A two-dimensional coupled dynamics model for a moored autonomous underwater vehicle (AUV) was developed using the lumped mass method for mooring cable dynamics and the Newton-Euler method for rigid body dynamics. This model enables the integrated simulation of AUV motion, flow field interactions, and mooring cable behavior. The study investigates the effects of varying ocean current velocities and mooring cable lengths on AUV motion responses. The results indicate that under the influence of mooring forces, the AUV stabilizes near its equilibrium position after release and undergoes periodic oscillatory motion. Specifically, when the X-direction oscillation completes two cycles and the Y-direction oscillation completes four cycles, the AUV demonstrates an 8-shaped trajectory, with maximum motion amplitudes observed. These findings provide insights into the dynamic behavior of moored AUVs in ocean environments, contributing to the design and operation of long-term underwater monitoring systems.