Next, we show results from simulations using the two models, explicitly keeping the model WEC power capture characteristics the same in both, so that we can illustrate how the scattering and radiation affect the ability of the SWAN model (with the associated WEC parameterization) to simulate the wave shadow. The results also demonstrate the impact of the scattering and radiated fields on the severity of the wave shadow, which has implications for the overall nearshore wave effects of WEC arrays.
The simulation conditions bookmark the range of scattering behavior seen in both the model and experimental results in the previous section. In particular, model results are obtained for two regular wave cases with T = 1 and T = 2 s and four
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spectral seas cases—unidirectional waves and directionally spread seas both with Tp= 1 and Tp= 2 s. As can be seen in Fig.8, the two wave periods chosen have nearly the same model RCW value of∼0.35. This enables a comparison of their differing scattered and radiated wavefields in a setting where the expected power capture is the same. All simulations have the same incident wave height, but the two different spectral peak periods have somewhat different spectral shapes that follow the Pierson–Moskowitz model (also shown in Fig.8). Directional spreading (two cases) used a cos2sdistribution with a spreading parameter of s = 10.
All SWAN runs were carried out with and without the diffraction option, except for the regular wave T = 2 s case where convergence could not be attained for SWAN with diffraction (see missing panel in Fig.9). To allow for a more direct comparison, the power capture characteristics are kept the same in both models by using the RCW performance curve computed by WAMIT (shown in Figs.3and8) for the SWAN simulations.
To assess the utility of SWAN in estimating the wave shadow, we begin by analyzing the simulations involving regular waves (see top two rows in Fig.9).
Because the WEC model in SWAN is based solely on energy extraction, the SWAN results (with no diffraction effects) for both periods are identical. For these cases, the wave shadow produced by SWAN extends onshore as a narrow streak, and there is almost no recovery in wave height with distance to the lee of the WEC.
In contrast, the WAMIT wavefields for the two periods are quite different from one another. The scattered and radiated wave components are more energetic for the shorter period case, as evidenced by the stronger standing wave ridge patterns.
Because these scattering processes redistribute the wave energy spatially, the wave shadow is also clearly more pronounced for the shorter period case, even though the amount of energy extracted from the wavefield is similar for both periods. When the diffraction option in SWAN is used, the shadow spreads alongshore more readily, as expected, and the resulting shadow region is little more similar to the Fig. 8 Wave spectra
(1-second peak period in solid blue and 2-second period in dashed blue) and
WAMIT-computed RCW (green line, also shown in Fig.3)
Analyses of Wave Scattering and Absorption Produced by WEC… 91
Fig. 9 WAMIT-SWAN wavefield comparisons for regular waves (rows 1 and 2), unidirectional random waves (rows 3 and 4), and directionally spread random waves (rows 5 and 6). Each type has both 1-second and 2-second peak periods. The SWAN solution did not converge for T = 2 s regular waves w/diffraction
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WAMIT results. However, the spatial variability related to the scattered and radi-ated waves is not reproduced.
In the previous section, we noted from Fig.7that the SWAN model consistently underestimated the observed wave shadow magnitude for regular wave conditions from 1.0 to 1.4 s, i.e., for waves with smaller periods than those of the peak (experimental) RCW. This under-prediction occurs because the wave shadow associated with these shorter period waves is only partially controlled by the amount of wave energy absorption by the WEC; it is also affected by the increased wave-scattering processes at these wave periods. Note that Beels et al. (2010) observed a similar phenomenon in their modeling of the Wave Dragon WEC.
Specifically, they noted that the wave height reduction behind the device could not always be explained by energy absorption; it could instead be related to wave reflection. This is also supported by the WAMIT results in Fig.9, which shows that the short-period cases consistently have a greater wave shadow magnitude than the longer period cases (for both regular and spectral sea states).
For wave periods around the RCW peak, the wave energy flux deficit shown in Fig.7 indicates that the SWAN model could better represent the observed wave shadow. This is because at these periods, the wave shadow is most closely linked to the absorbed power. For even longer periods, for which the RCW is near zero, the experimental shadow observations are again dominated by the redistribution due to scattering processes, and the SWAN simulations do not produce wave shadows because there is no expected power capture at those wave periods.
For the unidirectional sea simulations (Fig.9middle panels), the shorter period WAMIT results display more spatial variability, a more pronounced shadow region, and a distinct wave amplification region in the shape of a parabola around the wave shadow. Similar to its performance in the regular wave cases, the SWAN model is not able to capture any of these features. In the WAMIT simulation, the wave height modification is less pronounced for the longer period case, and the standing wave ridge pattern offshore is almost absent. This is again due to the reduced scattering and radiation and also to the smoothing induced by the phase relationships between the set of wave periods present. Here, SWAN, considering spectral wave conditions and with the diffraction option, is better able to reproduce the wave height vari-ability in the lee of the WEC as compared to SWAN performance in the regular wave case.
WAMIT results associated with the directionally spread seas results (bottom two rows in Fig.9) show a much smoother wave height modification pattern, as would be expected in the presence of wave components from a variety of directions. Here, the results from the different periods are more similar, though the amplitude of the wave shadow is still larger for the short-period case. The effect of the diffraction option in the SWAN model is less important here, which is an expected result for directionally spread waves. Overall, the SWAN results for the longer peak period most closely resemble the WAMIT wavefield, but only in the lee of the device. In general, the SWAN results for the directionally spread cases are a better match to the WAMIT results than those for either the unidirectional or regular wave cases.
Analyses of Wave Scattering and Absorption Produced by WEC… 93
Conclusions
In this chapter, we have presented results from a laboratory experiment conducted using an array of 1:33 scale WEC devices to ascertain the wavefield modifications caused by the presence of the WECs. Further, two commonly used numerical models—the phase-resolving model WAMIT and the phase-averaged model SWAN—were applied to the conditions of the experiment and validated using the available observations. The SWAN simulations took into account the frequency-dependent nature of the wave energy absorption through a nested domain approach, whereby the spectra at the locations of the devices were altered based on preexisting knowledge of the power absorption curve leading to the simulated wave field modifications in the lee of the devices.
We found that the short-scale variability predicted by phase-resolving models such as WAMIT is indeed consistent with the observations from an array of wave gages both offshore and in the lee of the WECs. The short-scale variability is linked to a standing wave ridge pattern that arises because of wave scattering by the WEC device. The scattered waves are generated by scattering from the device and radi-ated waves generradi-ated by device motion. At short-wave periods, this high short-scale wave height variability complicates the interpretation of point observations. The issues arise either because the variability cannot be adequately resolved, or the observations are biased toward either ridges or valleys in the partial standing wave pattern.
Overall, the results indicate two things: First, the WEC parameterization we have used in the SWAN model can be effective at simulating the wave shadows induced by WEC arrays under conditions where the wave shadow is primarily controlled by the WEC power capture characteristics rather than by the redistribution of wave energy due to scattering and radiation. Generally speaking, these conditions occur when much of the wave energy lies at wave periods around the RCW peak period and higher when the RCW is still nonzero. The parameterization will underestimate the wave shadow when the significant energy lies below the RCW peak period, where scattering and radiation are of increased importance. The parameterization does not capture the partial standing wavefield offshore of WEC arrays because it is caused by scattering and radiation and not power capture.
Second, the analysis of wave shadows induced by WECs using the WAMIT simulations has indicated that under similar power capture characteristics, it is possible to have significantly different wave shadows. Specifically, the WAMIT results demonstrate that the shorter period cases have shadows of larger magnitude and more complicated offshore structure, even when frequency and directional spreading are included. It is reasonable to argue that a characteristic potential environmental effect of WEC arrays is the amount of wave field modification induced by the presence of an array. Hence, these results indicate that even when the potential for wave energy capture is normalized for (i.e., similar power capture conditions), the environmental effects of WEC arrays (i.e., the wave shadow) are
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reduced when WECs are designed to operate such that the expected wave climate lies on the longer period side of the WEC RCW curve.
Acknowledgements This work was supported by the US Department of Energy (Award
#DE-EE0002658), Sandia National Laboratories, and Columbia Power Technologies under Research Subagreement NO. 2010-1698. Additional support came from the Oregon Wave Energy Trust through Award Number OIC-0911-109. We also wish to thank Ken Rhinefrank, Joe Prudell, Al Schacher, Erik Hammagren, Tim Maddux, and the staff of the Hinsdale Wave Research Laboratory for their help in the experimental effort.
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