Large-scale offshore aquaculture vessels provide an effective approach for expanding marine aquaculture; however, the complex flow characteristics induced by water circulation systems and vessel motion remain insufficiently understood. In this study, a numerical model based on the volume of fluid (VOF) method and the k-$\omega$ SST-DES turbulence model was developed to investigate the vortex flow characteristics. The developed numerical model accurately captured the vortex flow characteristics and free-surface fluctuations in the aquaculture tank, and the dominant coherent structures were identified using Q-criterion-based proper orthogonal decomposition (POD). The results show that the mean vortex structure is mainly concentrated around the central axis, while higher-order POD modes reveal vortex-core oscillation, deformation, and interactions with surrounding flow structures. Furthermore, the effects of roll excitation and its coupling with inlet jet flow were investigated. The results demonstrate that roll motion induces significant periodic fluctuations in the flow field, while the inlet jet flow maintains the stability of the central vortex structure and reduces velocity variations. These findings provide new insights into the hydrodynamic mechanisms governing vortex evolution under combined vessel motion and water circulation and offer a scientific basis for optimizing flow conditions in large-scale offshore aquaculture tanks.