Underwater wireless sensor networks (UWSNs) have been developed for underwater applications, such as resource exploration, pollution monitoring, and tactical surveillance. The topology control techniques of UWSNs and terrestrial wireless sensor networks are significantly different because of the particularity of underwater environments and acoustic communication, such as mobility pattern, propagation delay and energy consumption. Due to multifarious factors of underwater environments, node mobility becomes a non-negligible issue. However, GPS may not be feasible because of the limitations of satellite coverage or obstructions in adverse underwater environments. In particular, anchored sensor nodes towed by wires are prone to offset around their static positions, causing each node to move within a spherical crown surface (spherical crown mobility pattern). Nevertheless, most previous studies have not focused on this specific mobility pattern. In the current paper, a mobility model for UWSNs nodes is constructed, and three representative topology control objectives are attained. A distributed radius determination algorithm is designed for the mobility-based topology control problem. Results of theoretic analysis prove that the proposed algorithm is convergent, and it has preferable approximate ratios and polynomial complexity. Performance of the algorithm is analyzed through simulation experiments, which indicate a well-constructed topology. Every objective can still be upgraded without the dynamic location information of mobile nodes.