# Turbulent Kinetic Energy Distribution around Experimental Permeable Spur Dike

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## Abstract

**:**

## 1. Introduction

## 2. Physical Model

_{t}= 7.5 cm, the dike height H = 10 cm, the dike bottom width W

_{b}= 42.5 cm, the upstream slope ratio m

_{1}= 1:1.5, the backwater slope ratio m

_{2}= 1:2, and the downstream slope ratio m

_{3}= 1:2.5. The specific layout is shown in Figure 1.

_{p}as 0.025, the flow velocity scale λ

_{V}, roughness scale λ

_{n}, and the model roughness n

_{m}in the test are:

_{1}= 11 cm (Q

_{1}= 65 L/s), h

_{2}= 14 cm (Q

_{2}= 95 L/s), and h

_{3}= 17 cm (Q

_{3}= 135 L/s); dike porosity: P

_{1}= 6.8%, P

_{2}= 14.1% and P

_{3}= 22.5%. The pore sizes of the spur dikes are R

_{1}= 16 mm, R

_{2}= 20 mm, and R

_{3}= 32 mm. Table 1 shows the specific test conditions. In the test, the incoming flow velocity range is 0.25~0.4 m/s. A total of 13 cross sections for the velocity observation were arranged in the experimental section near the spur dike, and seven observation points were arranged on each cross section, where acoustic Doppler velocimeter (ADV) data were collected at 13 cross sections through the flume (Figure 1). The velocity data were collected at each observation point using the three-point method (0.2h, 0.6h, and 0.8h). The arrangement of the observed sections of groin and velocity is shown in Figure 1.

## 3. Calculation Method of Turbulent Kinetic Energy

_{0}(0.6h flow velocity) is used to treat the dimensionless turbulent kinetic energy, and the dimensionless form $E/{V}_{0}^{2}$ is obtained.

## 4. Flow Turbulence Kinetic Energy Distribution

#### 4.1. Effect of Submergence Degree on Kinetic Energy of Flow Turbulence

_{1}= 16 mm) and void ratio (P

_{1}= 6.8%) remain unchanged. Three submerged conditions, i.e., control water depth h

_{1}= 11 cm (Q

_{1}= 65 L/s), h

_{2}= 14 cm (Q

_{2}= 95 L/s), and h

_{3}= 17 cm (Q

_{3}= 135 L/s), are selected. The distributions of the turbulent kinetic energy at 0.2h, 0.6h, and 0.8h along the front section (2# cross section), the axis section (4# cross section), and the rear section (6# cross section) of the dike were analyzed.

#### 4.2. Effect of Porosity on Kinetic Energy of Flow Turbulence

_{2}= 20 mm) and control water depth (h

_{2}= 14 cm) remain unchanged. Three porosity conditions, P

_{1}= 6.8%, P

_{2}= 14.1%, and P

_{3}= 22.5%, were selected to analyze the distribution of the turbulent kinetic energy at 0.2h, 0.6h, and 0.8h along the front section (2# cross section or 3# cross section), the axis section (4# cross section), and the rear section (5# cross section or 6# cross section).

_{1}= 6.8% and P

_{2}= 14.1%, the turbulent kinetic energy near the two sides of the model flume was larger, but when P

_{3}= 22.5, the turbulent kinetic energy on both sides of the model flume was significantly reduced, especially near the groin side. At the cross section behind the dike, from the front of the dike head to the side of the dike root, the turbulent kinetic energy is the largest at 0.2h, the second largest at 0.6h, and the smallest at 0.8h. At the opposite side of the groin, the variation of the turbulent kinetic energy is opposite. The turbulent kinetic energy decreases first and then increases with the increase of the void fraction. The maximum turbulent kinetic energy section appears in the rear section of the dike under any void ratio conditions.

#### 4.3. Effect of Pore Size on Kinetic Energy of Flow Turbulence

_{3}= 17 cm) and void ratio (P

_{2}= 14.1%) remain unchanged. Three void size conditions, R

_{1}= 16 mm, R

_{2}= 20 mm, and R3 = 32 mm, are selected. The distributions of the turbulent kinetic energy at 0.2h, 0.6h, and 0.8h along the front section (2# cross section or 3# cross section), the axis section (4# cross section), and the rear section (5# cross section or 6# cross section) of the dike were analyzed.

_{1}= 16 mm is the smoothest, R

_{2}= 20 mm is relatively smooth, and R

_{3}= 32 mm fluctuates the most. From the dike root to the front end of the dike head, with the increase of the void size, the phenomenon that the turbulent kinetic energy first increases and then decreases gradually disappears, and it turns into a gradually decreasing phenomenon. Regardless of the size of the void, the section with the maximum turbulent kinetic energy appears in the section behind the dike.

## 5. Conclusions

- Near the front of the spur dike, the turbulent kinetic energy is the smallest at 0.2h, followed by 0.6h, and it is the largest at 0.8h. The turbulent kinetic energy increases with the increase of the submerged degree, increases with the increase of porosity, and shows a trend of first increase and then decrease with the increase of pore size;
- Near the dike axis, the turbulent kinetic energy is the smallest at 0.2h, followed by 0.6h, and it is the largest at 0.8h. The turbulent kinetic energy decreases with the increase of the submerged degree, firstly decreases and then increases with the increase of the porosity, and increases with the increase of the pore size. The position of the maximum turbulent kinetic energy moves from the dike root to the front end of the dike head with the increase of the submergence degree and porosity, and from the front end of the dike head to the dike root with the increase of pore size;
- The turbulent kinetic energy behind the spur dike has the maximum value in the entire experimental observation range, and the turbulent kinetic energy is the largest at 0.2h, followed by 0.6h, and it is the smallest at 0.8h. This change gradually decreases as it moves away from the dike body.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Turbulent kinetic energy distribution in front of the super dike under different submerged conditions. (

**a**) h

_{1}= 11 cm (2# section); (

**b**) h

_{2}= 14 cm (2# section); (

**c**) h

_{3}= 17 cm (2# section).

**Figure 3.**Turbulent kinetic energy distribution in dike axial section under different submerged conditions. (

**a**) h

_{1}= 11 cm (4# section); (

**b**) h

_{2}= 14 cm (4# section); (

**c**) h

_{3}= 17 cm (4# section).

**Figure 4.**Turbulent kinetic energy distribution in cross section behind spur dike under different submerged conditions. (

**a**) h

_{1}= 11 cm (6# section); (

**b**) h

_{2}= 14 cm (6# section); (

**c**) h

_{3}= 17 cm (6# section).

**Figure 5.**Turbulent kinetic energy distribution in front section of the super dike under different porosity conditions. (

**a**) P

_{1}= 6.8% (2# section); (

**b**) P

_{2}= 14.1% (2# section); (

**c**) P

_{3}= 22.5% (2# section).

**Figure 6.**Turbulent kinetic energy distribution in dike axial section under different porosity conditions. (

**a**) P

_{1}= 6.8% (4# section); (

**b**) P

_{2}= 14.1% (4# section); (

**c**) P

_{3}= 22.5% (4# section).

**Figure 7.**Turbulent kinetic energy distribution in cross section behind spur dike under different porosity conditions. (

**a**) P

_{1}= 6.8% (6# section); (

**b**) P

_{2}= 14.1% (5# section); (

**c**) P

_{2}= 22.5% (5# section).

**Figure 8.**Turbulent kinetic energy distribution in front section of the super dike under different pore size conditions. (

**a**) R

_{1}= 16 mm (2# section); (

**b**) R

_{2}= 20 mm (2# section); (

**c**) R

_{3}= 32 mm (2# section).

**Figure 9.**Turbulent kinetic energy distribution in dike axial section under different pore size conditions. (

**a**) R

_{1}= 16 mm (4# section); (

**b**) R

_{2}= 20 mm (4# section); (

**c**) R

_{3}= 32 mm (4# section).

**Figure 10.**Turbulent kinetic energy distribution in cross section behind spur dike under different pore size conditions. (

**a**) R

_{1}= 16 mm (6# section); (

**b**) R

_{2}= 20 mm (6# section); (

**c**) R

_{3}= 32 mm (6# section).

Run Title | Porosity (%) | Water Depth (cm) | Flow Rate (L/s) |
---|---|---|---|

TR1 | 6.8 | 11 | 65 |

TR2 | 6.8 | 14 | 95 |

TR3 | 6.8 | 17 | 135 |

TR4 | 14.1 | 11 | 65 |

TR5 | 14.1 | 14 | 95 |

TR6 | 14.1 | 17 | 135 |

TR7 | 22.5 | 11 | 65 |

TR8 | 22.5 | 14 | 95 |

TR9 | 22.5 | 17 | 135 |

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**MDPI and ACS Style**

Yu, T.; Yun, B.; Wang, P.; Han, L.
Turbulent Kinetic Energy Distribution around Experimental Permeable Spur Dike. *Sustainability* **2022**, *14*, 6250.
https://doi.org/10.3390/su14106250

**AMA Style**

Yu T, Yun B, Wang P, Han L.
Turbulent Kinetic Energy Distribution around Experimental Permeable Spur Dike. *Sustainability*. 2022; 14(10):6250.
https://doi.org/10.3390/su14106250

**Chicago/Turabian Style**

Yu, Tao, Baoge Yun, Pingyi Wang, and Linfeng Han.
2022. "Turbulent Kinetic Energy Distribution around Experimental Permeable Spur Dike" *Sustainability* 14, no. 10: 6250.
https://doi.org/10.3390/su14106250