Wave Energy Period Research Articles

“Assessment of combined wind and wave energy in European coastal waters using satellite altimetry.”

In this study, the combined wind and wave energy potential assessment is presented for various locations in European coastal waters. The objective is to investigate the feasibility of satellite altimetry-based assessments of combined wind/wave renewable energy potential on the European shelf. The study is motivated by the potential reduction in energy supply variability by combining wind and wave. The method consists of using a homogenized multi-mission altimeter database available by the European Space Agency Sea State Climate Change Initiative (Sea_State_cci) that comprises 26 years of data, from January 1991 to December 2018, that allows extending the time range and spatial coverage to estimate site wind and wave power densities. An empirical model is used to estimate the wave energy period from the altimeter Ku band significant wave height and radar backscatter coefficient required to compute the wave power density. The results show that wind/wave energy is relatively correlated in the Mediterranean but not in the North Atlantic sites studied. Thus, the Western North Atlantic sites are the most adequate places for wind and wave farms, from the point of view of combined exploitation.The different characteristics of the studied sites show some correspondence between variability and mean wave power, which is an essential input to a marine renewable energy strategy in any jurisdiction. The level of overall variability decreases with an increase in mean wave power, related to the higher power swell waves are not highly correlated with the local wind.

Design analysis of a wave energy converter for hydrogen generation near shoreline of Black Sea

The generation of electricity from waves has attracted a lot of attention from researchers lately. Despite the vastness and accessibility of wave energy across the majority of the planet, there is a dearth of literature on the production of electricity and hydrogen from wave power. In this paper, a comprehensive simulation related to hydrogen production with an oscillating wave surge converter (OWSC) system was employed for the Black Sea region. The simulations were performed by means of Homer-Pro software and the data were provided thanks to European Marine Observation and Data Network (EMODnet) as well as a novel web-based tool with regards to wave resources. Initial results of web-based tool showed that the hydrogen generation was directly impacted by considerable wave height and wave energy period. As a result, it may change based on the days and months. May had the lowest monthly energy production (3 MWh), while December had the highest monthly energy production (27 MWh). Moreover, the electrolyzers with different efficiencies were investigated with Homer-Pro. The electrolyzer with an efficiency of 85% at 100 kW produced 3301 kg annually, whereas the electrolyzers with 90% and 95% efficiency at 100 kW produced 3419 kg annually and 3422 kg annually, respectively. Apart from those findings, when more efficient electrolyzers were employed in the system, both the capital and replacement costs dropped at the same time.

A reconnaissance-level characterization of wave energy resource in the exclusive economic zones of Bay-of-Bengal

Bordering the Bay-of-Bengal, Bangladesh, India, Sri Lanka, Indonesia, and Myanmar possess significant potential for harnessing wave energy to address their growing energy crisis. This study aims to comprehensively characterize wave energy resources in the exclusive economic zones of the Bay-of-Bengal's littoral countries. The study utilizes 13 years of wave hindcasts obtained from WAVEWATCH-III, a widely used third-generation numerical wave model. Various approaches for characterizing wave energy resources were employed, including site accessibility analysis and extreme event analysis, which were overlooked in prior studies on Bay-of-Bengal. The research revealed that the mean wave energy flux in the Bay-of-Bengal is higher (16–39 kW/m) during the summer-monsoon season (July–October) and lower (2–12.5 kW/m) during the post-monsoon season (November–February). Consequently, the summer-monsoon season is deemed appropriate for energy harvesting, while the post-monsoon season is ideal for wave energy converter installation, servicing, or maintenance. The sea-state analysis demonstrated that the significant wave height and energy period of the most frequent and energetic sea-states in the Bay-of-Bengal range from 0.5 to 3.5 m and 4–16 s, respectively. Based on considerations of annual energy storage, resource stability, and wave energy converter survivability, the locations in the exclusive economic zones of Sri Lanka, Indonesia, and India's Andaman and Nicobar Islands were identified as the most suitable for constructing wave power plants. The research findings presented herein can assist local authorities and stakeholders in the energy sector by facilitating a comparison of wave energy resources across different locations and determining the most suitable sites for wave power plant construction that align with their energy needs and goals. Additionally, the results can aid wave energy converter developers in planning tests in the Bay-of-Bengal, maintaining their devices, and evaluating potential sites for opportunities and risks.

Field observations of Hurricane Ian’s wave and surge impact in the areas of Fort Myers Beach and Sanibel Island, USA

On September 18, Category 4 Hurricane Ian made landfall near Fort Myers Beach and Sanibel Island, two barrier islands on the northern Gulf of Mexico. In this paper, we present a novel set of observations from a post-event High Water Mark field survey as well as wavelet analysis of in-situ wave data. We also present a qualitative overview of some erosive effects and infrastructure damage. Measured peak surge elevations exceed 5 m, and wave plus surge elevations exceed 6.0 m (NAVD88). High Water Mark observations are consistent within the expected range produced by numerical hindcast models. A wavelet analysis, from one of the few wave records available during the storm, demonstrates the presence of long-period basin mode waves at a 40-min period. The 40-min wave appeared on the wave record before the storm surge, and the peak of this motion also occurred before the peak of the surge. In addition, the wavelet analysis reveals the presence of infragravity wave energy (periods between 30 s and 20 min). Together, these intermediate and long-period waves add over 40 cm to the total water level at peak energy. The measured field data shows a rapidly decreasing surge elevation within the first 300 m from the pre-storm shoreline, and we observe no statistically meaningful attenuation difference between the highly developed shoreline of Fort Myers and the more vegetated shoreline of Sanibel Island. However, the structural survey team observed more infrastructure damage in Fort Myers than Sanibel Island.

Long-term variability analysis of wave energy resources and its impact on wave energy converters along the Chinese coastline

The long-term variability of wave energy resources will affect the practical decadal application of wave energy converters. This paper has evaluated the distributions and long-term trend of wave energy resources in the sea regions along the Chinese coastline for 83 years based on reliable ERA5 wave reanalysis data from 1940 to 2022 after verifying by 39 local buoys, and found that it is of great potential to develop and apply wave energy resources projects. The long-term trend analysis of the wave energy density and its major contributing wave parameters, significant wave height, and wave energy period, is carried out using Theil-Sen estimation showing the general positive tendency. And the impacts of the decadal variation on four wave energy converters are evaluated via computing the decadal mean power production by combining the wave energy density and the wave energy characteristic. It is verified that the long-term wave energy density in this region increases along with the decrease in power production and the capture width. This study shows that long-term variability of wave energy resources and wave energy characteristics should also be considered in the designing of WECs and the identification of energy hotspots.

Discussions on Wave energy period in higher wave energy potential marine waters of Taiwan

For evaluating wave energy, wave energy period Te is commonly adopted. However, the in-charge government agencies in Taiwan traditionally provided with peak frequency Tp without giving information on the transferring relationship between Te and Tp. This results in difficulties on correctly evaluating wave energy potentials at certain marine waters. Thus, existing spectrum data need to be derived to calculate values of Tp and Te so as to derive representative transferring coefficient Cep for long-term evaluations on wave energy. This study aims at deriving values of Cep at relatively higher potential marine waters of Taiwan. As shown in Figure 1, the data were collected from two stations in Keelung marine waters and one station within marine waters for offshore wind of Changhua. By choosing different criteria for Cep, selected data were regressed for obtaining representative Cep in different seasons. For conservative point of views, the values of Cep ranging from 0.85~0.87 from data in northeaster monsoon months, as shown in Figure 2, being generally slightly smaller than those of the whole year, were adopted at the three stations. It is also found that the representative values of Cep were derived mainly from data comprising of exploitable wave power densities of between 2~80 kW/m2. Data collection instruments, selection criteria and associated outcomes shall be detailed in the full paper.

On spatial interpolation of ocean energy source variables: A comparative analysis

In the context of wave energy systems development, the estimation of wave parameters such as significant wave height (Hs) and energy period (Te) over the entire ocean surface is of paramount importance. These information are crucial for estimating the energy harvesting potential of deployment sites, designing wave energy converters (WECs), planning optimal maintenance intervention frequency, and assessing the impact of waves on coastal communities. However, measuring Hs and the Te at every point in the ocean is impossible due to the vastness of the ocean and due to the cost and difficulties of installing and maintaining wave instrumentation buoys, since these have to survive in marine environment, which is particularly hostile. As a consequence, the amount of data is too limited and sparse in space for the practical and precise performance of these analyses. To address such data scarcity and sparsity, we analyse in this paper various spatial interpolation techniques employed to fill the spatial gaps in the wave parameter datasets. These techniques are compared in their performances in estimating the wave parameters in space given a set of known measurements in limited sampling locations. Three types of interpolators are considered: linear interpolator, spline interpolator, and radial basis functions (RBFs) interpolator. These algorithms are trained and tested on a public dataset of wave parameters from Copernicus Marine Service in an area between the coastlines of South England and North France. To simulate the available data scarcity and sparsity, only limited percentages of the ocean area are considered covered and available in the training stage (from 0.01% to 1%). The performance of each interpolator is evaluated on the remainder of the considered area in terms of Normalized Root Mean Square Error (NRMSE) and on the Normalized Mean Absolute Error (NMAE) achieved by the algorithm in reconstructing the parameters at these unsampled locations. The results of this study demonstrate the feasibility of spatial gap-filling of wave parameters, and demonstrates that the RBF algorithm outperforms the other two algorithms both in performances and, even more, in terms of robustness to different training points sampling.

Spectral wave energy period and peak period statistics concomitant with maximum significant wave heights

Spectral wave energy period and peak period statistics concomitant with maximum significant wave heights

On the Estimation of the Wave Energy Period and a Kernel Proposal for the Peru Basin

The energy period is a crucial parameter needed for assessing wave energy. This parameter is regularly approximated using standard wave spectrums that do not always characterise an actual ocean region, even more if this region is far from the Northern Hemisphere, where most of the energy period approximations have been developed. In this work, diverse approximations for the energy period were evaluated using spectral data from a region of the Peru Basin. It included the assessment of a proposed Kernel “coefficient” curve. They were assessed regarding their time series, wave climate, and temporal variability. The time series analysis showed that the approximations based on the peak period do not have a realistic physical representation of ocean waves. On the other hand, the proposed Kernel correlation gave the best results for computing the energy period and the monthly/seasonal variability indexes for temporal variability analysis. Additionally, the correlations based on the zero-up-crossing period generated the best results for computing the coefficient of variation. Conversely, the highest errors were calculated for the correlations based on the traditional Bretschneider and JONSWAP spectrums. The wave climate indicated an annual average energy period equal to 9.8 s, considered stable due to its low variability.

Effect of Al/O ratio on underwater explosion energy characteristics of CL‐20‐based aluminized explosives

AbstractTo study the underwater explosion energy characteristics of CL‐20‐based aluminized explosives with different Al/O ratio, underwater detonation parameters of explosives, including the shock wave peak pressure, the decay time, the bubble pulsation period, the shock wave energy and the bubble energy at 1 m, were measured by a series of underwater explosion experiments. The calculation model of CL‐20‐based aluminized explosive in the pool was established by using Ansys LS‐DYNA software and was calculated the shock wave energy and bubble pulsation period. The results showed that Al/O ratio significantly changed the energy output structure of CL‐20‐based aluminized explosives. With increasing Al/O ratio, the proportion of shock wave energy in the total energy decreased, while the proportion of bubble energy increased. When Al/O ratio was 0.35, the shock wave peak pressure and shock wave energy of the explosive were the largest, and when the ratio was 0.6, the bubble period and total energy reach their maximum; when the ratio was 0.94, the bubble energy and the bubble pulsation reached the maximum. The experimental values are in good agreement with the simulation results, and the model can be used to estimate the underwater detonation parameters of CL‐20‐based aluminized explosives with different Al/O ratio.

Simulation of Low Energy Waves during Fair-Weather Summer Conditions in the Northern Gulf of Mexico: Effect of Whitecapping Dissipation and the Forcing Accuracy

Simulating WAves Nearshore (SWAN) on a structured grid over the Louisiana shelf in the northern Gulf of Mexico is used to evaluate the performance of three different classes of formulations for quantifying wind input and whitecapping dissipation. The formulations include Komen based on the mean spectral parameters, Westhuysen based on the saturation concept of the wave groups, and the most recent observation-based physics package ST6. The evaluation was implemented for two summer months (July and August 2015) to assess these formulations for a low wave energy period. The modeling area consists of the Louisiana inner shelf with the offshore open boundary located beyond the continental shelf. The model was forced using the spatially variable Climate Forecast System Reanalysis (CFSR) wind field and wave parameters obtained from the NOAA’s WAVEWATCH-III (WWIII) model along the open boundaries. Simulated wave parameters and spectra regarding each formulation were evaluated and compared with measured wave data at NDBC stations; comparisons showed that the most appropriate formulation for the simulation of low energy waves for the study area to be ST6. The e performance of each whitecapping formulation was described by examining 1D/2D spectra and the source term balance at different met-ocean conditions during the simulation period. It was also shown that the inaccuracies in the input wind field and boundary conditions can substantially contribute to the model inaccuracy.

Analysis of Wave Energy Behavior and Its Underlying Reasons in the Gulf of Mexico Based on Computer Animation and Energy Events Concept

The complexity and variability of ocean waves make wave energy harvesting very challenging. Previous research has indicated that wave energy was mainly generated and transferred by wind, but the detailed correlation between wind and wave energy has not been discovered. Wave energy in the Gulf of Mexico (GoM) has high variability with distinct seasonal behavior. However, the underlying reasons for this unique behavior have not been discussed and discovered yet. In this paper, a computer animation-based dynamic visualization method was created to conduct exploratory and explanatory analyses of 36 years of meteorological data in the GoM from the WaveWatch III system to identify preliminary patterns and underlying reasons for the unique behavior of wave energy in the GoM. These preliminary patterns and underlying reasons were further analyzed using Energy Events and Breaks concepts. During both high and low levels wave energy periods, the detailed correlation between wave energy and the wind was analyzed and determined. High level wave power in the GoM was mainly generated by the local inland wind from northern weather patterns, while low level wave power was mainly generated by swells from the Caribbean and the Atlantic oceans, which entered the GoM through the two narrow pathways, the Straits of Yucatan and the Florida Straits. The results from this paper will also be able to help the design, placement, and operation of future wave energy converters to improve their efficiency in harvesting wave energy in the GoM.

Statistics of the Distribution of Spectral Wave Energy Periods Conditioned on Significant Wave Height Maxima

Statistics of the Distribution of Spectral Wave Energy Periods Conditioned on Significant Wave Height Maxima

Annual and seasonal trend detection of significant wave height, energy period and wave power in the Mediterranean Sea

An analysis of a 40-year long wave time series was carried out in the Mediterranean basin to identify ongoing trends of three wave parameters: significant wave height, energy period and wave power. Synthetic wave data were deduced from the global atmospheric reanalysis ERA-Interim by the ECMWF. After a preliminary data examination, a trend analysis, at annual and seasonal scales, was performed on the mean and maximum values through the Mann-Kendall test. Moreover, the application of the Theil-Sen estimator allowed us to quantify the magnitude of the increase/decrease in the wave parameters. Results highlighted different behaviours between the mean and the maximum values. In general, an overall increase in the mean wave quantities was observed, particularly for the energy period, while the increase in the maximum wave parameters was limited to a few grid points. For both the mean and the maximum values, negative trends were identified in specific areas of the Mediterranean Sea, especially for the significant wave height and the wave power. The study findings could be useful for analyses linked to various activities such as coastal inundations and erosions, the design of marine structures and the identification of optimal sites for field installations of Wave Energy Converters.

Wave energy flux in the Caribbean Sea: Trends and variability

Wave Energy Flux (WEF) in the Colombian Caribbean Sea is assessed using a 60 years wave reanalysis from 1958 to 2017. Significant wave height (Hs) and mean wave energy period (Tm_1,0) are validated against in situ buoy data from the National Oceanic and Atmospheric Administration and from the Dirección General Marítima in the Central Caribbean Sea and in front of the Colombian shelf. WEF is calculated at virtual buoys allocated in the central Caribbean, at the continental shelf and around insular territories revealing a long-term decrease in magnitude with an annual rate between 0.01 and 0.2% with different regional behavior. In addition, WEF variations at interannual scale are found to be associated with ENSO phases. Wave energy power decreased from 1989 to 2017 in all analyzed locations.

Optimal Design of a U-Shaped Oscillating Water Column Device Using an Artificial Neural Network Model

A U-shaped oscillating water column (U-OWC) device has been investigated to enhance power extraction by placing the bottom-mounted vertical barrier in front of a conventional OWC. Then, the optimal design of a U-OWC device has been attempted by using an artificial neural network (ANN) model. First, the analytical model is developed by a matched eigenfunction expansion method (MEEM) based on linear potential theory. Using the developed analytical model, the input and output features for training an ANN model are identified, and then the database containing input and output features is established by a Latin hypercube sampling (LHS) method. With 200 samples, an ANN model is trained with the training data (70%) and validated with the remaining test data (30%). The predictions on output features are made for 4000 random combinations of input features for given significant wave heights and energy periods in irregular waves. From these predictions, the optimal geometric values of a U-OWC are determined by considering both the conversion efficiency and wave force on the barrier. It is found that a well-trained ANN model shows good prediction accuracy and provides the optimal geometric values of a U-OWC suitable for wave conditions at the installation site.

Effects of power take-off parameters and harvester shape on wave energy extraction and output of a hydraulic conversion system

Considering nonlinear hydrodynamic forces of a harvester in irregular waves and a nonlinear hydraulic power take-off system, a time-domain nonlinear motion model and nonlinear hydraulic power take-off models are established to investigate the harvester motion response, the hydraulic system dynamic performance, the power extraction, the motor output power and efficiency. Matlab/Simulink is used to establish and simulate the system models. The convolution identification of nonlinear radiation force is based on a state-space model. The parameters of the state-space model and the infinity frequency added mass are fitted based on the least square method. The nonlinear hydrostatic storing force is considered for cone and hemisphere. The Pierson–Moskowitz 2-parameter spectrum is adopted for the irregular waves. The Coulomb friction force and viscous friction force based on the pressure difference and hydraulic cylinder parameters are modeled in the power take-off force. Under a given sea state, for cone, cylinder and hemisphere, the optimal hydraulic power take-off parameters are predicted based on a genetic algorithm for the maximum motor output power. The effects of the hydraulic cylinder piston working area, the motor displacement, the high pressure accumulator pre-charge pressure and initial volume, the significant wave height and energy period, the harvester diameter, draft and shape on the extracted power, the extraction efficiency, the motor output power and the hydraulic conversion efficiency are investigated. The extraction ability of the cone harvester is the highest among three shapes under the same diameter and draft. The conversion efficiency increases as the motor displacement decreases.

Advanced extreme learning machines vs. deep learning models for peak wave energy period forecasting: A case study in Queensland, Australia

The peak period of an energy-generating wave is one of the most important parameters that describe the spectral shape of the oceanic wave, as this indicates the duration for which the waves prevail with respect to their maximum extractable energy. In this paper, a half-hourly peak wave energy period (TP) forecast model is constructed using a suite of statistically significant lagged inputs based on the partial auto-correlation function with an extreme learning machine model developed and its predictive utility is benchmarked against deep learning models, i.e., convolutional neural network (CNN/CovNet) and recurrent neural network (RNN) models and other traditional M5tree, Conditional Maximization based Multiple Linear Regression (MLR-ECM) and MLR models. The objective model (ELM) vs. the comparison models (CNN, RNN, M5tree, MLR-ECM, and MLR) were trained and validated independently on the test dataset obtained from coastal zones of eastern Australia that have a high potential for implementation of wave energy generation systems. The outcomes ascertain that the ELM model can generate significantly accurate predictions of the half-hourly peak wave energy period, providing a good level of accuracy relative to deep learning models in selected coastal study zones. The study establishes the practical usefulness of the ELM model as being a noteworthy methodology for the applications in renewable and sustainable energy resource management systems.

Trend Detection of Wave Parameters along the Italian Seas

In this paper, trend detection of wave parameters such as significant wave height, energy period, and wave power along the Italian seas was carried out. To this purpose, wave time series in the period 1979–2018 taken from the global atmospheric reanalysis ERA-Interim by European Center for Medium-Range Weather Forecasts (ECMWF) were considered. Choosing a significance level equal to 90%, the use of the Mann–Kendall test allowed estimating ongoing trends on the mean values evaluated at yearly and seasonal scale. Furthermore, the assessment of the magnitude of the increase/decrease of the wave parameters was performed through the Theil–Sen estimator. The obtained results underlined that the mean values of the considered wave parameters were characterized by a high occurrence of positive trends in the different Italian seas. The findings of this study could have implications for studies of coastal flooding, shoreline variations, and port operations, and for the assessment of the performances of Wave Energy Converters.

HF Radars for Wave Energy Resource Assessment Offshore NW Spain

Wave energy resource assessment is crucial for the development of the marine renewable industry. High-frequency radars (HF radars) have been demonstrated to be a useful wave measuring tool. Therefore, in this work, we evaluated the accuracy of two CODAR Seasonde HF radars for describing the wave energy resource of two offshore areas in the west Galician coast, Spain (Vilán and Silleiro capes). The resulting wave characterization was used to estimate the electricity production of two wave energy converters. Results were validated against wave data from two buoys and two numerical models (SIMAR, (Marine Simulation) and WaveWatch III). The statistical validation revealed that the radar of Silleiro cape significantly overestimates the wave power, mainly due to a large overestimation of the wave energy period. The effect of the radars’ data loss during low wave energy periods on the mean wave energy is partially compensated with the overestimation of wave height and energy period. The theoretical electrical energy production of the wave energy converters was also affected by these differences. Energy period estimation was found to be highly conditioned to the unimodal interpretation of the wave spectrum, and it is expected that new releases of the radar software will be able to characterize different sea states independently.