# Performance Evaluation of Seawalls in Mitigating a Real-World Tsunami Wave Using a Nonhydrostatic Numerical Wave Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Governing Equations and Turbulence Model

#### Governing Equations

## 3. Wave Condition

^{2}(*)) to describe the tsunami wave profile recorded during the 2011 Tohoku tsunami. This method has also been applied in some recent studies [10,42,47,48]. The combination of three sech

^{2}(*) waves proposed by Chan and Liu [37] can be formulated as:

^{−1}, and ${t}_{i}$= [9.67 16.33 21.63] min by Chan and Liu [37], as shown in Figure 1. It seems that the observed tsunami wave profile can be accurately reproduced by the combined sech

^{2}(*) wave, whereas the solitary wave profile does not closely resemble the observations. In the following sections, the wave profile described by Equation (9) is referred to as a “tsunami-like wave”.

#### 3.1. Solitary Wave Runup Processes on a Plane Beach

#### 3.2. Solitary Wave Overtopping the Seawall

## 4. Results and Discussion

#### 4.1. Hydrodynamic Phenomena

#### 4.2. Effects of Wave Height and Water Depth

#### 4.3. Effects of the Side Slope of the Seawall

#### 4.4. Effects of Beach Slope

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Comparison of the time series of wave profiles from field observation, solitary wave, and tsunami-like wave.

**Figure 2.**Comparison of the time series of the wave profiles of the solitary wave and the tsunami-like wave with $h$= 1 m and $H$ = 0.2 m.

**Figure 4.**Comparisons of the time series of water surface elevation at different wave gauges for $H/h$ = 0.054; (

**a**) WG1; (

**b**) WG2; (

**c**) WG3; (

**d**) WG4; (

**e**) WG5; (

**f**) WG6; (

**g**) WG7; (

**h**) WG8; (

**i**) WG9; (

**j**) WG10; (

**k**) WG11; (

**l**) WG12.

**Figure 5.**Comparisons of the time series of water surface elevation at different wave gauges for $H/h$ = 0.208; (

**a**) WG1; (

**b**) WG2; (

**c**) WG3; (

**d**) WG4; (

**e**) WG5; (

**f**) WG6; (

**g**) WG7; (

**h**) WG8; (

**i**) WG9; (

**j**) WG10; (

**k**) WG11; (

**l**) WG12.

**Figure 6.**Comparisons of the time series of water surface elevation at different wave gauges for H/h = 0.338; (

**a**) WG1; (

**b**) WG2; (

**c**) WG3; (

**d**) WG4; (

**e**) WG5; (

**f**) WG6; (

**g**) WG7; (

**h**) WG8; (

**i**) WG9; (

**j**) WG10; (

**k**) WG11; (

**l**) WG12.

**Figure 9.**Comparisons of the time series of water surface elevation at different wave gauges; (

**a**) WG1; (

**b**) WG2; (

**c**) WG3; (

**d**) WG4; (

**e**) WG5.

**Figure 10.**Comparisons of the spatial distributions of water surface elevations at different time instances; (

**a**) t = 9 s; (

**b**) t = 10 s; (

**c**) t = 11 s; (

**d**) t = 12 s; (

**e**) t = 13 s.

**Figure 13.**Snapshots of the velocity contours of the water body at different time instances; (

**a**) t = 42.5 s; (

**b**) t = 52.1 s; (

**c**) t= 53.2 s; (

**d**) t = 55.8 s.

**Figure 15.**Comparisons of the temporal evolutions of wave energies of the whole water body in the computational domain; (

**a**) $KE$; (

**b**) $PE$; (

**c**) $TE$.

**Figure 25.**Snapshots of the velocity contours of the water body at the moment of the tsunami-like wave climbing over the seawall with different sidewall slopes; (

**a**) side slope = 1:1; (

**b**) side slope = 1:2; (

**c**) side slope = 1:3; (

**d**) side slope = 1:4; (

**e**) side slope = 1:5.

**Figure 30.**Snapshots of the velocity contours of the water body at the moment of the wave crest climbing over the seawall with different sidewall slopes; (

**a**) beach slope = 1:30; (

**b**) beach slope = 1:25; (

**c**) beach slope = 1:20; (

**d**) beach slope = 1:15; (

**e**) beach slope = 1:10; (

**f**) beach slope = 1:5.

**Figure 32.**Variations in maximum runup height of overtopping water surge bores with different beach slopes.

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**MDPI and ACS Style**

Huang, J.X.; Qu, K.; Li, X.H.; Lan, G.Y.
Performance Evaluation of Seawalls in Mitigating a Real-World Tsunami Wave Using a Nonhydrostatic Numerical Wave Model. *J. Mar. Sci. Eng.* **2022**, *10*, 796.
https://doi.org/10.3390/jmse10060796

**AMA Style**

Huang JX, Qu K, Li XH, Lan GY.
Performance Evaluation of Seawalls in Mitigating a Real-World Tsunami Wave Using a Nonhydrostatic Numerical Wave Model. *Journal of Marine Science and Engineering*. 2022; 10(6):796.
https://doi.org/10.3390/jmse10060796

**Chicago/Turabian Style**

Huang, J. X., K. Qu, X. H. Li, and G. Y. Lan.
2022. "Performance Evaluation of Seawalls in Mitigating a Real-World Tsunami Wave Using a Nonhydrostatic Numerical Wave Model" *Journal of Marine Science and Engineering* 10, no. 6: 796.
https://doi.org/10.3390/jmse10060796