Experimental Study on the Hydrodynamic Analysis of a Floating Offshore Wind Turbine Under Focused Wave Conditions

Abstract

The strong nonlinearity of shallow-water waves significantly affects the dynamic response of floating offshore wind turbines (FOWTs), introducing additional complexity in motion behavior. This study presents a series of 1:80-scale experiments conducted on a 5 MW FOWT at a 50 m water depth, under regular, irregular, and focused wave conditions. The tests were conducted under regular, irregular, and focused wave conditions. The results show that, under both regular and irregular wave conditions, the platform’s motion and mooring tension increased as the wave period became longer, indicating a greater energy transfer and stronger coupling effects at lower wave frequencies. Specifically, in irregular seas, mooring tension increased by 16% between moderate and high sea states, with pronounced surge–pitch coupling near the natural frequency. Under focused wave conditions, the platform experienced significant surge displacement due to the impact of large wave crests, followed by free-decay behavior. Meanwhile, the pitch amplitude increased by up to 27%, and mooring line tension rose by 16% as the wave steepness intensified. These findings provide valuable insights for the design and optimization of FOWTs in complex marine environments, particularly under extreme wave conditions. Additionally, they contribute to the refinement of relevant numerical simulation methods.

1. Introduction

The global expansion of offshore wind power has accelerated in response to the increasing demand for clean energy [1,2]. As of the end of 2024, the total installed capacity of offshore wind turbines has reached 83.2 GW. Notably, the cumulative installed capacity of floating offshore wind turbines (FOWTs) is estimated to be around 0.5 GW [3].

FOWTs have become prominent research objectives in the offshore wind energy sector. Given the relatively shallow continental shelf along the eastern coast, China has successfully installed several FOWTs, with most of the installed floating offshore wind farms located nearshore. For example, several representative FOWTs have been deployed in China, including the “YinLing” by China Three Gorges (Wuhan, China) [4], operating at a working depth of 32 m; the “FuYao” by CSSC (Shanghai, China) [5], at 65 m; the “TianCheng” by MINGYANG (Zhongshan, China) [6], exceeding 35 m; and the “Gongxiang” by CHN ENERGY (Beijing, China) [7], at approximately 35 m, as depicted in Figure 1. As water depth decreases, FOWTs face increasing challenges for design [8,9]. The nonlinear wave loads acting on FOWTs differ significantly from those in deep-water conditions, leading to more complex dynamic response characteristics. Therefore, studying the dynamic response characteristics of FOWTs in shallow water is crucial for understanding their performance and ensuring the long-term safety and stability of their operation [10,11,12].

FOWTs are complex integrated systems that involve various fields such as hydrodynamics, aerodynamics, structural dynamics, and automatic control [13,14]. Currently, full-coupled numerical simulation software for FOWTs involves various simplifications in the calculation process. As a result, compared to numerical simulation, model testing provides a more accurate representation of the dynamic response of FOWTs in complex marine environments [15]. Field research has already been conducted to carry out model tests on FOWTs.

Ikoma et al. [16] conducted a 1:100-scale wave tank experiment on a 2 MW vertical-axis FOWT with four-month tanks, investigating the motion response characteristics of the FOWT in wave conditions. Yang et al. [17] performed a 1:20-scale wave tank experiment on a barge-type FOWT, examining the dynamic response of the FOWT under both regular and irregular wave conditions. Field tests were also conducted to study the dynamic response of the FOWT under various wind speeds, wind directions, and wave heights. Liu [18] carried out wave tank experiments on 1:50-scale semi-submersible and spar-type FOWTs, testing the system’s dynamic response under different sea states and wind speeds. Luo et al. [19] experimentally investigated the impact of extreme waves on tension-leg platforms (TLPs) during various impact processes, including the morphological changes of waves upon impact, wave-induced pressure on the platform deck, platform motion, and anchor chain forces. Chen et al. [20] studied the interaction between extreme waves and vertical cylinders using a three-dimensional two-phase flow model and validated the accuracy of their numerical model with experimental data. Their research explored the effects of wave steepness and wave group bandwidth on the downstream wave forces and wave surge phenomena around the cylinder. Furthermore, they proposed a new empirical formula to predict the downstream wave forces based solely on the free surface height around the cylinder, with results that closely matched the simulation outcomes. Sun et al. [21] introduced a method for generating extreme waves in experimental tanks via wave focusing. Li et al. [22] employed wave energy-focused techniques to simulate multi-directional extreme waves in a wave tank, aiming to investigate the force characteristics exerted by these waves on vertical cylinders. Their experiments explored the effects of various wave parameters (e.g., focused wave height, spectral peak frequency, frequency bandwidth, and directional distribution) on the impact characteristics of multi-directional focused waves. Recent work has also investigated the motion reduction of FOWTs using a centerboard–heave plate system in a wave–wind flume environment, demonstrating its effectiveness under combined sea states [23]. Although prior experimental studies have explored FOWTs in model basins, most have focused on deep-water environments (>100 m) or regular and irregular wave conditions. Shallow water conditions (<60 m), which involve distinct hydrodynamic challenges—such as enhanced wave nonlinearity, seabed interactions, and mooring slack effects—remain insufficiently studied. Existing shallow-water experiments rarely address focused wave loading, which is critical for evaluating structural response under extreme sea states. The 50 m depth adopted in this study represents a transitional regime typical of several nearshore FOWT deployments in China, where wave loading, mooring dynamics, and platform motion are tightly coupled. To this end, a braceless semi-submersible platform was selected for its structural simplicity and shallow draft, making it well suited for experimental modeling in limited-depth environments. This study thus fills a critical gap by experimentally investigating the behavior of a floating wind turbine under focused wave excitation at a representative shallow water depth. Furthermore, due to the strong nonlinearity associated with extreme waves, numerical simulations often involve simplifications in the dynamic coupling between platform and mooring systems. Hence, wave tank experiments remain essential for validating and improving numerical prediction methods for shallow-water FOWTs.

To address the aforementioned challenges, this study investigated the dynamic response characteristics of FOWTs in shallow water under various wave conditions through model-scale experiments. A series of model tests were conducted for a FOWT at a water depth of 50 m, focusing on its dynamic response under typical wave conditions. The model tests were performed at a 1:80 scale, with experimental conditions including regular, irregular, and focused waves. The structure of this paper is as follows: Section 2 introduces the theory of similarity and focused wave theory. Section 3 presents the model design and the experimental setup. Section 4 compares the experimental and numerical simulation results of free decay. Section 5 analyzes the dynamic response characteristics of the floating wind turbine under different wave conditions. Section 6 provides the conclusions of the study.

2. Theory

2.1. Similarity

To more accurately forecast the mooring-coupled dynamic response of FOWTs, both the prototype and model wind turbine systems must satisfy geometric, kinematic, and dynamic similarities [24].

(1)

Geometric Similarity

In FOWT model tests, all scale parameters must satisfy the condition of geometric similarity, such as length, draft, water depth, wave height, etc. Specifically, the following relationship holds:

$${\displaystyle \frac{L_s}{L_m}}=\lambda$$

(1)

where $\lambda$ is the geometric scale ratio of the FOWT, and s and m denote the prototype and experimental model, respectively.

(2)

Kinematic Similarity

In model tests, the corresponding points on the model and prototype should maintain the same proportionality in physical quantities, such as velocity and acceleration, at any given moment during their motion.

(3)

Dynamic Similarity

FOWT model tests aim to study their hydrodynamics under the action of environmental loads such as wind and waves. Therefore, it is necessary to ensure that the gravitational and inertial forces of the model are similar to those of the prototype, which is achieved by satisfying the Froude number similarity [25]:

$$F_r={\displaystyle \frac{V_s}{\sqrt{g{L}_s}}}={\displaystyle \frac{V_m}{\sqrt{g{L}_m}}}$$

(2)

where vs. and L_s are the characteristic velocity and characteristic length scale of the prototype, respectively, while V_m and L_m are the corresponding quantities for the model. The acceleration due to gravity g is taken as 9.8 m/s².

Given the periodic variation in the rotation and forces experienced by the blades of FOWT under wind actions, the rotational speed of the turbine blades in the model must satisfy the Strouhal number similarity:

$${\displaystyle \frac{V_m{T}_m}{L_m}}={\displaystyle \frac{V_s{T}_s}{L_s}}$$

(3)

where T_s and T_m represent the characteristic periods of the prototype and model, respectively.

Moreover, the FOWT model also ensure that inertial forces and viscous forces are similar. This is achieved by satisfying the Reynolds number similarity:

$$R_e={\displaystyle \frac{{\rho }_m{U}_m{L}_m}{\nu }}={\displaystyle \frac{{\rho }_s{U}_s{L}_s}{\nu }}$$

(4)

where U is the average velocity of the structure relative to the flow field, and $\nu$ is the fluid viscosity. It should be noted that it is generally impossible to satisfy both Froude number similarity (gravity-dominated behavior) and Reynolds number similarity (viscous-dominated behavior) in the same scale test. This study considers the Froude similarity scale as the principal dimensionless number to satisfy, since the frictional forces hence the Reynolds similarity are of secondary importance in this case. The key physical quantities are summarized in

Table 1. Proportional relationship between model and prototype.

Items	Symbol	Ratio
Line scale	Ls/Lm	λ
Area	As/Am	λ2
Volume	Vs/Vm	λ3
Linear acceleration	as/am	1
Angle	θs/θm	1
Period, speed	Ts/Tm, Us/Um	λ0.5
Frequency	fs/fm	λ0.5
Mass	∆s/∆m	λ3
Force	Fs/Fm	λ3
Moment	Ms/Mm	λ4
Moment of inertia	Is/Im	λ5

1. Subscripts s and m denote prototype and model quantities, respectively. 2. Mass is derived from $\nabla \times \rho$; therefore, the scaling of mass follows the scaling of displacement volume. 3. Velocity and period are scaled to ensure equality of the Froude number: $F_{r_s}=F_{r_m}={\displaystyle \frac{U}{\sqrt{gL}}}$.

.

2.2. Focused Wave Theory

Focused waves are typically formed when multiple waves in a wave group converge. In shallow-water regions, the influence of topography on wave propagation is more pronounced, and the nonlinear effects of waves become particularly significant. During the propagation of waves, the amplitude and phase of the waves change over time and space, leading to the accumulation of wave energy and the formation of an instantaneous high-energy wave. This phenomenon is primarily dominated by two factors: the nonlinear interactions of waves and phase synchronization [26].

The focused wave generation technique offers advantages such as modeling simplicity and reduced computational time, making it an effective and widely adopted method in wave simulation studies. The New Wave theory proposed by Tromans et al. [27] is currently one of the most widely used theories. The New Wave shape is represented by an autocorrelation function describing each frequency component’s phase. According to this model, different wave spectra (such as equal amplitude spectrum, equal wave steepness spectrum, Jonswap spectrum, etc.) can be selected, with the improved Jonswap spectrum being commonly used, as shown in Equation (3).

$$S({\omega }_i)={\displaystyle \frac{a\cdot g^2}{{\omega }_i^5}}\cdot \exp (-1.25\cdot {({\displaystyle \frac{{\omega }_p}{{\omega }_i}})}^4)\cdot {\gamma }^{\exp (-0.5\cdot {({\displaystyle \frac{{\omega }_i-{\omega }_p}{\sigma \cdot {\omega }_p}})}^4)}$$

(5)

where a is the energy scale parameter, typically taken as 0.0081. $\gamma$ is the spectral peak factor, usually set to be 3.3, both of which are commonly adopted for fully developed sea states [27,28]. ${\omega }_i$ is the angular frequency of the i-th wave component, ${\omega }_p$ is the angular frequency of the spectral peak wave, and $\sigma$ is the peak shape parameter that can be determined as follows [29]:

$$\sigma =\left\{\begin{array}{l}0.07 {\omega }_i\le {\omega }_p\\ 0.09 {\omega }_i>{\omega }_p\end{array}\right.$$

(6)

The wave elevation $\eta$ as a function of time t and position x can be calculated using Equation (7):

$$\eta (x,t)={\displaystyle \sum _{i=1}^N{a}_i}\cos (k_i(x-x_c)-{\omega }_i(t-t_c))$$

(7)

where N is the number of constituent waves, a_i and k_i, denote the amplitude and wavenumber of the i-th wave, respectively, and c_x and c_t represent the position and time of wave focusing, respectively.

The wave amplitude can be determined using Equation (8):

$$a_i(\omega )=A_{total}{\displaystyle \frac{S({\omega }_i)\Delta \omega }{{\displaystyle \sum _{i=1}^{N}S({\omega }_i)\Delta \omega }}}$$

(8)

where $A_{total}$ is the amplitude of the wave group, and $S({\omega }_i)$ is the wave spectrum.

3. Model Test Preparation

3.1. Test Arrangements

The experimental tank used in this study is an L-shaped wave tank, measuring 45 m in length, 40 m in width, and 1 m in depth. The L-shaped wave maker is equipped by 145 wave-generating units, with a maximum wave height capacity of 0.4 m and a period range from 0.6 s to 4.0 s. The wave maker operates based on linear wave theory, generating waves through the superposition of individual components derived from input spectra or time series. The wave maker is capable of simulating regular, irregular, and strongly nonlinear waves (such as focused waves and breaking waves). The tank is also equipped with an active absorption system, achieving over 90% absorption efficiency for incident reflected waves.

This study aimed to investigate the dynamic response characteristics of FOWTs under a water depth h of 50 m. In alignment with the tank’s conditions, 1:80 was selected as the model scale, with the test water depth set at 0.625 m. To assess the undisturbed wave height and the reflection coefficient in the tank before installing the model, 13 wave gauges were arranged at specific locations, as shown in Figure 2. During the model tests, the model was moored at the center of the tank, with wave gauges WP1–WP11 remaining in the water, while WP12–WP13 were removed (used solely for fitting the experimental wave field). Platform motion was captured using a Northern Digital Inc. (Waterloo, ON, Canada) (NDI) optical tracking system, which tracked the 3D coordinates of reflective markers mounted on the platform. Tension sensors were connected in series between the mooring chains and the fairleads, allowing for an accurate measurement of mooring line tension under various wave conditions. All sensor signals were collected using a synchronized National Instruments data acquisition system. To ensure the reliability of experimental results, each test condition was repeated three times under the same settings, and the reported results represent the average of the repeated runs.

3.2. Model Design

This study aimed to investigate the impact of different wave conditions on the dynamic response of FOWTs in shallow water, with a primary focus on the hydrodynamic behavior of the substructure. Specifically, the response in surge, heave, and pitch motions was analyzed to evaluate wave-induced effects, while the aerodynamic effects of the superstructure were not considered. The NREL-5MW wind turbine [30] (including the blades, hub, and nacelle) was simplified as a mass block in the experiment. The tower design of the wind turbine is based on the OC3-Spar project [31], while the floating platform prototype is a braceless semi-submersible platform [32]. The braceless semi-submersible design was chosen for its shallow draft and minimal structural interference, making it more appropriate for shallow-water testing and simplifying hydrodynamic evaluation. The mooring system was redesigned for a water depth of 50 m. A schematic diagram of the overall model is shown in Figure 3. The inertia moments of the platform were measured using a dedicated inertia measurement rig. The model was suspended and allowed to oscillate freely around each of the three principal axes. The corresponding oscillation periods were recorded, and the moments of inertia were calculated using classical pendulum-based equations. The main inertial parameters of the experimental model are listed in

Table 2. Physical parameters of the experimental model.

Parameters	Units	Model Test (Scaled to Prototype Size)	Designed	Diff.
Mass	kg	10,385,020.5	10,337,318	0.46%
Center of gravity	m	(−0.104, 0.008, −17.89)	(0, 0, −18.87)	(/, /, 5.19%)
Ixx, Iyy, Izz	Kg·m2	1.45 × 1010, 1.45 × 1010, 8.51 × 109	1.43 × 1010, 1.42 × 1010, 8.35 × 109	1.40%, 2.11%, 1.92%

.

Accurately scaling the tower to preserve mass properties, geometric dimensions, and natural frequencies presented considerable challenges. To address this, we prioritized the structural parameters most critical to the coupled dynamic behavior between the nacelle and the platform. Specifically, the first-order natural frequency and height of the tower were aligned to scale down properly with the prototype model. As a result, the model tower was not designed strictly according to geometric similarity. Instead, its dimensions were redefined, and the requirements for tower mass parameters were eased. The model tower was constructed as a hollow cylindrical section with a uniform cross-section, featuring flanges welded at both ends, and was made of aluminum alloy 6061. A comparison of the model tower and the prototype tower parameters from the OC3-Spar project is shown in

Table 3. Tower parameters comparison of the model and the prototype.

Parameters	Units	Model Test (Scale to Prototype Size)	Design	Diff.
Mass	kg	270,010	249,718	8.13%
Length	m	77.6	77.6	0
Center of gravity	m	0, 0, 34.2	0, 0, 33.4	2.40%
1st natural frequency	Hz	0.576	0.567	1.59%

, with the first-order natural frequency of the model tower determined through impact modal testing [33]. Although the resulting tower mass deviated from the full-scale design by 8.13%, this adjustment was necessary to match the scaled natural frequency with high precision (1.59% error). Since the dynamic response is more sensitive to modal frequency than to absolute mass, this trade-off is justified. Moreover, the overall model mass error was tightly controlled within 0.46%, ensuring overall experimental accuracy.

The prototype of the floating platform is the braceless semi-submersible platform, designed and published by Luan et al. [24] from the Norwegian University of Science and Technology. This platform consists of four vertical columns and a submerged pontoon, with a column diameter of 6.5 m, a draft of 30 m, a platform weight of 9738 t, and a displacement of 10,555 t. Further details can be found in references [32,34]. Compared to traditional semi-submersible platforms, the braceless design eliminates the need for complex support structures, thereby reducing both cost and maintenance requirements. The scaled model was fabricated using acrylic material, with the platform and tower connected to the central column via six bolts.

The mooring system was redesigned for a water depth of 50 m, incorporating a catenary configuration with weighted clumps to enhance mooring restoring capacity. The system consists of three evenly distributed mooring chains, with the layout of the mooring system shown in Figure 4. The design parameters of the system are listed in

Table 4. Mooring system design parameters.

Parameters	Units	Values
Diameter	m	0.18
Unstretched length	m	650
Dry density	kg/m	648
Clump mass	t	35.68
Clump position from the fairlead	m	20
Pretension	kN	984.5
Stiffness	N	2.92 × 109
Mooring radius	m	684.3

. The model mooring chains were made of steel, with lead-wire weights used for ballast, and the stiffness of the chains was supplemented by springs. The ballast blocks were composed of lead.

4. Comparison Between Model Test and Simulations

Free-decay tests of the FOWT model were conducted in still water by applying initial displacements in the surge, heave, and pitch directions of the model platform, followed by release. The free-decay motions were measured to determine the natural periods of the corresponding degrees of freedom (DOFs). The experimentally obtained natural periods of the FOWT were compared with those from numerical simulations. The numerical simulations were performed using the SIMA V 4.2 software [35], and the specific modeling methods and processes can be found in references [36,37]. The numerical FOWT model is shown in Figure 5. It is important to note that this study employed two methods to supplement the viscous damping acting on the platform. First, the quadratic damping term in the Morrison empirical formula was used. The drag coefficient C_D in the quadratic damping term was selected based on the recommended values from DNV-RP-C205 [29]. After supplementing the quadratic viscous damping using the Morrison empirical formula, the comparison between the free-decay curves from the model tests and numerical simulations still showed significant discrepancies. Therefore, a linear viscous damping matrix was added for further correction, with the linear damping set to approximately 8% of the critical damping, as shown in

Table 5. Linear damping matrix (N·s/m).

	x	y	z	rx	ry	rz
x	1.71 × 105	0	0	0	0	0
y	0	1.71 × 105	0	0	0	0
z	0	0	6.35 × 105	0	0	0
rz	0	0	0	0	0	0
ry	0	0	0	0	0	0
rz	0	0	0	0	0	0

.

The comparison between the natural periods obtained from the tank model tests and numerical simulations is shown in

Table 6. The natural period of a floating wind turbine.

Direction	Natural Period (s)		Diff. (%)
	Model Test (Scale to Prototype Size)	Sima
Surge	101.01	100	−1.01%
Heave	25.34	25.60	1.02%
Pitch	43.67	40	−8.4%

, and the free-decay time series are compared in Figure 6. The comparison between the model tests and numerical simulations reveals that the maximum error in the natural periods across different DOFs is −8.4%, indicating good agreement overall. Additionally, the free-decay time series from both the numerical simulations and model tests exhibit similar decay rates, suggesting that the experimental design is reasonable and the experimental results are reliable. While the comparison shows good agreement, it is acknowledged that both experimental and numerical results are subject to uncertainty [38]. A full uncertainty analysis is beyond the scope of this work but will be considered in future studies.

5. Results and Discussion

5.1. Regular and Irregular Wave Conditions

The parameters for the regular and irregular wave conditions are presented in

Table 7. Regular wave conditions at full scale and model scale (1:80).

Test	Wave Type	T (s)		H (m)		h/L	Repeated Wave Periods
		Model	Full	Model	Full
RE1	regular	0.8	7.2	0.025	2	0.6183	50
RE2		1.8	16.1			0.1611
RE3		2.8	25.04			0.0953

and

Table 8. Irregular wave conditions at full scale and model scale (1:80).

Test	Wave Type	Tp (s)		Hs (m)		h/L	Repeated Wave Periods
		Model	Full	Model	Full
IR1	irregular	1.20	10.73	0.070	5.60	0.2926	200
IR2		1.40	12.52			0.2287
IR3		1.60	14.31			0.1886

, respectively, with the spectrum of the irregular waves modeled using the JONSWAP spectrum. The selected wave conditions were based on statistical wave data from a typical shallow-water offshore site in the South China Sea, where FOWT deployment is under consideration. In both the regular and irregular wave tests, data collection began once the wave field had been stabilized. The data collection duration was 300 s (corresponding to 2683.28 s in real time). For the irregular waves, the stable segment between 1000 s and 2000 s was used for analyzing the dynamic response characteristics of the FOWT.

Taking the RE3 condition as an example, Figure 7 illustrates the time history of the FOWT motion in the surge, heave, and pitch degrees of freedom under this regular wave excitation. The results indicate that the FOWT exhibits uniform motion variations in all degrees of freedom corresponding to the wave period. Furthermore, the experimental outcomes demonstrate a high level of stability and reliability. Figure 8 presents the statistical values of the motion response of the FOWT and the mooring tension of ML2 under regular wave conditions. The platform’s motion is primarily characterized by surge, with smaller heave and pitch motions. As the wave period increases within the tested range of wave periods, the amplitude of motion in all directions gradually increases. Regarding the mooring tension, taking the mooring tension of ML2 as an example, it can be observed that as the wave period increases, the maximum tension increases slightly, and the fluctuation amplitude gradually grows. In the RE3 condition, the platform’s motion response reaches its maximum, and the corresponding mooring tension fluctuation is most significant, with the wave amplitude reaching 92.56 kN. This indicates that under regular wave conditions, the platform’s dynamic response is closely related to the wave period, and the mooring chain tension is sensitive to the platform’s motion response.

Table 9. Statistical values of FOWT motion and ML2 mooring tension under irregular wave conditions.

		Surge (m)	Heave (m)	Pitch (deg)	ML 2 Tension (kN)
IR1	Max.	3.05	0.60	1.40	1009.34
	Min.	−3.03	−0.61	−1.24	935.73
	Avg.	0.17	0.01	0.01	981.85
IR2	Max.	3.62	0.76	1.71	1020.04
	Min.	−3.16	−0.67	−1.45	986.74
	Avg.	0.22	0.01	0.04	1011.58
IR3	Max.	3.68	0.65	2.04	1169.47
	Min.	−3.53	−0.72	−1.46	989.73
	Avg.	0.32	0.01	0.09	1093.49

presents the statistical values of surge, heave, and pitch motion responses, as well as the ML2 mooring tension under irregular wave conditions. As the wave period increases, the surge and pitch motion amplitudes of the FOWT platform exhibit a general upward trend, suggesting that these degrees of freedom may be influenced by wave period variations. The heave motion shows comparatively smaller fluctuations, with only a slight increase in maximum and minimum values as the wave period changes. The variation in mooring line tension appears to align more closely with the surge motion trend, indicating a strong correlation between translational motion and mooring response under the tested conditions.

Taking the IR2 condition as an example, Figure 9 presents the time history of the FOWT’s motion responses and mooring tension, along with their corresponding power spectral density (PSD) analysis. The natural frequencies of the floating wind turbine are as follows: surge at 0.01 Hz, heave at 0.0395 Hz, and pitch at 0.0223 Hz. In the vicinity of the wave spectral peak frequency at 0.0799 Hz, the motion responses in the surge and heave directions are more pronounced, while the pitch motion response is relatively small within the wave frequency range. Notably, both surge and pitch responses exhibit spectral energy, not only at their individual natural frequencies but also across overlapping ranges, suggesting an inherent dynamic coupling between these two degrees of freedom. This surge–pitch interaction can be interpreted through an energy transfer perspective. When the platform experiences translational surge motion under wave forcing, its asymmetric mass distribution and mooring configuration induce rotational moments, particularly at low frequencies. These moments lead to pitch excitation, even in the absence of direct wave-induced pitching. Conversely, pitch motion affects the longitudinal water-plane area and hydrodynamic center of pressure, which feeds back into surge direction forces. This mutual influence facilitates an indirect energy exchange pathway, manifested in the observed spectral leakage across both modes. Such intermodal energy transfer is especially active when the excitation frequency overlaps with the natural modes, leading to local resonance amplification. From a hydrodynamic system viewpoint, this coupling behavior arises from non-diagonal terms in the added mass and hydrostatic stiffness matrices. The resulting interaction behaves like a distributed, two-way energy transmission network between surge and pitch, where energy injected at one mode is dynamically redistributed to another. The design implication is that this coupling may intensify the platform response under broadband or irregular sea states, and thus should be carefully considered during system-level dynamic analysis and mooring system optimization. The mooring tension of ML2 is primarily concentrated at the surge natural frequency and within the wave frequency excitation range, with some peaks also observed at the natural frequencies of heave and pitch, although the responses at these frequencies are relatively small.

5.2. Focused Wave Conditions

Compared to extreme waves generated through random wave simulations, focused waves, which are created by the superposition of component waves of different frequencies at specified times and locations to form wave crests or troughs, can effectively simulate extreme wave conditions in a short period. Therefore, the use of focused waves in FOWT tank experiments provides a significant advantage in studying the response of the turbine under extreme wave conditions [39]. In this study, focused waves were generated using crest focusing, and the focused location corresponds to the central column of the FOWT platform. The parameters of the focused wave conditions (FW1–FW2) are listed in

Table 10. Focused wave conditions at full scale and model scale (1:80).

Test	Fp (Hz)	a (m)	Focused Point	h/L	$\epsilon$ (Beji)
FW1	0.714	0.04	20.8	0.2041	0.0345
FW2	0.714	0.08	20.8	0.2041	0.0689

, where Fp denotes the peak frequency of the wave spectrum, a represents the amplitude of individual wave components, and the “focused point” indicates the spatial position in the tank where wave components converge. Based on the calculated relative depth h/L, all wave conditions tested in this study fall under the intermediate depth wave regime. Accordingly, the nonlinearity parameter ka—typically valid for deep-water conditions—was replaced with the generalized nonlinearity index $\epsilon =a/kh$, as proposed by Beji [40], where k is the wave number. This index provides a more consistent metric for evaluating wave nonlinearity across all relative depth regimes. These parameters together define the shape and intensity of the generated focused waves. As noted in Section 3.1, the wave generation in the basin follows linear theory, which may underrepresent nonlinear effects during wave focusing. As a result, the waves generated by the wave maker at the target location differ slightly from the input wave parameters. Therefore, the input parameters were adjusted to ensure that the waves generated at the target location matched the desired wave characteristics. The resulting wave time histories for the corresponding conditions in the tank tests are shown in Figure 10, measured at the FOWT installation location using the central wave probe positioned beneath the platform. The target wave parameters were successfully reproduced.

Under focused wave conditions, the time history curves of the FOWT’s motion responses and ML2 mooring tension, along with their corresponding PSD results, are presented in Figure 11 Initially, under the influence of focused waves, the surge motion of the FOWT exhibits a small amplitude, corresponding to a low wave height, and the platform primarily moves according to the wave frequency. Subsequently, under the intense impact of large wave crests in the focused wave, the FOWT undergoes significant surge displacement. Following the impact of the focused wave, the platform begins to exhibit free-decay motion. From the PSD curves, it is evident that the surge response of the FOWT under focused waves is mainly concentrated at the surge natural frequency (0.01 Hz) and the wave spectral peak frequency (0.0798 Hz), suggesting that low-frequency slow-drift motions are dynamically excited by transient wave loading. These slow-drift components contribute to dynamic amplification of the surge motion and, consequently, the mooring tension response. Additionally, due to the coupling between surge and pitch motions, the surge motion also shows spectral energy near the pitch natural frequency (0.0223 Hz), indicating intermodal energy transfer under nonlinear wave–structure interaction. While the mooring system does not explicitly simulate seabed contact or elastic elongation, the inclusion of clump weights and springs allows the partial reproduction of nonlinear restoring effects, which likely influence the tension response following the impact of focused wave crests. In the heave direction, the motion of the FOWT primarily follows the wave frequency due to wave excitation, with no apparent free decay observed, as in the surge motion. The PSD plot of the heave response shows that the response is mainly concentrated at the wave spectral peak frequency (0.0798 Hz) and the heave natural frequency (0.0395 Hz). For the pitch motion, the FOWT experiences significant displacement under the impact of large wave crests, followed by free-decay motion. The response is primarily concentrated at the pitch and surge natural frequencies. To provide a clearer visualization of the physical interaction between the focused wave and the floating platform, representative experimental photos are included in Figure 12. The image captures the moment of the wave crest’s impact on the FOWT model in test case FW2, highlighting the nonlinear hydrodynamic behavior and the platform’s large-amplitude surge and pitch response. This visual reference aims to support further understanding and numerical comparison of wave–structure interaction under extreme wave conditions.

Regarding the ML2 mooring tension, the tension variation follows a similar pattern to that of the surge motion. Initially, with small wave amplitudes, the mooring tension undergoes forced motion at the wave frequency. Under the intense impact of large wave crests, the platform experiences large displacements, after which the platform transitions to free-decay motion. During this phase, the mooring tension fluctuation frequency is close to the surge natural frequency. The PSD analysis reveals that the mooring tension response is primarily concentrated in the surge direction and within the wave frequency excitation range, which aligns well with expectations. A consistent trend is observed across both the time domain and PSD results, indicating that under the FW2 condition, the response amplitude and power spectral energy are significantly higher. This suggests that as the amplitude of the focused wave increases, its impact on the FOWT correspondingly intensifies.

6. Conclusions

This study investigated the dynamic response characteristics of a 5 MW FOWT under various wave conditions in shallow water, with the following key conclusions:

• A model test of a FOWT was conducted at a water depth of 50 m. The model design and experimental methodology were described in detail, with the overall mass error of the scaled model controlled within 0.46%.
• Comparative analyses between the experimental and numerical results of free-decay tests were performed. The maximum relative error across different degrees of freedom did not exceed 10%, demonstrating the accuracy and reliability of the experimental design.
• Under regular wave conditions, platform motion was dominated by surge and pitch, with increasing amplitudes at longer wave periods. In test case RE3 (T = 1.6 s), the pitch amplitude reached 6.85 mm, and the mooring line ML2 exhibited a peak tension fluctuation of 92.56 kN, the highest among regular conditions. The motion and mooring loads were synchronized with the wave excitation frequency.
• Under irregular wave conditions, the surge and heave responses were mainly concentrated within the wave excitation frequency band and the platform’s natural frequency. The pitch response showed dominant energy near the pitch natural frequency, with evident surge–pitch coupling. In test case IR3 (Tp = 1.6 s), the mooring tension in ML2 increased to 1169.47 kN, representing a 16% rise compared to the moderate condition IR1.
• Focused wave tests revealed a distinct free-decay motion in surge and pitch following wave crest impact, a behavior not observed under regular or irregular wave conditions, highlighting transient dynamics critical for extreme wave response assessment.
• Under focused wave conditions, the platform initially followed the linear wave profile, but after the crest impact, it experienced a rapid motion increase followed by free decay. From FW1 to FW2 (as wave steepness increased), the pitch amplitude rose by 27%, and ML2 mooring tension increased by 16%, indicating significant nonlinear amplification effects due to wave focusing.

Due to wave basin limitations, the experimental analysis was constrained to a representative 50 m water depth. Future studies will extend this work through numerical simulations to investigate sensitivity to water depth and associated wave nonlinearity effects.