## 3 Calculations of Wave Power
### Bulk Parameters and Nonlinear Wave Properties  
The extraction of renewable energy from ocean waves, via WEC devices, can alter coastal hydro- and morpho-dynamics. This may be due to the actual extraction process or to the WECs altering wave propagation (reflection, diffraction, and dissipation), which is especially important if the devices are placed close to the shore. It could be argued that the placing of WECs closer to the shore would be beneficial if the design of the WEC farm fulfils a double purpose: carbon-free energy generation and coastal protection [38]. A WEC device mounted on a buoy could act as a floating breakwater, dissipating wave energy and mitigating erosional effects on the coast. Two parameters are important in this case: the immersion ratio (the water depth above the device, divided by the water depth) and the relative length (the length of the buoy, divided by the water depth, \(w/h\), where \(w=L_{b}+R\)): in a brakewave, the reflection coefficients increase with the relative length [39]. A knowledge of the reflection, dissipation, and transmission coefficients produced by a WEC can be key to the installation of single or multiple devices. These types of wave bulk parameters are useful not only for assessing the effects on the coast, but also on other WECs, as in the case of a WEC farm or array, or on other marine structures. The reflection coefficient (\(K_{r}\)) is calculated as the ratio of the reflected and incident wave heights (\(H_{r}/H_{i}\)). This is usually evaluated where the incoming waves are approaching the WEC at the seaward end. The transmission coefficient (\(K_{t}\)) is defined as the ratio between the transmitted and incident wave heights (\(H_{t}/H_{i}\)). This is usually evaluated on the protected side of the WEC: the shoreward side. Finally, a coefficient must be added to compensate for the energy being dissipated or absorbed by the wave-structure interaction (\(K_{d}\)). This is calculated using the ratio between the assumed loss in wave height, denoted by \(H_{d}\), to the incident wave height, \(H_{d}/H_{i}\). This energy loss is related to the aforementioned coefficients to achieve wave energy conservation [40]:  
\[K_{t}^{2}+K_{r}^{2}+K_{d}^{2}=1 \tag{12}\]  
According to Equation (12), the balance between reflected, transmitted, and dissipated wave heights must fulfil the following equation:  
\[H_{t}^{2}+H_{r}^{2}+H_{d}^{2}=H_{i}^{2} \tag{13}\]  
Equation (13) quantifies the wave energy loss as the wave field interacts with the WEC. In these experiments, \(H_{i}\) and \(H_{r}\) were evaluated with the gauges at points \(P_{1}(-9.95,0,0)\), \(P_{2}(-8,0,0)\), and \(P_{3}(-7,0,0)\), with probe spacing values of \(x_{12}=1.95\) and \(x_{13}=2.95\). Finally, for \(H_{t}\), the point evaluated was \(P_{4}(+10,0,0)\). Incident and reflected wave heights were measured by the methodology proposed by [PERSON] and [PERSON] [41]. This method is based on applying a least squares method to separate the incident and reflected spectra assuming Fourier components on the decomposition of the free surface. They suggest the use of three gauges placed in the flume at suitable positions relative to the wavelength. We used 21 gauges, placed one meter apart in the \(x\) direction. To quantify the wave energy absorption from a single WEC with the applied methodology [42], part of the wave height can be related to energy dissipation. This, in turn, is related to the energy absorbed by the buoy. Therefore, the wave energy absorption/dissipation (\(H_{d}^{2}\)) can be calculated from Equation (13) as \(H_{d}^{2}=H_{i}^{2}-\left(H_{t}^{2}+H_{r}^{2}\right)\). In this paper, a CFD model was used to assess the effects of the WEC buoy in modifying the non-linear wave properties known to contribute to onshore sediment transport, such as velocity skewness and vertical asymmetry [11; 43].