This study examines the strongly nonlinear cross-media dynamics of a deep-sea umbilical cable–payload system during free-surface crossing under different sea states and lifting speeds. A two-dimensional time-domain lumped-mass model was established, in which the cable was discretized into node–axial elements. Morison-type hydrodynamic loading, added mass, and a continuous air–water parameter transition governed by an immersion factor were included for both the cable and the lower-end payload. To improve numerical robustness in long-duration simulations, a segmented ODE15s integration scheme was adopted, together with a smooth-start lifting–heave boundary condition and an adaptive lift-height correction procedure to ensure a stable cross-media response window. The results show a clear spatially segmented response: the upper cable remains nearly straight, whereas the middle and lower sections accommodate most of the lateral offset and curvature redistribution, which intensify under stronger environmental forcing. Top tension shows a gradually increasing mean component superimposed on quasi-periodic oscillations, while bottom tension, detrended vertical payload displacement, and vertical hydrodynamic force are more sensitive to sea-state severity and lifting speed. These results provide a comparative numerical basis for identifying response trends, screening lifting speed options, and interpreting cross-media load transfer mechanisms. Because the formulation is two-dimensional and has not yet been validated against model-scale or full-scale measurements, the results should not be interpreted as equipment-specific safety limits.
Cp et al. (Tue,) studied this question.