## 1 Introduction  
With the continuous exploitation of marine resources, underwater wireless sensor networks (UWSNs) composed of underwater nodes have made great achievements in disaster warning, target tracking, and other fields [1]. In the target region of the UWSNs, nodes obtain the required data through the Internet of underwater devices [2]. These underwater nodes have data acquisition, transmission, and communication capabilities for the interaction of physical and logical information via hydroacoustic signals [3]. The ability of underwater acoustic communication is correlated with channel, transmission power, array, etc., and the quality of underwater acoustic communication is usually measured as the product of underwater communication rate and distance. According to statistics from the US Naval Research Laboratory, the product of most underwater acoustic communication rates and distances is 40 kbps \(\times\) km, which means the maximum communication distance at a communication rate of 40 kbps is 1 km. In 2020, Zhejiang University reported a communication distance of 6.2 km and a communication speed of 42.8 kbps under a ship speed of 4-6 knots, with a product of 265.36 kbps \(\times\) km long-distance communication. It is well known that hydroacoustic perception is superior to other sensing methods [4]. Hence, reasonable deployment of underwater nodes based on hydroacoustic communication is the basis of realizing efficient network monitoring [5]. Usually, random deployment results in a poor distribution density balance of nodes, resulting in coverage holes in UWSNs that cannot be effectively connected. When the network is not connected, the ground receiving station and the underwater node cannot communicate normally, and the data cannot be obtained, thus causing partial paralysis of the UWSNs [6]. Limited by the actual cost of underwater hardware, deploying as few sensors as possible to collect more information is an ideal option that has usually been pursued [7]. Underwater node location is crucial to the network coverage effect, and it needs to be updated constantly to complete the monitoring task. Achieving a maximum coverage rate for carrying out online monitoring is very important for improving the quality of services in UWSNs [8]. Some scholars have conducted a series of in-depth research on node coverage control. Considering the covering angle of nodes, a dynamic node deployment model with two-dimensional distribution was proposed to transmit the aggregated data, but it did not consider how the sensor node drift would be affected by water flow in dynamic open waters [9]. To address the coverage black hole caused by node drifts, a virtual force is introduced to drive the underwater sensor node to repair the covering black hole, and the boundary of the black hole is obtained using a geometric solution [10]. However, the motion of the sensor node perpendicular to the ground is ignored. [PERSON] et al. used the depth direction mobility of nodes for topology optimization and designed corresponding optimization criteria [11]. [PERSON] et al. anchored the nodes randomly on the seabed; the nodes can move in the depth direction. On the premise of ensuring mutual communication, a weighted complete bipartite graph is generated to simulate the coverage of each node [12]. The scheme with the minimum number of nodes obtained using the cooperative path topology achieved target optimization, and a coverage strategy of limited and full communication redundancy was obtained [13]. Considering the coverage black hole problem in three-dimensional environments, [PERSON] et al. used the semicircular plate rotation method to transform the two-dimensional coverage problem into a three-dimensional coverage problem [14]. The proposed strategy is feasible within the aquatic boundary.