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Dynamic Wave Energy Converter (WEC) models utilize a wide variety of fundamental hydrodynamic theories. When incorporating novel hydrodynamic theories into numerical models, there are distinct impacts on WEC rigid body motions, cable dynamics, and final power production. This paper focuses on developing an understanding of the influence several refined hydrodynamic theories have on WEC dynamics, including weakly nonlinear Froude-Krylov and hydrostatic forces, body-to-body interactions, and dynamic cable modelling. All theories have evolved from simpler approaches and are of importance to a wide array of WEC archetypes. This study quantifies the impact these theories have on modelling accuracy through a WEC case study. Theoretical differences are first explored in a regular sea state. Subsequently, numerical validation efforts are performed against field data following wave reconstruction techniques. Comparisons of significance are WEC motion and cable tension. It is shown that weakly nonlinear Froude-Krylov and hydrostatic force calculations and dynamic cable modelling both significantly improve simulated WEC dynamics. However, body-to-body interactions are not found to impact simulated WEC dynamics.

Wave energy has the potential to power significant portions of economies around the world. Standard International Electrotechnical Commission methods for determining wave energy quantifies the gross wave resource available in the ocean, yet a significant portion of this resource is not usable by specific wave energy converters (WECs). This can provide a misleading assessment of the spatiotemporal opportunities for wave energy in deployment locations. Therefore, there is a need to develop a new technique to assess potential wave power from a device point of view that is generally applicable across WEC sizes. To address this challenge, a novel net power assessment methodology is proposed, which implements Budal’s upper bound (which describes the power available to a WEC based on its stroke), the radiation power limit (which describes the maximum radiation-based amount of wave power a WEC can absorb), and total gross incident wave power as absorbable power upper bounds. Spatiotemporal opportunities for WECs were re-evaluated based on this new technique. Numerical simulations were conducted to quantify the net wave resource available for different sized WECs (1, 2, 5, 10) at five different ocean sites in the U.S. based on wave data. The simulation results show the predicted potential wave power through the net power assessment for a 5 m device is 0.8% of the International Electrotechnical Commission assessment results at PacWave, Oregon. For the monthly average power, the results show PacWave has the most energetic wave resource (up to 406 kW in January) and WETS, Hawaii, has the steadiest wave power available (maximum COV of 0.8) among the sites. Regarding the size of the devices, results show that larger devices (e.g., 10 m) have better performance in terms of both magnitude and steadiness of power available at WETS and Los Angeles, California. Finally, the wave power potential of different sized WECs at varying locations was compared at a 3-h resolution. The maximum instantaneous power available for a 1 and 10 m device at PacWave throughout the time period was 47.8 and 3.52 × 103 kW, respectively.

Future nearshore wave energy converter (WEC) arrays will influence coastal wave and sediment dynamics, yet there are limited numerical methodologies to quantify their possible impacts. A novel coupled WEC-Wave numerical method was developed to quantify these possible influences on the nearshore coastal wave climate. The power performance of an Oscillating Surge Wave Energy Converter (OSWEC) array was simulated to quantify the wave energy dissipation due to the array. The OSWEC’s effect on the local wave climate was quantified by a novel coupling of two numerical models, WEC–Sim and XBeach. WEC–Sim characterizes the power extraction and wave energy transmission across the OSWEC, while XBeach captures the change in wave dynamics due to the WEC and propagates the waves to shore. This novel methodology provides the ability to directly quantify the impact of the effect of a WEC array on the local wave climate. Three case studies were analyzed to quantify the impact of a single WEC on breaking conditions and to quantify the impact of number of WECs and the array spacing on the local nearshore wave climate. Results indicate that when the WEC is placed 1100 m offshore, one WEC will cause a 1% reduction in wave height at the break point (Hsbp). As the WEC is placed further offshore, the change in Hsbp will become even smaller. Although the change in wave height from one WEC is small, WEC arrays magnify the cross–shore extent, area of influence and the magnitude of influence based on the spacing and number of WECs. For arrays with 10 or 15 WECs, the cross–shore extent was on average 200–300 m longer when the WECs were placed one to two WEC widths apart, compared with being spaced three or four widths apart. When the spacing was one WEC width apart (18 m), there was a 30% greater spatial impact on the nearshore region than arrays spaced three or four widths apart. The trend for the average transmission coefficient is within 5% for a 5, 10 or 15 WEC array, with a cumulative average of 78% transmission across all conditions.

The worldwide effort to design and commission floating offshore wind turbines (FOWT) is motivating the need for reliable numerical models that adequately represent their physical behavior under realistic sea states. However, properly representing the hydrodynamic quadratic damping for FOWT remains uncertain, because of its dependency on the choice of drag coefficients (dimensionless or not). It is hypothesized that the limited degree of freedom (DoF) drag coefficient formulation that uses only translational drag coefficients causes mischaracterization of the rotational DoF drag, leading to underestimation of FOWT global loads, such as tower base fore-aft shear. To address these hydrodynamic modeling uncertainties, different quadratic drag models implemented in the open-source mid-fidelity simulation tool, OpenFAST, were investigated and compared with the experimental data from the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project. The tower base fore-aft shear and up-wave mooring line tension were compared under an irregular wave loading condition to demonstrate the effects of the different damping models. Two types of hydrodynamic quadratic drag formulations were considered: (1) member-based dimensionless drag coefficients applied only at the translational DoF (namely limited-DoF drag model) and (2) quadratic drag matrix model (in dimensional form). Based on the results, the former consistently underestimated the 95th percentile peak loads and spectral responses when compared to the OC5 experimental data. In contrast, the drag matrix models reduced errors in estimates of the tower base shear peak load by 7–10% compared to the limited-DoF drag model. The underestimation in the tower base fore-aft shear was thus inferred be related to mischaracterization of the rotational pitch drag and the heave motion/drag by the limited-DoF model.

Power production of wave energy converters (WEC) predicted in the time domain use wave resource parameters and time-domain hydrodynamic model simulations that provide high temporal resolutions (10s of Hz). However, wave resource parameters are often based on frequency-domain calculations with temporal resolution of 30 min to an hour. Real ocean wave conditions vary on much shorter time scales. Relying on frequency-domain calculations will not be sufficient to capture short-term variability and accurately predict WEC power production for a standardized methodology that follows power system requirements. Low temporal resolution data sets are being used in a majority of studies to generate representative wave conditions as inputs to numerical simulations by generating wave spectra. Spectra are then used to predict the efficiency of systems that will not accurately capture the variability of waves in short timeframes. Creating a standardized methodology to increase the temporal resolution of metaocean conditions to inform model development can provide better power production forecasting. In this paper, random amplitude, Fourier coefficient methods have been used for WEC simulations of finite durations to improve the observed variability in wave heights and power production. Variability using this method does increase for finite durations compared to the commonly used deterministic amplitude method.

The worldwide effort to design and commission floating offshore wind turbines (FOWT) is motivating the need for reliable numerical models that adequately represent their physical behavior under realistic sea states. However, properly representing the hydrodynamic quadratic damping for FOWT remains uncertain, because of its dependency on the choice of drag coefficients (dimensionless or not). It is hypothesized that the limited degree of freedom (DoF) drag coefficient formulation that uses only translational drag coefficients causes mischaracterization of the rotational DoF drag, leading to underestimation of FOWT global loads, such as tower base fore-aft shear. To address these hydrodynamic modeling uncertainties, different quadratic drag models implemented in the open-source mid-fidelity simulation tool, OpenFAST, were investigated and compared with the experimental data from the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project. The tower base fore-aft shear and up-wave mooring line tension were compared under an irregular wave loading condition to demonstrate the effects of the different damping models. Two types of hydrodynamic quadratic drag formulations were considered: (1) member-based dimensionless drag coefficients applied only at the translational DoF (namely limited-DoF drag model) and (2) quadratic drag matrix model (in dimensional form). Based on the results, the former consistently underestimated the 95th percentile peak loads and spectral responses when compared to the OC5 experimental data. In contrast, the drag matrix models reduced errors in estimates of the tower base shear peak load by 7–10% compared to the limited-DoF drag model. The underestimation in the tower base fore-aft shear was thus inferred be related to mischaracterization of the rotational pitch drag and the heave motion/drag by the limited-DoF model.

Robertson, B.; Hall, K.; Nistor, I.; Zytner, R., and Storlazzi, C., 2015. Remote sensing of irregular breaking wave parameters in field conditions. The analysis of wave breaking in shallow water has been ongoing for almost 150 years. Numerous research papers have been published that approximate both the local conditions and geometric characteristics of breaking waves. However, much of this knowledge is based on laboratory results or limited field investigations because traditional methods of extracting breaking wave measurements from the surfzone are expensive, dangerous, and feature low-resolution data. Unfortunately, laboratory studies are prone to scaling and friction effects that introduce unwanted variability in the data. This study presents a novel, safe, and low-cost method of extracting relevant breaking-wave properties from irregular waves in the surfzone, using optical and in situ measurement systems. Published, contradictory breaking-water depth definitions are compared, and the water depth at the wave-trough depth, corrected for optical offsets using a still-water correction of one-third of the wave height, is found to exhibit the least variability. A new, effective seafloor-slope definition, based on individual, breaking wavelength-to-depth ratios, was found to increase predictive ability over previously variable seafloor slope extraction methods. Collected field data are compared against established breaking-wave height formulas with the general exponential form consistently finding the best correlation. Finally, an optimized breaking-wave height-prediction method finds a root mean square relative error of just 1.672% within the ranges of the measured data set. Irregular waves investigated on an individual wave basis are shown to follow regular wave-breaker height and depth prediction methods.

Whereas large planets, such as gas giants, are more likely to form around high-metallicity stars, terrestrial-sized planets are found to form around stars with a wide range of metallicities, indicating that they may be widespread in the disk of the Galaxy. Exoplanets around metal-poor stars A key discovery of the past decade in the field of exoplanet research was the realization that stars of high metallicity are those most likely to harbour giant exoplanets, supporting the model in which planets form by the accumulation of dust and ice particles. Whether the planet–metallicity correlation holds for terrestrial planets remained unclear, but the Kepler mission's discovery last year of hundreds of small exoplanet candidates provided an opportunity to find out. The spectroscopic metallicities of the host stars of 226 small exoplanet candidates have now been determined. The smaller ones, of less than four Earth radii, were found around stars with a wide range of metallicities, on average close to that of the Sun. Larger planets were more common around stars of high metallicity. These findings suggest that terrestrial planets may be widespread in the disk of the Galaxy, with no special requirement of enhanced metallicity for their formation. The abundance of heavy elements (metallicity) in the photospheres of stars similar to the Sun provides a ‘fossil’ record of the chemical composition of the initial protoplanetary disk. Metal-rich stars are much more likely to harbour gas giant planets 1 , 2 , 3 , 4 , supporting the model that planets form by accumulation of dust and ice particles 5 . Recent ground-based surveys suggest that this correlation is weakened for Neptunian-sized planets 4 , 6 , 7 , 8 , 9 . However, how the relationship between size and metallicity extends into the regime of terrestrial-sized exoplanets is unknown. Here we report spectroscopic metallicities of the host stars of 226 small exoplanet candidates discovered by NASA’s Kepler mission 10 , including objects that are comparable in size to the terrestrial planets in the Solar System. We find that planets with radii less than four Earth radii form around host stars with a wide range of metallicities (but on average a metallicity close to that of the Sun), whereas large planets preferentially form around stars with higher metallicities. This observation suggests that terrestrial planets may be widespread in the disk of the Galaxy, with no special requirement of enhanced metallicity for their formation.