## 2 Theory  
CFD simulations were conducted using STAR-CCM+ software (v. 2022.1, Siemens PLM Software, Plano, TX, USA). This section elucidates the salient theories and formulas underpinning numerical simulations. In light of the paper's brevity, supplementary theories are presented within the confines of the Appendix A.  
RANS (Reynolds-averaged Navier-Stokes) equations are used to model the flow around ships and are nearly identical to the original Navier-Stokes equations. Turbulence models provide closure relations for the RANS equations, which govern the transport of the mean-flow quantities, and the mean mass and momentum transport equations can be expressed as follows [35]:  
\[\frac{\partial\rho}{\partial t}+\
abla\cdot\left(\rho\overline{v}\right)=0 \tag{1}\]  
\[\frac{\partial}{\partial t}\left(\rho\overline{v}\right)+\
abla\cdot\left( \rho\overline{v}\otimes\overline{v}\right)=-\
abla\cdot\overline{p}\mathbf{I }+\
abla\cdot\left(\mathbf{T}+\mathbf{T}_{t}\right)+\mathbf{f}_{b} \tag{2}\]  
where \(\rho\) is the density; \(\overline{v}\) and \(\overline{p}\) are, respectively, the mean velocity and pressure; \(\mathbf{I}\) is the identity tensor; \(\mathbf{T}\) is the viscous stress tensor; \(\mathbf{T}_{t}\) is the Reynolds stress tensor; and \(\mathbf{f}_{b}\) is the resultant of the body forces (e.g., gravitational and centrifugal).  
The RANS equations were discretized using the finite volume method (FVM). The turbulence model employed was the k-\(\varepsilon\) model. To handle the coupling between pressure and velocity, the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm was utilized. The segregated flow model solves the equation in a segregated manner, and the convection term is discretized using the second-order upwind scheme. Cables are introduced through coupling modules of multiple floating bodies. The volume of fluid (VOF) method was employed to accurately depict the evolution of the free surface in the two-phase flow. To account for ship motions, the dynamic fluid body interaction (DFBI) module, in conjunction with the overset mesh, was implemented.  
The VOF wave model simulates surface gravity waves at the interface between light and heavy fluids. Typically, this model is used with the 6 DOF model for marine applications. A convenient model involves a steadily progressing periodic wave train to describe fluid velocities, pressures, and surface elevations resulting from waves. This wave train can be defined and solved by considering three fundamental physical length scales: water depth, wavelength, and wave height. [PERSON]'s wave theory is one of the primary theories for addressing the steady wave problem. When using the [PERSON]'s wave theory to simulate waves, the horizontal wave velocity is determined as follows:  
\[v_{h}=a\omega cos(K\cdot x-\omega t)e^{Kz} \tag{3}\]  
The velocity of the wave in the vertical direction is as follows:  
\[v_{v}=a\omega sin(K\cdot x-\omega t)e^{Kz} \tag{4}\]  
The height of the wave surface is as follows:  
\[\eta=a\omega cos(K\cdot x-\omega t) \tag{5}\]  
The wave period (\(T\)) and wavelength (\(\lambda\)) are as follows:  
\[T=\frac{2\pi}{\omega},\ \lambda=\frac{2\pi}{K} \tag{6}\]  
The dispersion relation (between wave period \(T\) and wavelength \(\lambda\)) in finite water depth \(d\) is as follows:  
\[T=\left[\frac{g}{2\pi\lambda}tanh\left(\frac{2\pi d}{\lambda}\right)\right]^{ -1/2} \tag{7}\]