# Experimental Investigation of Coastal Flooding Hydrodynamics Using a Hybrid Defense System

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Apparatus and Procedures

_{tank}= 0.40, 0.50, and 0.60 m) and a constant water level (H

_{c}= 0, 0.07, 0.10, and 0.14 m). A minimum of three tests were conducted for each case; then their average was presented.

#### 2.2. Measurement Method

#### 2.3. Examined Parameters

#### 2.3.1. Flow Velocity Reduction

^{−1}] and ${V}_{t}$ is the velocity of the bore after the platform by considering the measured data of St.3 and St.4 [ms

^{−1}].

#### 2.3.2. Reflection Coefficient

_{R}) was used to examine the reflected wave characteristics of the studied defense systems as a representative of the reflected energy. We adopted a similar approach to Huang et al. [44] as follows:

_{Bore}is the maximum bore height at St.1 for the test section [m] and H

_{R}is the maximum height of the reflected bore at St.1 [m].

#### 2.3.3. Hydrodynamic Force

^{−3}], ${C}_{D}$ is the drag coefficient, ${A}_{f}$ is the frontal area of the models [m

^{2}], u is the flow velocity [m s

^{−1}], ${C}_{M}$ is the inertia coefficient, $\forall $ is the volume of the submerged model [m

^{3}], and $\frac{\partial u}{\partial t}$ is the horizontal flow acceleration [ms

^{−2}]. As Imai and Matsutomi pointed out, at the early stage of inundated flow, the inertia force reaches 50% of the maximum drag force; whereas after the bore is developed to the quasi-steady state condition, the drag force becomes dominant. Therefore, the drag force is considered the main component of the total instantaneous hydrodynamic force absorbed by the vegetation model in the test section [45]:

#### 2.3.4. Force and Moment Indices

_{t}) and the water depth at St.4 (h

_{t}). The maximum reduction rates of the drag force index (RFI) and the moment index (RMI) are calculated as follows:

## 3. Results and Discussion

#### 3.1. Generated Bore Characteristics

_{Bore}is in the range of 0.093 to 0.172 m. Due to the presence of the defense system models, the bore front collision causes the water to splash over the models, accompanied by turbulence in the initial moments.

_{t}) versus the incident bore height (H

_{Bore}). As seen, due to the amplification of the bore height and the streamlines through the test section, the transmitted flow height H

_{t}measured at St.4 does not show a remarkable decrease for the control case compared with both the STDS and RCDS cases. The same observation is also reported by Zaha et al. [29] and Ahmed and Ghumman [46] for their hybrid defense systems. This might be attributed to the experimental limitations and narrow width of the modeled forest.

_{t}) versus the incident bore velocity (V

_{Bore}). As seen, contrary to the bore velocity upstream of the test section, the transmitted velocity decreases downstream of the test section. Flow velocity in the presence of the STDS model and the RCDS model, respectively, decreased by an average of 29.5% and 56.2%. The fitted graphs’ growth rate compared to the control case decreased by 47.5% and 68.7%, respectively. A close look at Figure 3, Figure 4 and Figure 5 indicates that in the hybrid defense system, by changing flow conditions, the drag forces reduced and the reef ball arrangement may influence the mitigation effect of the defense system.

_{Bore}and V

_{t}) and the height values at St.1 and St.4 (H

_{Bore}and H

_{t}), showed similar changes in the flow Froude number and flow velocity. As seen in Figure 6, the Froude numbers upstream and downstream of the platform were reduced, respectively, by 49% and 79% for the STDS model and the RCDS model. Also, the growth rate of the fitted graphs decreased by 68% and 91% compared to the control case for the STDS and RCDS models.

#### 3.2. Drag Forces

_{D}) of the STDS and RCDS models are depicted in Figure 7. The measured reduced drag force is equal to the maximum shear force absorbed by the defense section when the bore is passing through it. As expected, the drag force is decreased for the tests with defense system models under similar flow conditions. The exerted force imposed on the defense system models is evaluated for the vegetation and reef balls with a similar method to Husrin [47] and Fathi-Moghadam et al. [43]. As can be seen from Figure 7, by increasing the bore Froude number (Fr

_{Bore}), more force is absorbed by both defense systems.

_{f}grows, and more force will be induced into the models. Using the RCDS instead of the STDS in a constant flow increases the absorption of the induced forces. This is partly due to the increased A

_{f}, which the reef ball models added to the STDS. The absorbed force by the compound model increased by 89% to 249% compared to the STDS model for the flow with the minimum and maximum Fr

_{Bore}, respectively. On average, the RCDS produced a 150 percent improvement in flow-damping performance.

_{D}with the incident flow Froude number (Fr

_{Bore}) is shown in Figure 8 for both defense systems. The drag coefficient (C

_{D}) for each defense system is calculated using Equation (5), considering the models’ frontal area (A

_{f}), incident flow velocity (V

_{bore}) passed through St.1 and St.2 from ultrasonic sensors and the drag force. As mentioned earlier, the incident bore with a higher Froude number has higher velocities and induces higher hydrodynamics force.

_{f}and covered surface density which causes a decrease in the drag coefficient for the RCDS. This reduction in C

_{D}values is the result of the mutual interaction of the defense system elements. The used equation for the calculation of C

_{D}(see Equation (5)) does not consider the possible interaction of models and their different behavior for different interactions. This reduction in drag coefficient range due to the amplification of vegetation density because of mutual interaction has been reported in previous studies see among others [43,44,46,51].

#### 3.3. Defense System Performance

#### 3.3.1. Effect on Velocity Reduction Rate

_{f}and the increase in turbulence behind the test section due to the presence of the porous structures.

#### 3.3.2. Effect on Reflection Coefficient

_{reef}) is assumed to greatly impact the bore reflection seaward, RFI, and RMI [29,30]. Therefore, ‘the non-dimensional bore height’ (${H}^{*}$) was defined by dividing the maximum bore height by the root of the reef ball frontal area as follows:

_{r}versus the non-dimensional bore height are presented in Figure 10. As seen for the RCDS model, this varied from 0.71 for the lowest ${H}^{*}$ to 0.35 for the highest ${H}^{*}$. As the height of the incident bore increases, the inundation depth increases, while the frontal area engages a smaller percentage of the current. Hence, a reduction in the value of C

_{r}seems reasonable.

#### 3.3.3. Effect on RFI and RMI

_{40}represents 40 rows of tree models, and V

_{S40}represents 40 rows of submerged tree models.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Experimental setup: (

**a**) picture of designed lifting gate, (

**b**) schematic sketch of experiments.

**Figure 6.**Comparison of transmitted flow Froude number (Fr

_{t}) with bore Froude number (Fr

_{bore}).

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**MDPI and ACS Style**

Yeganeh-Bakhtiary, A.; Kolahian, M.; Eyvazoghli, H.
Experimental Investigation of Coastal Flooding Hydrodynamics Using a Hybrid Defense System. *Water* **2023**, *15*, 2632.
https://doi.org/10.3390/w15142632

**AMA Style**

Yeganeh-Bakhtiary A, Kolahian M, Eyvazoghli H.
Experimental Investigation of Coastal Flooding Hydrodynamics Using a Hybrid Defense System. *Water*. 2023; 15(14):2632.
https://doi.org/10.3390/w15142632

**Chicago/Turabian Style**

Yeganeh-Bakhtiary, Abbas, Mohammadreza Kolahian, and Hossein Eyvazoghli.
2023. "Experimental Investigation of Coastal Flooding Hydrodynamics Using a Hybrid Defense System" *Water* 15, no. 14: 2632.
https://doi.org/10.3390/w15142632