# Identifying Flow Eddy Currents in the River System as the Riverbank Scouring Cause: A Case Study of the Mekong River

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site Selection

^{3}/s (10th largest river in the world) [23]. The discharge varies by season (rainy and dry), and the discharge at TC is approximately four times greater than that at CD [23]. The Mekong River in Vietnam has many riverbank failure cases (including the Vam Nao area) [24], which have caused serious livelihood loss and infrastructure damages.

#### 2.2. Mesh Generation

_{j}is the value of the points to be interpolated; z

_{i}is the value of the points adjacent to z

_{j}; d

_{i}

_{j}the distance between z

_{j}and z

_{j}, and n is the coefficient of the distance weight adjustment.

#### 2.3. Saint–Venant Equations

^{2}); v

_{t}is the diffusive coefficient (m

^{2}/s); Z is the water elevation (m); t is the time (s); S

_{h}is the source (m/s), and S

_{x}, S

_{y}: sources (m/s

^{2}).

#### 2.4. Navier–Stokes Equations

_{x}and F

_{y}are the sources (i.e., Coriolis) and component velocities of $\overrightarrow{U}$ with U (t, x, y, z). The input discharge at Nang Gu and the input water elevation at Binh Thuy were extracted from the outcome of TELEMAC2D, while the input discharge at Vam Nao station was measured data. In this study, we ran TELEMAC3D with the timestep of 4 s to obtain the major outputs of velocity (m/s), water elevation (m), and the eddy currents’ directions by layer.

#### 2.5. Model Assessment

_{sim}

_{,i}is the simulated water elevation, D

_{obs}

_{,i}is the observed water elevation, and i is hour. We expected to obtain the computed NSE (hourly) at 15 days, 3 months, and a year greater than 0.6, which indicates a satisfactory model [32]. The model performance was assessed for water elevation at the Vam Nao station. Because the simplification of TELEMAC3D is TELEMAC2D, the model assessment for TELEMAC2D also represents TELEMAC3D. The eddy currents and depth-averaged velocity vector directions can be directly and mathematically computed from TELEMAC2D and TELEMAC3D. The quality of the eddy currents depends upon the performance of TELEMAC2D and TELEMAC3D. This study verified the existence of the eddy currents confirmed by two local people who live in the area.

#### 2.6. Equipment and Tools

## 3. Results

#### 3.1. Model Calibration and Assessment

#### 3.2. Eddy Currents

#### 3.3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Simulated and observed water elevation H over 15 days for the friction of 0.016 (m). Notes: H_obs is the observed and H_sim is the simulated water elevation.

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**MDPI and ACS Style**

Nguyen, T.T.N.; Shih, D.-S.; Chua, L.H.; Kieu, H.N.; Ha, L.H.; Nguyen, L.H.; Luu, N.V.; Huynh, T.V.; Duong, L.M.; Ngo, A.T.;
et al. Identifying Flow Eddy Currents in the River System as the Riverbank Scouring Cause: A Case Study of the Mekong River. *Water* **2022**, *14*, 2418.
https://doi.org/10.3390/w14152418

**AMA Style**

Nguyen TTN, Shih D-S, Chua LH, Kieu HN, Ha LH, Nguyen LH, Luu NV, Huynh TV, Duong LM, Ngo AT,
et al. Identifying Flow Eddy Currents in the River System as the Riverbank Scouring Cause: A Case Study of the Mekong River. *Water*. 2022; 14(15):2418.
https://doi.org/10.3390/w14152418

**Chicago/Turabian Style**

Nguyen, Tanh T. N., Dong-Sin Shih, Lloyd HC Chua, Huyen N. Kieu, Linh H. Ha, Linh H. Nguyen, Ninh V. Luu, Thai V. Huynh, Linh M. Duong, An T. Ngo,
and et al. 2022. "Identifying Flow Eddy Currents in the River System as the Riverbank Scouring Cause: A Case Study of the Mekong River" *Water* 14, no. 15: 2418.
https://doi.org/10.3390/w14152418