# Hydrodynamic Investigation on a Land-Fixed OWC Wave Energy Device under Irregular Waves
## 4 Results and Discussions
### Water Motion inside the Chamber  
In order to examine the spatial distribution of the free surface inside the chamber, four numerical wave gauges were used to record the surface displacements at different internal chamber locations as described in Figure 1. The energy distribution of the free surface elevation is obtained by FFT. Figure 11 shows the difference in the dimensionless wave elevation for \(k_{p}h=2.186\) and \(k_{p}h=1.258\) along the numerical wave tank close to the chamber. It is found that the wave profile becomes sharper and the higher harmonic wave is more obvious with \(k_{p}h\) increasing due to the magnified wave nonlinearity. In addition, energy is transferred from the fundamental frequency to the higher frequency and waves are reflected by the chamber wall. This results in reduced wave transmission into the chamber interior. Thus, the water free surface elevation in the chamber with wave frequency \(k_{p}h=1.258\) (low frequency) is higher than that of wave frequency \(k_{p}h=2.186\) (high frequency). A comparison of the incident wave spectrum with the free surface elevation spectra at G1 (external to the chamber) and G4 (chamber mid-point) is shown in Figure 12. There is a clear cut off frequency at approximately 1 Hz for the free surface spectrum at the chamber center for both \(k_{p}h=1.258\) and \(k_{p}h=1.819\). This is due to the high frequency waves being reflected by the front wall of the device; thus, the wave energy cannot transmit into the OWC chamber. Therefore, in high wave-frequency conditions, the energy at the chamber center is less than the energy of the incident wave. In addition, the amplified complex energy oscillation phenomena are recorded in the energy spectrum outside the chamber  
Figure 11: Profile of the free-surface elevations along the numerical wave tank when the wave crest arrives at front wall of the OWC. (**a**) Overall view, (**b**) magnified view at OWC front wall. Figure 10: Comparison of the hydrodynamic conversion efficiency versus peak wavenumber between regular and irregular wave conditions. at the high-frequency region due to the strong wave nonlinearities and the interactions between incident waves and reflected waves. Figure 13 presents the free surface elevation profiles at the interior of the chamber for \(k_{p}h=3.010\) and \(k_{p}h=0.750\) when the difference between the surface elevation at G2 and G5 reaches its maxima and minima, respectively. The wave profile is antisymmetric inside the chamber with the surface rising at one wall, whilst simultaneously falling at the other wall. Furthermore, the absolute value of the elevation difference between G2 and G5 in high frequency wave conditions (i.e., \(k_{p}h=3.010\)) is greater than that at the lower frequency wave (i.e., \(k_{p}h=0.750\)). This is manifest by the surface elevation inside the chamber becoming flatter under the longer wave conditions. Considering the antisymmetric and fluctuating wave profiles inside the chamber in the irregular wave conditions, sloshing modes are used to analyze the sloshing motion of the free surface. Sloshing modes can be determined from \(kB=n\pi\), where \(n\) represents the \(n\)th mode. All odd harmonic modes are asymmetric while even harmonic modes are symmetric. The fundamental harmonic mode is excited when the OWC chamber width is half the incident wavelength (i.e., \(B/\lambda_{p}=0.5\)). Other harmonic modes manifest with wavelengths equal to one half, one third, one fourth etc., of the wavelength of the fundamental mode. Since the chamber width in this model is 0.55 m, only the first mode of sloshing can be observed at frequency 1.19 Hz (\(k_{p}h=4.563\)). The free surface elevation spectra calculated from numerical wave gauges G3 and G4 at the interior of the chamber for six different \(k_{p}h\) are shown in Figure 14. There is clear evidence of sloshing energy at frequency 1.19 Hz for some higher incident wave frequencies, most notably at \(k_{p}h=3.010\) and 2.578. The sloshing becomes weaker as the wave frequency increases.