds stress with bursting continually increased, and then it exceeded the value of τ

_{D}with non-bursting. At T = 5 h, there was a great reduction in the frequency of bursting, and the lifting of sediment was also reduced. The calculation of the dimensionless mean absolute Reynolds stresses was averaged over all stages (before, during, and after) of bursting. Additionally, the τ

_{D}was slightly larger during bursting than non-bursting. It was also found that the dimensionless mean absolute Reynolds stress was larger than the critical shear stress when bursting occurred. Only after T = 5 h, due to the reduction in the frequency, did the average of τ

_{D}become smaller than the critical shear stress.

#### 3.3. Discussion of the Experimental Results with Scouring Exceedance Probability

_{t}) pulsation. Our statistical analysis adopted their ideas in this study to analyze the instantaneous Reynolds stress and then calculate the scouring exceedance probability (P

_{exc}):

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Plan view of the experimental channel (from Lu et al. [18]).

**Figure 2.**The actual photos and their schematic diagram of the bursting of the initial development of scouring at time (

**a**) 15 min 20 s, (

**b**) 15 min 23 s, and (

**c**) 15 min 28 s.

**Figure 3.**The actual photos and their schematic diagram of bursting near scouring equilibrium at time (

**a**) 2 h 58 min 14 s, (

**b**) 2 h 58 min 20 s, (

**c**) 2 h 58 min 35 s, (

**d**) 2 h 58 min 41 s, and (

**e**) 2 h 59 min 3 s.

**Figure 4.**Relationship between the frequency of bursting at T = 1 h and the cumulative maximum depth of the scour hole (y

_{ms}) of cases (

**a**) M1, (

**b**) M2, (

**c**) M3, (

**d**) S1, (

**e**) S2, and (

**f**) S3.

**Figure 5.**Relationship between the frequency of bursting at T = 5 h and the cumulative maximum depth of the scour hole (y

_{ms}) of cases (

**a**) M1, (

**b**) M2, (

**c**) M3, (

**d**) S1, (

**e**) S2, and (

**f**) S3.

**Figure 6.**Comparison of the measured mean velocity profiles in the scour hole during bursting for M2: (

**a**) T = 15 min, (

**b**) T = 1 h, and (

**c**) T = 5 h.

**Figure 7.**Comparison of the Reynolds stress ($\overline{\left|{\tau}_{t}\right|}{/U}_{*}{}^{2}$) near the bed during bursting for M2: (

**a**) T = 15 min, (

**b**) T = 1 h, and (

**c**) T = 5 h.

**Figure 8.**Comparison of the scouring exceedance probability (${P}_{exc}$) near the bed of the scour hole during bursting for M2: (

**a**) T = 15 min, (

**b**) T = 1 h, and (

**c**) T = 5 h.

Case | S (%) | H (m) | q (m ^{2}/s) | U (m/s) | ${\mathit{U}}_{*}$ (m/s) | F_{r} | R_{e} | B/h |
---|---|---|---|---|---|---|---|---|

M1 | 1.0 | 0.017 | 0.0167 | 0.98 | 0.0397 | 2.41 | 15757 | 35 |

M2 | 1.0 | 0.025 | 0.0283 | 1.13 | 0.0476 | 2.29 | 26045 | 24 |

M3 | 1.0 | 0.034 | 0.0475 | 1.40 | 0.0547 | 2.42 | 45533 | 18 |

S1 | 1.5 | 0.016 | 0.0167 | 1.04 | 0.0473 | 2.63 | 17327 | 38 |

S2 | 1.5 | 0.023 | 0.0283 | 1.23 | 0.0561 | 2.59 | 26206 | 26 |

S3 | 1.5 | 0.030 | 0.0475 | 1.58 | 0.0634 | 2.92 | 43053 | 20 |

_{r}= Froude number; R

_{e}= Reynolds number; and B/h = aspect ratio (flume width: B = 0.6 m).

**Table 2.**Exceedance probability of scouring at the maximum scouring depth for bursting or non-bursting on the case of T = 15 min and D

_{50}= 2.7 mm.

M1 | M2 | M3 | S1 | S2 | S3 | |
---|---|---|---|---|---|---|

Scouring exceedance probability with bursting | 53% | 52% | 43% | 35% | 47% | 47% |

Scouring exceedance probability without bursting | 11% | 13% | 27% | 18% | 19% | 32% |

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**MDPI and ACS Style**

Chang, C.-K.; Lu, J.-Y.; Lu, S.-Y.; Hsiao, K.-T.; Shih, D.-S.
Using a PIV Measurement System to Study the Occurrence of Bursting in the Flow Over a Movable Scour Hole Downstream of a Groundsill. *Water* **2020**, *12*, 1396.
https://doi.org/10.3390/w12051396

**AMA Style**

Chang C-K, Lu J-Y, Lu S-Y, Hsiao K-T, Shih D-S.
Using a PIV Measurement System to Study the Occurrence of Bursting in the Flow Over a Movable Scour Hole Downstream of a Groundsill. *Water*. 2020; 12(5):1396.
https://doi.org/10.3390/w12051396

**Chicago/Turabian Style**

Chang, Cheng-Kai, Jau-Yau Lu, Shi-Yan Lu, Kuo-Ting Hsiao, and Dong-Sin Shih.
2020. "Using a PIV Measurement System to Study the Occurrence of Bursting in the Flow Over a Movable Scour Hole Downstream of a Groundsill" *Water* 12, no. 5: 1396.
https://doi.org/10.3390/w12051396