## 3 Results and Discussions
### Behavioral Characteristics of the Flap
As depicted in Figure 8a, \(H_{i}/L\) for patterns D and E increased linearly when \(D/L\) increased, and the rapid increase of \(H_{i}/L\) was confirmed in the range of 0.4 \(<\)\(D/L\)\(<\) 0.5. In particular, pattern D was predominant at \(D/L\)\(\approx\) 0.55. Additionally, as depicted in Figure 8b, in the designed WEC system, a \(P_{wave}\)\(>\) 11 W is required in the range of \(D/L\)\(<\) 0.4, and a \(P_{wave}\) of 16 W is required in the range of 0.4 \(<\)\(D/L\)\(<\) 0.45 for comfortably generating electricity. In the range of 0.58 \(<\)\(D/L\), electricity can be produced at \(P_{wave}\)\(>\) 4 W. From Figure 8, it is suggested that the flap installation position should avoid the range of 0.45 \(<\)\(D/L\)\(<\) 0.58. On the other hand, pattern C was observed randomly near the boundaries of patterns A and B and patterns D and E and in the area of A and B. \(H_{i}/L\) and \(P_{wave}\) for pattern C are similar to or larger than those of patterns D and E; thus, the tendency of pattern C occurring is considered to be affected by other factors rather than \(H_{i}/L\) and \(P_{wave}\), such as the initial water depth. Figure 8: Tendency for the respective patterns depending on (**a**) \(D/L\) and \(H_{i}/L\), and (**b**) \(D/L\) and \(P_{wave}\). The effect of the initial water depth \(h\) on the behavior of the flap was examined. The initial water depth \(h\) was nondimensionalized by the height of the flap \(h_{f}\). Figure 9 depicts the patterns of the flap depending on \(h/h_{f}\) and \(P_{wave}\). The results in the range of \(0.45<D/L<0.58\), in which the invalid pattern was dominant, were excluded in Figure 9 because the effect of \(D/L\) on the flap behavior was dominant rather than \(h\). From Figure 9a, which depicts patterns C, D, and E, the behavior of the flap tends to become an invalid pattern despite a relatively large \(P_{wave}\) in the water depth equal to and greater than the height of the flap (\(h/h_{f}\geq 1\)). In particular, the \(P_{wave}\) to become pattern E at \(h/h_{f}\geq 1\) is larger than the \(P_{wave}\) at \(h/h_{f}<1\). Similarly, it is confirmed in Figure 9b, which depicts patterns A and B, that more wave power is required to generate electricity normally at \(h/h_{f}\geq 1\). Focusing on pattern C at \(h/h_{f}<1\), even with a \(P_{wave}\) that is smaller than pattern E, pattern C can be observed at \(h/h_{f}=0.89\) and 0.93 where the initial water depth is less than the height of the flap. For example, \(P_{wave}=1.74\) W for \(h=0.93\) (\(D/L\) = 0.5870 in Figure 8b) and \(P_{wave}=4.67\) W for \(h=0.89\) (\(D/L\) = 0.4328 in Figure 8b). Though pattern C is the invalid pattern as well, the flap is rotated irregularly for pattern C, differently from patterns D and E, which are halted without motion. Therefore, this implies that if the initial water depth is smaller than the height of the flap (\(h/h_{f}<1\)), the flap can easily rotate even with a relatively small \(P_{wave}\). On the other hand, focusing on pattern C occurred for \(P_{wave}>10\) W, which coexisted with patterns A and B, as shown in Figures 8b and 9b; the relevant results can be found at \(h/h_{f}\geq 1\) in Figure 9a. This implies that the possibility of the behavior of a flap being unstable increases given the condition of \(h/h_{f}\geq 1\) for relatively small \(P_{wave}\). These tendencies suggest that it is more effective to install the flap in the condition of \(h/h_{f}<1\) in terms of avoiding the invalid pattern. The position of \(D/L\) = 0.5 is well known as the anti-node of the standing waves formed by the incident and reflected waves. Near this position, as pointed out by [PERSON] et al., (2015), most of the water particles move up and down. Consequently, the external force available to rotate the flap is significantly small. Figure 10 illustrates a screenshot of a movie taken from the side of the wave flume for the case of \(D/L\) = 0.4463 in pattern E. From the figure, it can be confirmed that the anti-node of a standing wave is formed on the offshore side with respect to the flap.