# Numerical Study of the Hydrodynamics of Waves and Currents and Their Effects in Pier Scouring

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Numerical Model: REEF3D

#### 2.2. Hydrodynamics Calibration Test

#### 2.3. Hydrodynamics Behavior of the Flow around a Cylindrical Pile

#### 2.4. Scour around a Cylindrycal Pile

^{3}in density, a 30° angle of repose, and a dimensionless critical shear stress (${\tau}_{cr}^{*}$) equal to 0.036, in order to make the results obtained in this investigation for E01 and E02 comparable to those previously presented by Qi and Gao [26].

## 3. Results

#### 3.1. Hydrodynamics Calibration Test

#### 3.2. Hydrodynamics Behaviour of the Flow Around a Cylindrycal Pile

#### 3.3. Scour around a Cylindrycal Pile

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Identification of the comparison points of the average velocity profiles obtained from the numerical modeling and those published by Miles et al. [51].

**Figure 3.**Phase-average surface displacements comparison between experimental data (Umeyama [3]) and numerical results.

**Figure 4.**Instantaneous horizontal velocity profile comparison between the experimental data (Umeyama [3]) and numerical results for different time steps, for cases with waves alone.

**Figure 5.**Instantaneous horizontal velocity profile comparison between the experimental data (Umeyama [3]) and numerical results for different time steps, both for waves alone and for current cases.

**Figure 6.**Total flow velocity comparison between the experimental data (Qi and Gao [26]) and numerical results for waves alone and for current cases in the presence of a cylindrical pile.

**Figure 7.**Mean velocity profiles comparison between the experimental data (Miles et al. [51]) and numerical results associated with case C04, for waves perpendicular to the current cases in presence of a cylindrical pile.

**Figure 8.**Temporal behavior for velocities and vorticities near to the pile, waves and current are coming from the left to the right.

**Figure 9.**General description of the mean velocities and vorticities near the pile for the longitudinal and cross profiles (associated to the scenario E01). Waves and currents are move from the left to the right.

**Figure 11.**Bed shear stress made dimensionless with undisturbed bed shear stress amplification for each simulated case.

**Figure 12.**Maximum scour development comparison between the experimental data (Qi and Gao [26]) and numerical simulation results for cases E01 and E04.

**Figure 13.**The equilibrium scour estimated from numerical data and its comparison with the equilibrium scour obtained by other authors.

**Figure 14.**Equilibrium scour distribution according to absolute Froude number proposed by Qi and Gao [58].

**Figure 15.**Equilibrium scour distribution according to the absolute Froude number (${F}_{ra}^{\prime}$) proposed in this research.

Configuration | Definition |
---|---|

Boundary condition | Non-slip for velocities |

Non-slip for$\text{}k$ and $\omega $ | |

Logarithmic profile for inlet | |

Fix pressure at inlet | |

Zero-gradient outflow | |

Active wave absorption at outlet (waves) | |

Initialization | Potential flow for velocities |

Hydrostatic for pressure |

Case | $\mathit{L}$ (m) | $\mathit{W}$ (m) | ${\mathit{h}}_{\mathit{t}}\text{}\left(\mathbf{m}\right)$ | $\mathbf{\Delta}{\mathit{x}}_{\mathit{i}}\text{}\left(\mathbf{m}\right)$ | N° Cells | ${\mathit{t}}_{\mathit{t}\mathit{e}\mathit{s}\mathit{t}}\text{}\left(\mathbf{min}\right)$ |
---|---|---|---|---|---|---|

W1 | 24.00 | 0.70 | 1.00 | 0.01 | 16,768,400 | 5.00 |

W2 | 24.00 | 0.70 | 1.00 | 0.01 | 16,768,400 | 5.00 |

W3 | 24.00 | 0.70 | 1.00 | 0.01 | 16,768,400 | 5.00 |

WC1 | 24.00 | 0.70 | 1.00 | 0.01 | 16,768,400 | 5.00 |

WC2 | 24.00 | 0.70 | 1.00 | 0.01 | 16,768,400 | 5.00 |

WC3 | 24.00 | 0.70 | 1.00 | 0.01 | 16,768,400 | 5.00 |

C01 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 7.00 |

C02 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 7.00 |

C03 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 7.00 |

C04 | 24.00 | 24.00 | 1.00 | 0.01 | 575,968,400 | 1.00 |

E01 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 30.00 |

E02 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 30.00 |

E03 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 30.00 |

E04 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 30.00 |

E05 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 30.00 |

E06 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 30.00 |

E07 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 30.00 |

E08 | 24.00 | 1.00 | 1.00 | 0.01 | 23,968,400 | 30.00 |

_{i}is the dimension for the x, y, and z axis, due to the model using regular element definitions.

Case | $\mathit{h}$ (m) | $\mathit{H}$ (cm) | $\mathit{T}$ (s) | ${\mathit{U}}_{\mathit{C}}\text{}(\mathbf{cm}/\mathbf{s})$ |
---|---|---|---|---|

W1 | 0.30 | 1.03 | 1.00 | 0.00 |

W2 | 0.30 | 2.34 | 1.00 | 0.00 |

W3 | 0.30 | 3.61 | 1.00 | 0.00 |

WC1 | 0.30 | 0.91 | 1.00 | 8.00 |

WC2 | 0.30 | 2.02 | 1.00 | 8.00 |

WC3 | 0.30 | 3.09 | 1.00 | 8.00 |

Case | $\mathit{h}$ (m) | $\mathit{D}$ (m) | $\mathit{H}$ (cm) | $\mathit{T}$ (s) | ${\mathit{U}}_{\mathit{C}}\text{}(\mathbf{m}/\mathbf{s})$ | Direction |
---|---|---|---|---|---|---|

C01 | 0.50 | 0.20 | 2.60 | 1.40 | 0.23 | Codirectional |

C02 | 0.50 | 0.20 | 5.20 | 1.40 | 0.23 | Codirectional |

C03 | 0.50 | 0.20 | 8.50 | 1.40 | 0.23 | Codirectional |

C04 | 0.50 | 0.20 | 4.00 | 1.25 | 0.25 | Perpendicular |

**Table 5.**Simulated cases for the analysis of hydrodynamics due to the combined action of waves and currents.

Case | $\mathit{h}$ (m) | $\mathit{D}$ (m) | $\mathit{H}$ (m) | $\mathit{T}$ (s) | ${\mathit{U}}_{\mathit{C}}\text{}(\mathbf{m}/\mathbf{s})$ | ${\mathit{U}}_{\mathit{m}}\text{}(\mathbf{m}/\mathbf{s})$ | ${\mathit{U}}_{\mathit{c}\mathit{w}}$ | $\mathit{K}\mathit{C}$ | Direction |
---|---|---|---|---|---|---|---|---|---|

E01 | 0.50 | 0.20 | 0.085 | 1.40 | 0.23 | 0.12 | 0.65 | 0.86 | Codirectional |

E02 | 0.50 | 0.20 | 0.085 | 1.40 | 0.23 | 0.12 | 0.65 | 0.86 | Opposite |

E03 | 0.50 | 0.20 | 0.129 | 1.40 | 0.22 | 0.19 | 0.54 | 1.31 | Codirectional |

E04 | 0.50 | 0.20 | 0.129 | 1.40 | 0.22 | 0.19 | 0.54 | 1.31 | Opposite |

E05 | 0.50 | 0.20 | 0.150 | 2.00 | 0.24 | 0.28 | 0.47 | 2.76 | Codirectional |

E06 | 0.50 | 0.20 | 0.150 | 2.00 | 0.24 | 0.28 | 0.47 | 2.76 | Opposite |

E07 | 0.50 | 0.20 | 0.150 | 3.00 | 0.10 | 0.31 | 0.25 | 4.61 | Codirectional |

E08 | 0.50 | 0.20 | 0.150 | 3.00 | 0.10 | 0.31 | 0.25 | 4.61 | Opposite |

Case | ${\mathit{\tau}}_{\mathit{c}}^{*}$ | ${\mathit{\tau}}_{\mathit{w}}^{*}$ | ${\mathit{\tau}}_{\mathit{w}\mathit{c}}^{*}$ | $\frac{{\mathit{\tau}}_{\mathit{w}\mathit{c}}^{*}}{{\mathit{\tau}}_{\mathit{c}\mathit{r}}^{*}}$ | Regimen |
---|---|---|---|---|---|

E01 | 0.023 | 0.003 | 0.023 | 0.63 | Clear water |

E02 | 0.023 | 0.003 | 0.023 | 0.63 | Clear water |

E03 | 0.021 | 0.005 | 0.021 | 0.58 | Clear water |

E04 | 0.021 | 0.005 | 0.021 | 0.58 | Clear water |

E05 | 0.025 | 0.008 | 0.025 | 0.69 | Clear water |

E06 | 0.025 | 0.008 | 0.025 | 0.69 | Clear water |

E07 | 0.004 | 0.008 | 0.004 | 0.15 | Clear water |

E08 | 0.004 | 0.008 | 0.004 | 0.15 | Clear water |

**Table 7.**Adjustment parameter for equilibrium scour estimate and the results obtained from the numerical simulation.

Case | ${\mathit{a}}_{1}$ | ${\mathit{a}}_{2}$ | ${\mathit{a}}_{3}$ | ${\mathit{a}}_{4}$ | $\frac{{\mathit{S}}_{1}}{\mathit{D}}$ | $\frac{{\mathit{S}}_{\mathit{t}}}{\mathit{D}}$ | $\frac{{\mathit{S}}_{\mathit{t}}}{{\mathit{S}}_{1}}$ |
---|---|---|---|---|---|---|---|

E01 | 0.095 | 0.408 | 0.423 | 0.029 | 0.251 | 0.518 | 2.064 |

E02 | 0.330 | 0.078 | 0.006 | 1.078 | 0.161 | 0.336 | 2.083 |

E03 | 0.330 | 0.091 | 0.100 | 0.091 | 0.304 | 0.430 | 1.414 |

E04 | 7.663 | 0.230 | −7.365 | 0.234 | 0.151 | 0.298 | 1.976 |

E05 | 2.553 | 0.068 | −1.878 | 0.070 | 0.132 | 0.675 | 5.120 |

E06 | 0.755 | 0.002 | 0.149 | 0.089 | 0.110 | 0.626 | 5.711 |

E07 | 0.020 | 0.058 | 0.083 | 0.070 | 0.085 | 0.103 | 1.213 |

E08 | 0.081 | 0.067 | −0.006 | 0.416 | 0.060 | 0.075 | 1.242 |

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**MDPI and ACS Style**

Quezada, M.; Tamburrino, A.; Niño, Y.
Numerical Study of the Hydrodynamics of Waves and Currents and Their Effects in Pier Scouring. *Water* **2019**, *11*, 2256.
https://doi.org/10.3390/w11112256

**AMA Style**

Quezada M, Tamburrino A, Niño Y.
Numerical Study of the Hydrodynamics of Waves and Currents and Their Effects in Pier Scouring. *Water*. 2019; 11(11):2256.
https://doi.org/10.3390/w11112256

**Chicago/Turabian Style**

Quezada, Matias, Aldo Tamburrino, and Yarko Niño.
2019. "Numerical Study of the Hydrodynamics of Waves and Currents and Their Effects in Pier Scouring" *Water* 11, no. 11: 2256.
https://doi.org/10.3390/w11112256