Modeling and Simulation of an Underwater Tether Cable Trajectory on Uniform Current and Constant Moving Vehicle

IntroductionThe analysis of cable states, particularly for underwater cables, is a critical task before the deployment of subsea systems because it ensures operational safety and efficiency in scientific research and offshore engineering applications.Cablebased systems, including tether management system (TMS) -remote operated vehicle (ROV) configurations, umbilical cables, towed cables or towedarray systems, and mooring lines, are subjected to distributed selfweight, buoyancy forces, and hydrodynamic loads induced either by ambient currents or by the relative motion of the cable during towing operations (Fig. 1).Therefore, accurate prediction of the static equilibrium configuration and tension distribution along the cable is essential for safe and efficient operation, and for establishing reliable initial conditions for subsequent dynamic analyses.Over the past several decades, several modeling strategies have been developed to describe the behavior of underwater cables under a distributed load.These approaches include quasistatic formulations, shootingbased methods, direct equilibrium formulations, lumpedmass models, and fully dynamic models based on finitedifference or finiteelement discretization.Early studies frequently used shootingtype formulations, in which unknown boundary forces are iteratively adjusted until a global equilibrium is achieved (De Zoysa, 1978).Although computationally efficient, these methods are extremely sensitive to initial guesses and may show convergence difficulties under strong hydrodynamic nonlinearities (Masciola et al., 2012).Quasistatic and directequilibrium methods have been widely adopted to overcome these limitations, especially for steady or slowly varying operating conditions.In such models, the cable configuration is assumed to evolve through a sequence of instantaneous equilibrium states, a strategy shown to be effective for many towedcable applications (Wang et al., 2008;Yoon et al., 2012;Zhang et al., 2023;Vo et al., 2024Vo et al., , 2025)).In parallel, discretizationbased formulations such as the lumpedmass approach have gained broad acceptance in academic research and industry because of their flexibility in representing complex geometries, boundary conditions, and coupled