*2.2. Potential Flow Theory*

The potential flow theory may be to calculate the hydrodynamic loads on marine structures. It is usually assumed that the fluid is non-rotating, non-viscous, and incompressible, and the fluid is assumed to be an ideal fluid [47,48]. Derived from the conservation of mass and the conservation of momentum, the governing equations of fluid motion, the Laplace equation are expressed as follows:

$$
\nabla^2 \phi = 0 \tag{13}
$$

$$\frac{\partial \mu}{\partial t} + (\mu \cdot \nabla)\mu = -\nabla \left(gz + \frac{p}{\rho}\right) \tag{14}$$

where *φ* represents the three-dimensional velocity potential function and *φ* = *φ*(*x*, *y*, *z*, *t*). The velocity potential can be decomposed into the following equation:

$$
\phi = \phi^i + \phi^d + \phi^r \tag{15}
$$

where *φ<sup>i</sup>* is the velocity potential function of the incident wave, *φ<sup>d</sup>* is the diffraction potential function, and *φ<sup>r</sup>* is the radiation potential function.

For the fluctuation problem of linear periodic motion, the time factor can be separated by the variable separation method, and the velocity potential can be expressed as follows:

$$\phi = \text{Re}\left[\varphi e^{-i\omega t}\right] \tag{16}$$

where *ω* is the angular frequency and Re represents the real part.

#### *2.3. Viscous Loads*

In potential flow theory, since the assumption is inviscidity, viscosity needs to be considered in practice. In this study, the Morrison model was added to consider the viscosity [48,49]. In AQWA, the viscosity was simulated by adding Morrison elements as follows:

$$f\_d = 0.5C\_d \rho D \mu |\mu|\tag{17}$$

where *Cd* represents the drag coefficient, and in this study, *Cd* = 1.2 was selected due to *d*/*L* ≥ 0.2 and *H*/*d* ≤ 0.2; *H*, *d*, and *L* represent the wave height, water depth, and wavelength, respectively; *μ*, D, and are the incoming flow velocity, structure diameter, and fluid density, respectively; and *fd* represents the drag force on a unit height of the structure.
