1. Introduction
Breakwaters are constructed to mitigate the impact of waves on coastal areas and protect shorelines, harbors, ports, and other coastal infrastructure from erosion and damage. They serve as barriers that absorb, reflect, or dissipate wave energy, reducing the intensity of waves reaching the protected area [
1,
2]. Floating breakwaters (FBWs) are designed as floating structures that are anchored or moored in place. They are typically constructed using a combination of concrete, steel, or composite materials [
3]. FBWs offer advantages such as cost-effectiveness, ease of installation, and flexibility in adapting to changing coastal conditions. Fixed breakwaters, on the other hand, are built on a solid foundation, usually extending from the coast into the water [
4,
5]. They are typically constructed using massive concrete blocks, rocks, or other durable materials. Fixed breakwaters provide robust protection against wave forces but are often more expensive and challenging to construct compared to FBWs [
6,
7]. FBWs are particularly suitable for calm coastal conditions where wave energy is relatively lower. They are commonly employed in areas with shallow waters, protected bays, or marinas. FBWs can also be advantageous in situations involving deep waters, difficult geotechnical conditions, severe sedimentation problems, and steep seabed slopes, where the installation of fixed breakwaters may be challenging or economically unfeasible [
8,
9]. The wave-structure interaction around breakwaters involves various components. Reflected waves refer to waves that bounce back off the breakwater, while turbulence-damped waves are waves that experience energy dissipation due to the presence of the breakwater [
10,
11]. Transmitted waves are the waves that pass through or around the breakwater, continuing their propagation beyond the protected area [
12,
13].
The effectiveness of an FBW is determined by the number of waves transmitted, and structures that reflect more waves generally perform better. An important parameter often analyzed when studying FBWs is the wave-transmission coefficient. It represents the ratio of transmitted wave height to incident wave height and serves as a measure of FBW performance. Various structural and hydrodynamic factors influence the wave-transmission coefficient and have been the focus of research by many scientists in this field [
14,
15]. Floating breakwaters effectively reduce wave energy and erosion. Research on different types of floating breakwaters, such as porous slope breakwaters [
16], floating breakwaters for emergent vegetation [
17], and floating breakwaters for wetlands [
18], have been shown to be able to attenuate waves by a significant percentage of 38% and up to 96%. Factors that influence wave attenuation include wave orbital velocity, wave period, stem spacing, and the ratio of stem spacing to wave height. Furthermore, integrating floating breakwaters and wave-energy converters is a valuable research area to improve wave attenuation performance and sustainable development of the marine environment. These results highlight the importance and effectiveness of floating breakwaters in controlling wave energy and erosion and provide valuable insights for coastal engineering applications [
19,
20].
The wave attenuation performance and movement of some types of floating breakwaters (FBs) have been reported by Ning et al. [
21], who used numerical and experimental approaches to study and develop a mooring system model to simulate FB limitations. The effectiveness of a series of porous breakwaters in reducing wave forces on a floating dock has been studied by Gayathri [
22], based on the theory of small-amplitude water waves at finite water depth. To detect hump formation in the approach channel of Cambert Bay, a regional wave model using wind time series as input was developed by Roger et al. [
23]. The results showed that the proposed solution using flooded breakwaters was effective in wave mitigation. Erosion occurs due to wave action. McCartney conducted a study comparing the performance of four different types of floating breakwaters. The findings of the study indicated that anchored pontoon breakwaters exhibited superior performance compared to the other types [
24]. In another work, Sannasiraj et al. studied FBWs using a two-dimensional finite element model and concluded that fixed placement had no effect on swimming performance [
25]. In their study, Lee et al. presented a methodology for determining the response of a floating pontoon pier. Their research demonstrated that the movement of the pontoon is directly related to its size, draft, and the characteristics of its anchoring system [
26]. In their innovative research, Wang and Son developed a novel experimental model for a porous floating breakwater. Their model employed a configuration of diamond-shaped blocks to effectively mitigate transmitted waves. Through their study, they reached the significant conclusion that porous floating breakwaters have the capability to decrease the height of incident waves [
27]. In a separate investigation, Pena et al. conducted experiments using multiple models to calculate the wave-transmission coefficient. Their study led them to the significant finding that the width of the pontoon plays a crucial role in determining the performance of the breakwater [
28]. Additionally, they introduced a new type of FBW that incorporates a pneumatic chamber. Through their research, they demonstrated that the inclusion of a pneumatic chamber in the FBW significantly enhances the system’s overall performance [
29]. Additionally, Martin et al. presented a computational fluid dynamics (CFD) model in their study to investigate the impact of various anchoring systems on floating breakwaters (FBWs) [
30]. Their research aimed to understand how different anchoring systems affect the performance of FBWs. In a separate study, Cho examined an FBW with a rectangular shape and vertical porous plates. Through analysis, Cho concluded that the specific selection of porous plates significantly contributes to reducing the permeability coefficient of the FBW [
31]. This finding highlights the importance of carefully choosing the characteristics of porous plates in enhancing the performance of FBWs. In another research effort, Penn et al. employed a numerical model to examine the interaction between waves and an FBW anchored in water [
32]. Their study focused on investigating the dynamics of wave interaction and its effects on the FBW system, providing valuable insights into the behavior of FBWs in different wave conditions.
McCartney provided a comprehensive discussion on the design principles and considerations for floating breakwaters in the Journal of Waterway, Port, Coastal, and Ocean Engineering. The study focused on providing guidelines and insights into the design process of floating breakwaters [
24]. In their paper published in Ocean Engineering, Sannasiraj et al. examined the mooring forces and motion responses of pontoon-type floating breakwaters. The study aimed to analyze the stability and behavior of these structures under various wave conditions, shedding light on the performance and structural aspects of pontoon-type floating breakwaters [
25]. In another study, Lee et al. investigated the dynamic and structural motions of a floating-pier system in waves, predicting the movement and response of such systems to wave actions. The study, published in Ocean Engineering, aimed to enhance the understanding of the behavior and performance of floating-pier systems under wave-induced loads [
26]. In another work, Wang and Sun conducted an experimental study on a porous floating breakwater, exploring its performance and wave-energy dissipation capabilities. Published in Ocean Engineering, the research aimed to evaluate the effectiveness of porous floating breakwaters in reducing wave energy and protecting coastal areas [
27]. In another study, Peña et al. performed an experimental study on wave-transmission coefficient, mooring lines, and module connector forces, evaluating the effectiveness and structural aspects of different designs of floating breakwaters. The study, published in Ocean Engineering, focused on assessing the performance and structural behavior of various floating breakwater designs [
28]. Moreover, He et al. investigated the hydrodynamic performance of a rectangular floating breakwater with and without pneumatic chambers in Ocean Engineering. The study aimed to analyze the impact of pneumatic chambers on wave-energy dissipation and enhance the understanding of the performance of such breakwater configurations [
29]. In another paper, Martin et al. conducted a numerical simulation of interactions between water waves and a moored-floating breakwater, providing insights into the behavior and performance of such systems. The study aimed to enhance the understanding of wave-breakwater interactions and their implications for floating breakwater design [
30]. In another work, Cho focused on investigating the wave-transmission characteristics of a floating rectangular breakwater with porous side plates in the International Journal of Naval Architecture and Ocean Engineering. The study aimed to analyze the specific design features that influence the wave-transmission properties of breakwaters [
31]. In another study, Peng et al. performed a numerical simulation of interactions between water waves and inclined moored submerged floating breakwaters, analyzing the behavior and effectiveness of such breakwater configurations. The study, published in Coastal Engineering, aimed to enhance understanding of the performance of inclined submerged floating breakwaters under wave conditions [
32]. In addition, Sannasiraj et al. conducted a study on the wave-transmission characteristics of a floating breakwater, analyzing its performance in reducing wave energy and protecting coastal areas. The research aimed to evaluate the effectiveness of floating breakwaters in attenuating waves and their role in coastal protection [
33]. In another work, Kim et al. presented a numerical study on the wave-transmission characteristics of a floating breakwater, examining its effectiveness in attenuating waves and reducing wave-induced forces. The study aimed to analyze the wave-transmission properties and the efficiency of floating breakwaters as wave-energy dissipators [
34].
In another work, Kim et al. investigated the wave-transmission characteristics of a trapezoidal floating breakwater, evaluating its performance in wave-energy dissipation and coastal protection [
35]. In another study, Sannasiraj et al. studied the wave-transmission characteristics of a floating breakwater with a porous barrier, assessing its effectiveness in reducing wave heights and protecting coastal structures [
36]. In another research, Kim et al. conducted an experimental study on the wave-transmission characteristics of a floating breakwater with a perforated barrier, analyzing its performance in wave-energy dissipation and coastal defense [
37]. In another study, Sannasiraj et al. investigated the wave-transmission characteristics of a floating breakwater with a sloping front face, evaluating its efficiency in reducing wave impacts and protecting coastal areas [
38]. In another paper, Kim et al. performed a numerical investigation on the wave-transmission characteristics of a floating breakwater with a sloping front face, assessing its effectiveness in wave attenuation and coastal defense [
39]. Also, Sannasiraj et al. analyzed the wave-transmission characteristics of a floating breakwater with a wave absorber, studying its performance in wave-energy dissipation and coastal protection [
40]. Moreover, Kim et al. conducted an experimental study on the wave-transmission characteristics of a floating breakwater with a wave absorber, evaluating its efficiency in reducing wave impacts and protecting coastal structures [
41]. In another study, Sannasiraj et al. investigated the wave-transmission characteristics of a floating breakwater with a wave reflector, analyzing its effectiveness in wave attenuation and coastal defense [
42].
Based on the above literature review, the aim of this paper is to understand the dynamic response of floating breakwaters to wave forces and utilize this knowledge to optimize their design and improve coastal protection. The focus is on investigating the response amplitude operator as a crucial parameter for accurately predicting structural response amplitudes at various frequencies and wave angles. By incorporating this understanding, adjustments can be made to enhance the effectiveness of floating breakwaters. Thus, in this study, a comprehensive 3D model of the mooring system is developed to simulate its behavior under different wave and current conditions. The model considers critical design factors such as pontoon shapes, anchor types, placements, and configurations. Through simulations, the study aims to provide valuable insights into the performance of the wing-plate floating breakwater mooring system across different operational settings. These insights will contribute to the optimization of floating breakwaters and their ability to protect coastlines from wave impacts, thereby enhancing coastal protection measures.