## 5 Conclusions  
The boundaries of a region were defined to distinguish a free tow point from a wall-attached tow point using a coupled system simulation method, which accurately captures the variations in position and attitude of the drag system cable resulting from its immersion in the wake. A transition zone has the possibility to change the pattern from a free tow to a wall-attached tow. Furthermore, the influence of wake on the towed cable is related to the maneuvering effect of submarines, resulting in a submergence effect and exhibiting significant differences compared to straight-line navigation.  
(1) The interaction between the wake in the upper area of the hull and the cable is a strong coupled effect, with the wake causing the cable to completely adhere to the surface of the hull.  
(2) During direct sailing, when the towed cable is not in the central area affected by the propeller's operation (the strong jet flow area caused by the propeller), the suction effect of the propeller can be ignored.  
(3) The low-speed wake area on the back of the hull and the hull absorbs energy, allowing the cable to adhere to the surface of the hull. During direct navigation and angle of attack movements, the attachment area absorbs energy, resulting in an angle of 1/105 between the cable shape and the direction of navigation in the free motion area. Under rotational motion, due to the more significant separation motion, the energy obtained in  
Figure 13: Relation between wake and attitude and position of cable at an 8\({}^{\circ}\) drift angle.  
the free motion zone increases compared to direct navigation, and the angle between the cable shape in the attachment zone and the navigation direction is 1/25 of that in the free motion zone. The gap between the two has significantly narrowed.  
(4) Under the action of the drift angle, the lateral separation flow around the vehicle gradually becomes stronger. Unlike the straight state, the spatial curvature of the cable motion under rotation is large, and due to the influence of the drift angle, the attitude and position of the cable is biased toward the y-axis, with the attitude and position of the cable being approximately 30\({}^{\circ}\) closer to the vessel body in the longitudinal direction compared to the straight-ahead cable.  
(5) During the maneuvering motion, the distance between the attitude and position of the cable and the navigating body varies in a consistent trend at different towed positions. Based on the relationship between the wake and the cable, the distribution of the towed area for the submarine maneuvering action and straight motion can be divided into free tow region, transition zone, and adjacent wall tow region by this FSI assessment method.  
Conceptualization, [PERSON] and Z.W.; methodology, [PERSON]; software, [PERSON]; validation, [PERSON] and Z.W.; formal analysis, [PERSON]; investigation, J.G.; resources, [PERSON]; data curation, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON]; visualization, [PERSON]; supervision, [PERSON]; project administration, [PERSON]; funding acquisition, [PERSON] All authors have read and agreed to the published version of the manuscript.  
The authors declare no conflicts of interest.