Abstract: Nuclear-powered unmanned underwater vehicles (UUVs) offer exceptional endurance, high maneuverability, and strong stealth capabilities, positioning them as critical components of future deep-sea equipment systems. The supercritical carbon dioxide (SCO₂) Brayton cycle, characterized by high cycle efficiency, compact configuration, and minimal auxiliary components, provides a viable pathway toward modular and miniaturized nuclear reactor designs for such platforms. Within a 200 kW turbine-motor-compressor power module developed for a nuclear UUV, the SCO₂ compressor serves as the core energy conversion component whose operational performance directly governs overall system efficiency, safety, and operational flexibility. The shaft-end dry gas seal (DGS) acts as a critical sealing element, offering near-zero leakage performance that significantly enhances cycle thermal efficiency. Nevertheless, under inclined and swaying hull motions, mounting misalignment, thermal deformation, and multi-source excitations, the DGS is susceptible to face rubbing and film instability failures. Consequently, investigating the dynamic characteristics of SCO₂ DGS under multi-source disturbances is essential for advancing deep-sea nuclear UUV technology. Existing studies predominantly simplify the gas film as a linear spring-damper system and employ perturbation-based linear analysis methods. The isothermal model is widely adopted, and although conjugate heat transfer approaches can better capture temperature distributions, the multi-physics coupling mechanisms behind macroscopic performance, particularly the interplay among real-gas property variations, turbulence effects, centrifugal inertia, and sonic choking, remain inadequately elucidated, limiting both predictive depth and engineering guidance. To address these gaps, this study first conducted an optimal design of the compressor shaft-end dry gas seal for the targeted 200 kW SCO₂ power module. A multi-scale, multi-physics mathematical model was then established, and a novel fully three-dimensional multi-frequency perturbation numerical method was developed, comprehensively incorporating real-gas effects, turbulence effects within the microscale clearance, centrifugal inertia effects in the radial momentum equation, and choking flow conditions at the seal exit. A systematic parametric study covering four inlet pressures (10, 11, 12, and 13 MPa), three inlet temperatures (80, 100, and 120 ℃), and three outlet back pressures (2, 3, and 4 MPa), amounting to 36 operating conditions, was performed. And the steady-state leakage rate, opening force, film pressure and temperature fields, and frequency-dependent dynamic stiffness and damping coefficients were computed and analyzed. Results demonstrate that increasing inlet pressure elevates film pressure, intensifies the outlet temperature drop, amplifies both opening force and leakage, and enhances film stability. Raising inlet temperature exerts minor influence on pressure distribution but markedly elevates the temperature field, reduces opening force and leakage, and degrades stability. Increasing outlet back pressure raises the overall film pressure level, elevates exit temperature, increases opening force while suppressing leakage, and strengthens the seal’s resistance to low-frequency external disturbances, though its influence on restoring equilibrium at higher frequencies remains limited. To ensure safe operation, the inlet temperature should be maintained above 80 ℃ and the outlet pressure above 2 MPa; violating these thresholds may trigger excessive leakage or negative damping, jeopardizing seal integrity. These findings elucidate the multi-scale coupling mechanisms from flow structure, energy transfer, phase-state transitions, and stability criteria perspectives, clarifying the intrinsic influence of key operating parameters on seal dynamic performance. The proposed methodology and results provide concrete design guidelines for reliable, long-life dry gas seals in advanced marine nuclear power systems.