## 2 Extension and Refinement of the Ocean Disturbance Simulation System Model
### Method Analyses  
Before starting the simulation, we must determine the ROV's path. As Figure 4 shows, its path was as follows. Figure 4: The path that the ROV travels. Figure 3: Real shape of an ROV. According to experimental observations, we defined \(d\) as the distance between the ROV and the target. When \(d\) was less than 4 m, the influence of the ocean wake flow should be taken into account in some cases. Figure 5 illustrates a typical wake flow pattern encountered as the ROV approached the target. As shown in Figure 5, the influence of wake flow varied significantly, depending on the ROV's relative approach direction to the target. When the ROV approached the target head-on (i.e., directly facing the current), the impact of wake flow was minimal and could often be neglected. In contrast, wake-induced disturbances became more prominent when the ROV approached from the side or the rear, either perpendicular to the flow or aligned, and they must be considered in the trajectory and control model because wake turbulence introduces unpredictable velocity fluctuations and pressure gradients, which can degrade control accuracy and cause trajectory deviation, especially when using PID-based or linear control strategies. Therefore, we divided the directions from which the ROV approached the target into three parts, as shown in Figure 6.  
Figure 5: A Typical type of wake flow. Figure 6: Illustration of wake flow near the target, segmented into three analytical regions. In the non-wake flow area, we only simulated the path under the influence of ocean currents, while in the wake flow area, both ocean currents and wake flow needed to be considered [19]. Based on Figure 6, in wake flow area 1, we considered the wake flow in the same direction as ocean currents, but in wake flow area 2, it was in the opposite direction. \(\omega\) denotes the angle between the ROV's approach direction and the ocean current (as shown in Figure 6). The flow field around the target was divided into three regions based on \(\omega\):  
* The non-wake flow area corresponded to \(\omega\in[-45^{\circ},+45^{\circ}]\), where the ROV approached from the front without entering the wake region;
* Wake flow area 1 covered the angular range \(\omega\in(45^{\circ},135^{\circ})\cup(225^{\circ},-45^{\circ})\), where the ROV encountered lateral wake effects;  
Wake flow area 2 was defined for \(\omega\in[135^{\circ},225]\), representing the direct downstream wake region behind the target. According to DNV RP C205 [20], the velocity within the wake region \(v_{f}\) can be estimated as a fraction of the freestream current velocity \(v\). The wake deficit coefficient \(\Delta\), which depends on the geometry and blockage of the upstream obstacle, was used to characterize the velocity reduction inside the wake region. The relationship is typically expressed as follows:  
\[v_{f}=v\;(1-\Delta), \tag{9}\]  
Thus, the wake velocity generally ranged from 30% to 80% of the freestream current velocity, consistent with engineering approximations suggested in DNV RP C205 and supported by empirical studies, such as those by [PERSON] et al. \(\Delta\) was set to 0.5 in wake flow area 1 and 0.3 in wake flow area 2. This region-based classification is informed by classical wake flow theory and offers clear physical interpretability and engineering practicality. Compared to continuous gradient models, discrete disturbances improve simulation stability while sufficiently capturing the dominant characteristics of the flow field, making it suitable for path planning and control algorithm development [21]. According to the standard DNV RP C205, when detailed field measurements are not available, the variation in shallow tidal current velocity with depth may be modeled as a simple power law.