First, the model was validated using the wave buoy data at Perranporth Beach from November 2007 to October 2008, missing out January 2008 owing to the lack of data.
Figure 5.5 and Figure 5.6 show the good fit achieved between the significant wave height computed by SWAN and the values from the wave buoy. The coefficient of determination, R2, and the Root Mean Square Error, RMSE, confirm the goodness of the fit: R2 = 0.94 and RMSE = 0.38 m.
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Figure 5.5 Time series of simulated (Hs, SWAN) and measured (Hs, buoy) significant wave height. The vertical lines depicted in the graph show the months 1, 3 and 6 after the first point of the simulation.
Figure 5.6 Scatter diagram: simulated (Hs, SWAN) vs. measured (Hs, buoy) significant wave height.
Second, having validated the numerical model, it was used to compare the wave patterns with and without the wave farm and to determine the wave conditions to be used as input to the morphodynamic model. As an example of the effects of the wave farm on the wave patterns, the wave propagation corresponding to the peak of a storm on 10 March 2008 is shown in Figure 5.7. The deep water wave conditions were:
significant wave height, Hs0 = 10.01 m; peak wave period, Tp = 15.12 s; and peak wave direction, θp = 296.38°. A substantial decrease of the significant wave height was
M1 M3 M6
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apparent in the lee of the wave farm. This decrease was less marked on the beach itself due to thewave energy diffracted from the edges into the shadow of the farm. In the northern section of the beach the reduction of wave height was more pronounced than elsewhere owing to the deep water wave direction (approx. WNW). For waves coming from northern direction the shadow brought about by the wave farm was expanded to southern sections of the beach, although the greatest impact was still found in the north part of the beach.
Figure 5.7 Significant wave height in the baseline scenario (Hs,b) and in the presence of the farm (Hs,f) at the peak of a storm (10 Mar 2008, 18:00 UTC) [Deep water wave conditions: Hs0 = 10.01 m, Tp = 15.12 s, θp =
296.38 °].
For a better quantification of the impacts of the wave farm on the wave conditions, the RSH index is applied, which refers to the reduction of the significant wave height in the lee of the wave farm (Figure 5.8). The greatest impact was found in the lee of the second row of devices, with RSH values exceeding 0.5. The reduction reached another peak towards the coastline as a result of the merging of the wakes caused by the WECs, with values of approx. 0.4. As mentioned above, these values decreased towards the coastline, however the alteration of the wave conditions cannot be overlooked and have a significant bearing on the evolution of the beach profile.
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Figure 5.8 Reduction of the significant wave height (RSH) brought about by the wave farm at the peak of a storm (10 Mar 2008, 18:00 UTC) [Deep water wave conditions: Hs0 = 10.01 m, Tp = 15.12 s, θp = 296.38 °].
The modification of the wave patterns in the lee of the wave farm could be affected by the division of the spectral space carried out by the wave propagation model, in which elementary bins with a constant directional resolution Δθ are employed (Zijlema, 2010). A priori this should not affect the accuracy of the results, as the number of directions used in this documents were 36; i.e. a directional resolution of 5 degrees. This value is recommended in the literature (SWAN, 2007), but even higher values (30 degrees) have been applied to conduct successfully wave propagations (Monbaliu et al., 2000). In addition, the wave energy is not just concentrated in one directional sector, as due to refraction and nonlinear interactions, wave energy shifts in the spectral space from one directional sector to another. Therefore, the results seem not to be altered by the spectral resolution, as can be seen in Figure 5.8, where the wakes caused by the WECs are smaller than the 5 degrees and are represented in the space domain.
Observing the effects on the wave power (J), similar patterns can be observed, with the greatest impact taking place in the north section of the beach (Figure 5.9). The
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average reduction of the wave power during the period studied at different points along the 10 m contour is shown in Table 5.2. In line with the results previously presented, the areas most sheltered by the wave farm are the middle and, especially, the north section of the beach. On these grounds two profiles in the north and middle sections of Perranporth Beach are selected for the analysis of the impacts of the wave farm on the beach profile (Figure 5.1).
Figure 5.9 Wave power in the baseline scenario (Jb) and in the presence of the farm (Jf) at the peak of a storm (10 Mar 2008, 18:00 UTC) [Deep water wave conditions: Hs0 = 10.01 m, Tp = 15.12 s, θp = 296.38 °].
Beach Point
Coordinates
ΔHs (%) ΔJ (%) Easting (°) Northing (°)
North -5.17 50.36 3.26 12.82
Middle -5.18 50.35 1.75 6.80
South -5.21 50.34 0.70 1.52
Table 5.2 Significant wave height reduction (ΔHs) and wave power reduction (ΔJ) caused by the wave farm at different points along the 10 m contour.
The evaluation of the resource in the wave farm was carried out by means of the indicator, which represents the annual mean wave power incident on a generic WEC of the wave farm. The resource was evaluated during the year used for the validation purposes (Nov 2007 – Oct 2008) to consider both summer and winter period.
JWEC
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The average resource found in the case of locating the wave farm at a distance of 6 km from the coast was 17.26 kW/m. Considering the 11 WECs that form the wave farm and the capture width of the WaveCat (90 m), the annual mean of the total incident wave power at the wave farm was 17 MW. Applying the values obtained in Fernandez et al. (2012) for the efficiency of the WaveCat, the annual mean production of a wave farm of 11 WECs would be 4 MW. As this technology is in a nascent stage, the performance of wave farms would be further discussed further in Section 10.1.3, comparing the performance presented with other WECs.
Third, the impact of the wave power reduction on the beach was studied through the evolution of the two profiles of Perranporth Beach. This was carried out using the spectra generated by the wave propagation model with and without the wave farm in the morphodynamic model. The series were split, as explained in the methodology, to describe suitably the behaviour of the beach in different periods. The results showed that type E segments are mainly responsible for the erosion of the profiles.
Figure 5.10 shows the evolution of the beach profiles 1 (P1) and 2 (P2) after a storm. The graph compares the initial beach profiles with those after three months of operation of the wave farm. Both graphs illustrate that the erosion of the profiles is concentrated mainly in the beach face, which is the section of the profile exposed to wave uprush. The eroded material was moved to lower sections of the profile.
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Figure 5.10 Bed level at beach profile P1 and P2: initial [1 Nov 2007, 0000 UTC] and after three months with and the wave farm [22 Jan 2008, 15:47 UTC]. The average wave conditions between these two points in time
were: Hs = 2.02 m and Tz = 939 s.
To better visualise the effect of wave energy extraction, the situation of profile P2 with and without the farm is shown in Figure 5.11. The reduction of the significant wave height in the lee of the wave farm led to a substantial reduction (of the order of 3 m) in the erosion of the dune delineating the landward limit of the beach. It is also noteworthy that the wave farm not only reduced the volume of material eroded, but also altered the sediment transport patterns, displacing the landward end of erosion towards the sea around 10 m after 3 months of simulation.
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Figure 5.11 Beach face level at Profile P2: initial [1 Nov 2007, 0000 UTC] and after three months with and without the wave farm [22 Jan 2008, 15:47 UTC]. The average wave conditions between these two points in
time were: Hs = 2.02 m and Tz = 939 s.
The impact of the wave farm on the beach profile was analysed through the parameters defined in Section 3.3.2. The Bed Level Indicator (BLI) along Profiles P1 and P2 is illustrated in Figure 5.12 for three different points in time: 1 month (M1), 3 months (M3) and 6 months (M6) after the beginning of the study period. The results for both profiles show a significant reduction of the erosion in the beach face and in the submarine bar (around x = 600 m). The bar forms part of the response mechanism of the natural system to protect the beach face from increased wave attack. Figure 5.12 proves that the effect of the wave farm was a reinforcement of the bar, and therefore enhanced protection for the beach face in storms. Advancing in time, the BLI values increased in the bar area, i.e., the aforementioned effect was intensified; results that go in line with the stated by (Neill & Iglesias, 2012).
Regarding the beach face area, the BLI values for both profiles were also significant and showed that the wave farm contributed to mitigating the erosion in that section.
This is nowhere more apparent than on the dune at the landward end of the profile, where BLI values exceed 1 m. In view of the importance of erosion on the beach face the FEA and NER indicators are applied. Table 5.3 shows the values of the eroded areas
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on the beach face (FEA) at the same points in time as in Figure 5.12. It is observed for both profiles, and particularly in Profile P1, that the erosion is higher at the first two points in time (M1 and M3) than at the last one, which is associated with less energetic conditions (Figure 5.7). Although the points M1 and M3 were associated to erosionary periods, they did not coincide with the end of these periods, where generally the greatest values of storm-induced erosion were found. This is reflected in the values of erosion found on the beach face, with the greatest FEA values found at the end of the period studied.
Figure 5.12 Evolution of BLI along Profiles P1 and P2 at different points in time: 1 month (M1), 3 months (M3) and 6 months (M6) after the beginning of the study period.
The reduction of the erosion brought about by the wave farm is studied by means of the NER indicator, which showed reductions over 30% in the profile P1 (located in the north section of the beach – the most sheltered by the farm) during the erosionary periods (M1 and M3). It is also noted that the effect of the wave farm was more
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significant in the north of the beach (Profile P1) than in the middle (Profile P2), as may be seen in Table 5.1. Analysing the evolution of the NER values over time, it is observed that the wave farm was more effective to mitigate storm-induced erosion during erosionary periods than accretionary, although still significant values (NER >
20% in the north section of the beach) are found at the end of the simulation for both profiles.
Table 5.3 Eroded area in the baseline scenario (A), in the presence of the farm (Af), and Erosion Impact (EI) index for Profiles P1 and P2 at different points in time: 1 month (M1), 3 months (M3) and 6 months (M6) after
the beginning of the study period