A rapid expansion in global offshore wind power capacity is underway, driven by the need to achieve sustainability and clean-energy targets. Offshore wind energy projects offer higher capacity factors due to the more reliable and robust wind resources found in the marine atmosphere. Technological advancements in the manufacturing of offshore wind turbines have led to a pronounced reduction in the cost of offshore energy. Modern offshore wind turbines are considerably larger than their onshore counterparts. Onshore turbines experience inflow turbulence that is mainly three-dimensional, as described by the standards. Conversely, offshore turbines experience weaker three-dimensional turbulence, while low-frequency structures are relatively more dominant. These structures influence the fatigue loading response of wind turbine towers and blades. Furthermore, the response of floating offshore wind turbines is even more susceptible to low-frequency wind fluctuations due to more degrees of freedom and low natural frequencies of rigid-body motions .

In the wind turbine design process, synthetic turbulent wind fields are used in aero-hydro-servo-elastic codes to analyze the effects of atmospheric turbulence on the loads and dynamic response of different system components. International Electrotechnical Commission (IEC) standards recommend two turbulence models to generate wind fields for the turbine design process: (i) the Mann uniform shear model and (ii) the Kaimal spectral model with exponential coherence . The main advantage of these two models over other high-fidelity methods for generating turbulent wind fields, such as large eddy simulations (LES), is their significantly lower computational cost. Their main drawback is that these models assume neutral stratification and represent stationary onshore atmospheric conditions. The marine atmosphere is characterized by large-scale quasi-two-dimensional turbulent eddies with timescales exceeding 500 s , which the recommended IEC turbulence models cannot accurately capture. Here, the 2D turbulence is characterized by eddies with a large aspect ratio, i.e., the ratio of the horizontal to the vertical length scales.

Numerous studies have highlighted the impact of large-scale coherent structures or low-frequency wind fluctuations on the response of large offshore wind turbines. For instance, investigated the global motion responses of an NREL 5 MW reference floating wind turbine and found that it is highly sensitive to low-frequency wind fluctuations, resulting in increased floating platform surge, pitch, and mooring line responses. They utilized the proper orthogonal decomposition (POD) method to decompose the input wind fields from the Mann and Kaimal models into coherent structures. It has been demonstrated that only a few of the lowest POD modes can characterize the low-frequency wind fluctuation response in wind turbines see. and concluded that the large-scale coherent structures are responsible for increased tower base fore–aft moments and blade root out-of-plane bending moments in the fixed-bottom wind turbines and additionally increased surge, pitch, and mooring line responses in floating wind turbines. These studies used standard turbulence models, suggesting that low-frequency wind turbulence may be underestimated or inaccurately modeled. and also compared the standard Mann and Kaimal turbulence models with the LES and TIMESR turbulence models. The TIMESR turbulence model is a feature of the TurbSim tool , developed by NREL, USA. It requires a time series of wind measurements as an input and outputs a constrained turbulence field. Only the TIMESR turbulence model could match the low-frequency energy observed in the measured wind spectra. However, the lowest frequency in these comparisons was 0.0017 Hz, corresponding to a timescale of less than 10 min. As documented in previous studies , the mesoscale turbulence or low-frequency wind fluctuations exhibit significant energy at frequencies below 2×10-3 Hz. The implications of wind turbulence at frequencies below 2×10-3 Hz on the loads and dynamic responses of wind turbines remain largely unexplored.

In our study, we use the low-frequency wind turbulence model (hereafter, the “2D turbulence model”) presented by . This model accurately predicts low-frequency longitudinal (u) and lateral (v) wind fluctuations within the mesoscale range, i.e., well below 10-3 Hz. We combine the 2D turbulence model with the Mann uniform shear model (hereafter, the “3D turbulence model”) to simulate turbulence in the frequency range down to 1 h-1. The model parameters are obtained from the undisturbed wind data collected at the FINO1 research platform in the North Sea. We investigate the impact of low-frequency wind fluctuations by evaluating the fatigue loads and aerodynamic response of the International Energy Agency (IEA) 15 MW reference wind turbine . The reference turbine design is available in two configurations: a fixed-bottom design with a monopile embedded in the soil and a floating design with a semi-submersible floating platform supported by mooring lines. The IEA 15 MW wind turbine is an open-source design that has undergone various response analyses and design studies .

In this study, we focus on evaluating the damage-equivalent loads (DEL) associated with blade and tower moments and how they respond to low-frequency wind turbulence. We also investigate the rigid-body dynamics of floater motions in the floating configuration of the IEA 15 MW wind turbine. Furthermore, we compare the aerodynamic loading and response under 2D+3D turbulent wind fields with a standard turbulence model and with a 3D-only turbulence model based on the Mann uniform shear model. Section 2 of this article describes the data and methodology employed. A brief description of the IEA 15 MW wind turbine in both monopile and floating configurations is presented. The procedure to generate synthetic wind fields containing 2D and 3D turbulence using the parameters obtained from FINO1 is also described. Additionally, the simulation setup is presented, including details of the aeroelastic code. Sections 3 and 4 contain loads and dynamic responses of the wind turbine in monopile and floating configurations, respectively. This is followed by the Discussion and Conclusion sections, which highlight and discuss the important outcomes of this analysis.

The presence of a large coherence in the longitudinal wind component (u) at frequencies below 10-3 Hz led to substantial tower base fore–aft and blade root out-of-plane bending moment loads for both fixed and floating wind turbines. The increase in DELs for these two moments was more pronounced at lower wind speeds, when the pitch regulation of the controller was not active. Furthermore, when the turbulent wind field consisted of 2D+3D turbulence, the load variation was more prominent for these moments. In contrast, the in-plane moments, namely the tower base side–side and blade root edgewise moments, decreased at higher wind speeds. The torsional moment, i.e., tower top yaw moment, decreased at all wind speeds in the 2D+3D turbulence case. This can be attributed to the presence of more coherent turbulence structures in the rotor plane in 2D turbulence, which leads to lower twisting moments.

Notably, tower fore–aft and blade root bending moments showed a stronger response at low frequencies for both fixed- and floating-turbine designs. These responses closely mirrored the wind spectra's behavior at low frequencies, indicating greater energy in low-frequency fluctuations at lower wind speeds than at higher wind speeds. In the case of platform motion responses in the floating wind turbine, surge and pitch displacements were most excited at low frequencies. These responses even exceeded the natural frequency excitation responses for surge and pitch motions at a wind speed of 4.5 ms-1. Consequently, the fairlead tension of the windward mooring line increased significantly, more so at lower wind speeds and less so at higher wind speeds, when the platform's surge natural frequency became the dominant factor.

An interesting topic of investigation is whether systematic changes in the anisotropy (ψ) of 2D turbulence structures have any implications for DELs? The dominant drivers of thrust-induced loading on the tall wind turbines are primarily the variance (σ2D2) and the spatial coherence of the wind components (mainly u) across the rotor disk. The coherence is mainly governed by L2D rather than the anisotropy ψ since for horizontal coherent structures with L2D≫Drotor (more than 500 times), the rotor is always embedded with a single eddy regardless of its horizontal shape. Oblate structures, where ψ<45°, would result in increased v fluctuations and thus a higher lateral coherence affecting side–side and yaw moments, and vice versa. However, these variations in ψ would have only a negligible effect on DEL due to the extremely large size of the structures in 2D turbulence. A dedicated sensitivity study of L2D and ψ on DELs would be valuable and is recommended as future work, particularly because measurements at sites with stronger atmospheric stability stratification or in other marine environments may yield stronger anisotropy .

The simulation setup utilized in this study deviates from the IEC standard in several aspects. The standard recommends specific values of the L3D and Γ parameters of the Mann turbulence model. According to the standard, the length scale parameter L3D=0.8Λ, where Λ is the turbulence scale parameter. For hub heights greater than 60 m, Λ=42 m, which suggests a length scale L3D=29.4 m. The anisotropy parameter Γ is fixed at 3.9, and the energy dissipation parameter αϵ2/3 is scaled to the target turbulence intensity (TI). These values are chosen to best match the Kaimal spectral model. However, , , have highlighted the strong dependence of these parameters on atmospheric stability. The use of these set parameters may not give the best match with measured spectra (also seen in Fig. ). A consequence is an inaccurate estimation of the simulated loads and turbine responses. In this study, we used the parameters obtained by fitting the measured spectra to the Mann turbulence model.

Furthermore, the IEC standards recommend linear detrending of measured wind data before calculating the standard deviation of the longitudinal wind component. noted that detrending causes the reduction in low-frequency content of a wind time series, resulting in reduced standard deviation. Although we applied criteria to remove extremely non-stationary time series see, we did not apply linear detrending before evaluating the measured spectra. The resulting spectra have large energy in the u and v components at low frequencies, even though the time series were considered stationary. Typically, 10 min time series are used in design load case (DLC) studies, which the standard turbulence models capture very well, especially for onshore turbines. However, the low-frequency wind fluctuations important for offshore wind turbines are not observable in a short time series. Therefore, we used the 1 h time series to capture the low-frequency part of the wind spectrum as comprehensively as possible.

Finally, it is essential to note that the present study covers only the normal operating mode of the wind turbine and does not account for extreme turbulence events, such as ramp-like increases in wind speed associated with large-scale meteorological processes, as investigated by . The study presented here can be closely associated with DLC 1.2 in IEC standards, which focuses on evaluating fatigue loads from normal operation. The misalignment between wind and waves can also have a significant impact on the dynamic response of a floating offshore wind turbine, as investigated by . Here, we did not delve into this aspect since our primary focus was to examine the aerodynamic response to wind turbulence. A wind-speed-dependent wave climate would provide more representative DEL estimates and could also affect the dynamic response of the floating wind turbine, especially at higher wind speeds when wave loading may dominate wind loading. We acknowledge this limitation and recommend that future work incorporate wind-speed-dependent wave conditions in aeroelastic simulations to improve the reliability of the results.

This study investigates the impact of low-frequency wind turbulence on the damage equivalent loads and dynamic response of the IEA 15 MW reference wind turbine. A model for low-frequency anisotropic wind fluctuations was employed to simulate wind fields resembling those of the marine atmosphere. Low-frequency wind turbulence was combined with high-frequency wind turbulence simulated by the Mann uniform shear model to span a wide frequency range. The model parameters were obtained from 1 h spectra measurements at the FINO1 offshore research site in the North Sea. It was observed that the Mann turbulence model underestimated the flow turbulence at low frequencies, resulting in reduced standard deviation of the u and v wind components.

The response of the IEA 15 MW wind turbine was investigated under three different wind fields: (i) a 3D turbulent wind field that underestimates the u and v turbulence at low frequencies, (ii) a 2D+3D turbulent wind field that accurately models also the low-frequency wind fluctuations, and (iii) a scaled 3D turbulent field that mimics the 3D turbulent field but is scaled up to match the measured standard deviation of the u and v wind components. The simulations were performed using the HAWC2 aeroelastic code for each wind speed between the cut-in and cut-out wind speeds. Both fixed- and floating-turbine designs were considered.

Damage equivalent load (DEL) assessments were performed for five moments: tower base fore–aft, tower base side–side, tower top yaw, blade root flapwise, and blade root edgewise moments. The scaled 3D turbulence resulted in the highest DEL for all five moments, indicating a greater impact of high-frequency turbulence on DEL than low-frequency turbulence. Compared with the unscaled 3D turbulence, the highest DELs were observed for the tower fore–aft and blade root flapwise moments at low wind speeds with the 2D+3D turbulence model. We observed strong coherence in the longitudinal wind component at low frequencies in the wind fields simulated by the 2D+3D turbulence model. This also resulted in reduced torsional moments acting on the rotor, as evidenced by the lower DEL values at the tower top yaw moment in this case. A similar trend was observed in the floating wind turbine, except that the magnitude of DEL for tower moments was almost twice as large due to a different tower design.

The dynamic response of the moments due to longitudinal forces showed behavior similar to that of the wind spectra. This includes the tower fore–aft and blade root flapwise moments. A heightened response of these moments was observed for frequencies below 2×10-3 Hz in the case of 2D+3D turbulence. However, this response was less pronounced at high wind speeds than at low wind speeds. Additionally, the rigid-body motion response of the floating platform was investigated in this study. It was observed that out of the six floating platform motions, only surge and pitch motions significantly responded to 2D turbulence. At a low wind speed of 4.5 ms-1, both surge and pitch motion showed a pronounced response to low-frequency wind turbulence. This response was attenuated at 10.5 ms-1, and in the case of the surge motion, the natural frequency response overshadowed it. Furthermore, the fairlead tension in the windward mooring line also increased at low frequencies in response to 2D+3D turbulence.

These results show that for large offshore wind turbines, the effect of low-frequency wind fluctuations can not be ignored. This study demonstrates the importance of accurately simulating low-frequency wind fluctuations to effectively assess the wind turbine's response.