## 1 Introduction  
In light of the inevitable exhaustion of fossil fuel resources and the accelerated global warming resulting from greenhouse gas emissions, it is imperative to actively pursue the development of renewable clean energy sources as a response to this global crisis [1, 2, 3]. Wind energy is regarded as one of the most prospective sources of clean energy, and it is primarily categorized into two types: onshore and offshore wind energy. In recent years, offshore wind energy has emerged as a highly promising form of wind energy [4, 5, 6]. Particularly, the advancement of floating offshore wind turbine (FOWT) technology has made it feasible to extract wind energy from deep sea locations [7, 8]. Currently, the primary types of floating platform used in FOWTs are semi-submerged, spar, and tension leg platform [9]. However, the spar platform is typically employed in greater water depths, while the tension leg platform experiences challenges related to tendon stress and incurs significant costs. These two types of platforms are not as prevalent as semi-submersible platforms. Therefore, the semi-submerged platform is one of the most used platform types in the industry of FOWTs. The mooring system is one of the important constituent parts of FOWTs and mooring cables can influence the forces on a floating structure. Based on the configurations, the mooring system can be categorized into catenary mooring system and taut leg mooring system. Due to the mooring cables being taut, the taut leg mooring system maybe too stiff for FOWTs. Consequently, the catenary mooring system is the most widely used system [10]. Generally, FOWTs are exposed to a variety of environmental loads, such as wind, waves, and currents under operational conditions [11; 12]. It is crucial to properly analyze the effects of those environmental loads on FOWTs on the performances of such floating structures [13]. The coupling influence of winds and waves on FOWTs has been extensively examined in research studies. [PERSON] et al. [14] analyzed the aero-hydrodynamic interference impacting on the National Renewable Energy Laboratory (NREL) 5-MW semi-submerged FOWT under rated wind and first-order regular wave conditions when experiencing surge motion. [PERSON] et al. [15] investigated the dynamic responses and mooring line failure of the fully semi-submerged FOWT under various typhoon and wave spectrum conditions. [PERSON] et al. [16] constructed a fully-coupled analysis of the NREL 5-MW spar-type FOWT with bionic fractal heave plates under wind-wave excitation conditions. [PERSON] et al. [17] examined the effects of various freak waves on dynamic responses of a spar buoy FOWT under rated wind conditions. [PERSON] et al. [18] explored the design strategy for resonance avoidance to improve the performance of TLP-type FOWTs. [PERSON] et al. [19] inspected the extreme responses of the NREL 5-MW spar-type FOWT under typhoon impact and their applications by use a joint probabilistic modeling. The aforementioned studies have examined the influence of wind and wave conditions on the dynamic responses and performance of different types of FOWTs. However, none of these studies took into account the influence of ocean currents. Ocean currents are a typical environmental factor that should not be overlooked due to their potential to influence the dynamic behavior of floating structures and mooring systems. Specifically, they may lead to vortex-induced vibration in mooring cables [20]. And the interaction of waves and currents is of interest in many fields, including applied mathematics and engineering [21]. For FOWTs, the interaction of waves and currents is essential in assessing the load effects on structures [22; 23]. Existing research has only superimposed the impact of waves and currents without taking into account their coupling interaction [24; 25] or only considered the interaction for a specific wave, such as a freak wave [26; 27]. Consequently, the dynamic response of the structure may not accurately reflect the real-world conditions.