# Study on the Formation Characteristics and Disaster Mitigation Mechanisms of Rip Currents on Arc-Shaped Beach

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## Abstract

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## 1. Introduction

## 2. Study Area Overview and Numerical Model

#### 2.1. Overview of the Study Area

#### 2.2. Numerical Model

#### 2.3. Test of the FUNWAVE-TVD Model in Simulating Rip Currents

## 3. Result of Rip Current Characteristics in Dadonghai Region under Different Wave Conditions

_{d}represents the bottom friction coefficient. The larger the value of C

_{d}, the greater the bottom friction, resulting in a more pronounced hindrance to fluid flow. Choi et al. [31,41] calculated and compared the coastal circulation on-site, with values falling between 0.001 and 0.003. In this study, a value of 0.0025 was selected within this range. The specific working condition parameter settings are shown in Table 2.

#### 3.1. Effect of Significant Wave Height and Peak Period on Rip Current Characteristics

^{−1}, where (u, v) is the depth-averaged instantaneous velocity components with (x, y) coordinates. This phenomenon is vividly depicted in Figure 12, which shows a series of vortex pairs emerging near the arc-shaped beach. Simultaneously, the trajectories of the vortices with the rip currents are observed in the cross-shore direction. As the significant wave height increases, the complexity of these vortices within the arc-shaped beach region increases. Furthermore, the vortices flanking both sides of the bay gradually migrate cross-shore with the increase in the significant wave height, leading to a concomitant decrease in their strength. The movement of vortices initially depends on the morphology of sandbar channels. Extensive research by Brocchini et al. [20] focused on the vortices formed near submerged breakwaters and structures, revealing that vortices move almost perpendicular to the shoreline. A similar phenomenon is observed near y = 900 m under the condition of a significant wave height of 0.75 m (Figure 12a) in this study. Vortices generated by wave breaking extend outward to the sea through self-advection, with the detachment of vortices also observed in their movement trajectories. Vortices generated by the sloping coastline remain consistently active and tend to move toward the channel. A similar trend is observed between y = 200 and 400 m. As the significant wave height increases, a number of shore eddies form near the coastline due to wave breaking, resulting in complex interactions between sandbars and shore eddies. These eddies move away from the shoreline, but their recirculation trajectories become intricate due to their interactions. The distribution of eddies simulated in this paper shows asymmetry, contrary to the findings of Brocchini et al. [20], which may be due to the excessive width of the channel in the computed region. In Figure 12, the intensity near the coast may be related to the weakening of the shore eddies due to wave refraction when the channel width is small, as mentioned in Kennedy’s paper [21]. Additionally, the migration trajectories of vortices can be observed on both sides of the bay entrance, where a substantial number of shore eddies are formed due to the influence of natural topography, with variations in the significant wave height minimally impacting the migration trajectories of vortices.

#### 3.2. Effect of Incident WAVE Angle on Rip Current Characteristics

## 4. Methods to Reduce Rip Currents

#### 4.1. Effect of Bottom Friction on Rip Current Characteristics

_{d}) of 0.0025 (Figure 18a), the trajectory extension of rip currents near the y = 800 m boundary of the computational domain is clearly observable. Notably, deflection rips with high flow velocity are also present on both sides of the bay. However, as C

_{d}is increased to 0.02 (Figure 18b), the strength of the deflection rips on both sides of the bay and the rip currents at y = 800 m within the arc-shaped beach area decreases. This trend becomes more pronounced as C

_{d}increases to 0.04 (Figure 18c). This observed phenomenon can be attributed to the fact that increased bottom friction leads to reduced wave propagation speed, wave breaking and wave height. In general, increased bottom friction reduces the strength of rip currents, providing valuable insights into rip current management. In practical marine environments, the introduction of rocks and other structures to enhance bottom roughness can effectively mitigate rip currents.

_{d}= 0.02 and C

_{d}= 0.04). The result is shown in Figure 19. Increasing the topographical roughness amplifies wave dispersion and attenuation, thereby changing wave velocity distributions. At a lower friction coefficient of 0.0025, representing a smoother seabed, wave attenuation is less pronounced, primarily impacting areas where nearshore rip currents are prevalent. However, as the topographical roughness increases, wave attenuation and the complexity of wave–current interactions in the nearshore zone increase substantially. In these scenarios, the current field forms structures such as turbulence and eddies, which, in turn, affect wave dynamics. Additionally, a rougher seabed augments bottom shear stress in the current field, thereby intensifying turbulence within the boundary layer. In the area between x = 400 and 600 m, a shallower water depth leads to more noticeable wave attenuation. Near y = 600 m, wave phase changes are evident, resulting from interactions between longshore currents and waves. Figure 18 further demonstrates a decrease in the longshore current velocity, attributed to the influence of the rough bottom in the nearshore region [48]. Along both sides of the bay, currents predominantly arise from wave breaking, primarily along the coastline. An increase in the topographical roughness correlates with a reduction in near-seabed currents, consequently diminishing the intensity of the resulting deflection rips.

#### 4.2. Influence of Water Depth at Channel Positions on Rip Current Formation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Topography and water depth setting map of Dadonghai. (

**a**) Topographic map; (

**b**) Depth setting chart.

**Figure 3.**Numerically simulated topography and water depth setting chart. (

**a**) Numerically simulated topography; (

**b**) Water depth setting of the numerical topography.

**Figure 6.**Computed spatial distributions of averaged velocities for different significant wave heights (T

_{p}= 5.0 s).

**Figure 7.**Computed spatial distributions of averaged velocities for different significant wave heights (T

_{p}= 10.0 s).

**Figure 14.**Computed spatial distributions of averaged velocities for incident wave direction (H

_{s}= 2.0 m, T

_{P}= 5.0 s the arrows in the figure indicate the direction of the wave).

**Figure 15.**Computed mean water levels for different incident wave directions (H

_{s}= 2.0 m, T

_{P}= 5.0 s the arrows in the figure indicate the direction of the wave).

**Figure 16.**Average vorticity of cases with varying incident wave directions (H

_{s}= 2.0 m, T

_{P}= 5.0 s the arrows in the figure indicate the direction of the wave).

**Figure 18.**Computed spatial distributions of averaged velocities for different bottom frictions (H

_{s}= 2.0 m, T

_{p}= 5.0 s, θ = 0°).

**Figure 21.**Computed spatial distributions of averaged velocities for different water depths in different channels (H

_{s}= 2.0 m, T

_{p}= 5.0 s, θ = 0°).

Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean monthly wave height (m) | 1.1 | 1.0 | 0.8 | 0.9 | 0.8 | 0.9 | 1.0 | 0.8 | 0.7 | 1.2 | 0.9 | 1.2 |

Mean monthly wave period (s) | 4.6 | 4.4 | 4.1 | 4.2 | 3.8 | 4.1 | 4.3 | 4.2 | 4.3 | 4.7 | 4.0 | 4.3 |

Tests | Significant Wave Height/m | Peak Period/s | Incident Angle/(°) | C_{d} |
---|---|---|---|---|

1 | 0.75 | 5 | 0 | 0.0025 |

2 | 1 | 5 | 0 | 0.0025 |

3 | 1.5 | 5 | 0 | 0.0025 |

4 | 2 | 5 | 0 | 0.0025 |

5 | 2.5 | 5 | 0 | 0.0025 |

6 | 0.75 | 10 | 0 | 0.0025 |

7 | 1 | 10 | 0 | 0.0025 |

8 | 1.5 | 10 | 0 | 0.0025 |

9 | 2 | 10 | 0 | 0.0025 |

10 | 2.5 | 10 | 0 | 0.0025 |

11 | 2 | 5 | 10 | 0.0025 |

12 | 2 | 5 | 20 | 0.0025 |

13 | 2 | 5 | 0 | 0.02 |

14 | 2 | 5 | 0 | 0.04 |

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**MDPI and ACS Style**

Ji, X.; Xu, C.; Ren, Z.; Yan, S.; Wang, D.; Yu, Z.
Study on the Formation Characteristics and Disaster Mitigation Mechanisms of Rip Currents on Arc-Shaped Beach. *J. Mar. Sci. Eng.* **2023**, *11*, 2381.
https://doi.org/10.3390/jmse11122381

**AMA Style**

Ji X, Xu C, Ren Z, Yan S, Wang D, Yu Z.
Study on the Formation Characteristics and Disaster Mitigation Mechanisms of Rip Currents on Arc-Shaped Beach. *Journal of Marine Science and Engineering*. 2023; 11(12):2381.
https://doi.org/10.3390/jmse11122381

**Chicago/Turabian Style**

Ji, Xinran, Chuanle Xu, Zhiyuan Ren, Sheng Yan, Daoru Wang, and Zongbing Yu.
2023. "Study on the Formation Characteristics and Disaster Mitigation Mechanisms of Rip Currents on Arc-Shaped Beach" *Journal of Marine Science and Engineering* 11, no. 12: 2381.
https://doi.org/10.3390/jmse11122381