Peak Wave Period Research Articles

A global climate analysis of wave parameters with a focus on wave period from 1979 to 2018

Ocean waves are crucial for the engineering community, both in the open ocean and in the coastal zone. By studying a 40-year (1979-2018) global hindcast, a systematic and long-term analysis on the temporal variation and spatial pattern of wave parameters is performed, with a focus on wave period. The mean and maximal conditions of peak period reflect the dominance of the swell and the region where it generates. The variabilities of the significant wave height and peak period show that high latitudes in the Southern Hemisphere (SH) have a generally large wave with a small dispersion. Trend patterns of peak period present similarities and differences, which can be associated with the climate mode. Spatial scopes of influence by this mode show the signal in the peak period, exceeding the local correlation zone and presenting a remote correlation. The joint characteristic of the significant wave height and peak period presents the differences of representative and extreme sea states in tropical regions and high latitudes, such as a large variation in high latitudes of the Northern Hemisphere (NH) and an extreme peak period occurring simultaneously with small significant wave height in tropical regions.

Estimating Met-Ocean Parameters during a Tropical Cyclone for Marine Science and Engineering

During a tropical cyclone (TC) worldwide, the Regional and Mesoscale Meteorological Branch (RAMMB) of NOAA/NESDIS (http://rammb.cira.colostate.edu/) issues real-time TC surface wind analyses. The purpose of this article is to provide value-added estimations of several meteorological and oceanographic (met-ocean) parameters including overwater friction velocity and turbulence intensity, variation of the wind speed with height, significant wave height, peak or dominant wave period, wind-driven currents and wind-stress tides. Since these proposed value-added parameters are also validated by other independent methods available from the literature, these met-ocean parameters may be used for marine science and engineering including offshore energy (such as oil, gas and wind power) research, development, operation and maintenance.

A statistical framework to project wave climate and energy potential in the Caspian Sea: application of CMIP6 scenarios

Caspian Sea as the largest inland water body plays an important role in economy of its neighbor countries apart from its environmental significance. This study explores wave climate in three locations in the southern Caspian Sea considering the socioeconomic pathway scenarios. In this regard, significant wave height, peak wave period and potential wave energy have been projected for a 20-year period of 2081–2100. To achieve reliable forecasts of wave characteristics and also to manipulate different sources of uncertainty, a new statistical framework is employed. The proposed framework gain Weibull distribution based technique for regionalization of near surface wind speed obtained from the climate model to feed the ANN (artificial neural network) model used for wave modeling. Furthermore, a post processing approach is used to ascertain consistency of the distribution of the model forecasts with those of the reference data. Considering two climate change scenarios, it was found that significant wave height and peak wave period do not change remarkably in terms of annual and seasonal variability when compared to the present climate. Moreover, wave energy analysis for the historical and future periods demonstrated sustainability of this renewable energy resources which is promising since clean energies are attracting much attention to meet the increasing demand for electricity. In the southern Caspian Sea, the middle part of the sea is subject to stronger waves indicating its higher potential for energy extraction than the western and eastern parts.

Numerical and experimental investigations into fluid resonance in a gap between two side-by-side vessels

When two vessels in a side-by-side configuration are under wave actions, fluid resonance occurs in a narrow gap between two vessels, termed ‘gap resonance’, leading to large free-surface responses. Large free-surface responses due to gap resonance can induce large relative motions and drift forces by both vessels, which influences operational safety. The present study aims at investigating the free-surface response near resonance in a narrow gap between two fixed, identical barges with square corners numerically and experimentally. Gap resonance is driven by three typical incident wave conditions including beam sea, quartering sea, and head sea. In light of the fact that the potential-flow theory overestimates the response in the gap, a potential-flow model with energy dissipation effects is developed based on the boundary element method. A dissipation surface is devised at the bottom opening as well as two end openings of the gap. Both linear and quadratic damping terms associated with laminar boundary layer wall friction and flow separation from sharp corners are accounted for. Physical experiments of gap resonance excited by irregular waves with different significant wave heights and peak periods are carried out and used for calibration and validation of the potential-flow model. Nonlinear correlation is observed between the incident wave amplitude and resonant gap response, which is predicted with satisfactory agreement by the developed potential-flow model. In-depth discussion on the mode shapes is made. It is found that the first mode is predominant in the beam sea, and the natural modes exhibit standing wave behaviors. Under quartering sea and head sea excitations, the second and third modes dominate over other modes. Waves propagate slowly along the gap in the head sea condition. Under the quartering sea excitation, the first and second modes propagate along the gap, but the third mode exhibits standing wave behavior, indicating the quartering sea response is a transition between head sea and beam sea. The significance of the present study is threefold. Firstly, the experimental measurements provide reference results for numerical simulation. Secondly, a simple but effective damping model to suppress unrealistic free-surface response near resonance is developed. Lastly, this work gives an insight into the spatial structure and dominance of natural modes under different wave conditions.

Modeling mean relation between peak period and energy period of ocean surface wave systems

Parametric spectrum models describing a frequency spectrum of ocean surface waves (e.g., Pierson-Moskowitz and JONSWAP (Joint North Sea Wave Project) spectrum) as a function of the significant wave height and peak period (Tp) have been used to estimate the energy period (Te) using a relation, Te=CTp, when the frequency wave spectrum is not available. This approach, however, introduces uncertainties in Te estimation for irregular waves. In the present study, a regression model for defining the coefficient (C) is developed to minimize the uncertainty in Te estimation using buoy wave measurements and WaveWatch III® hindcast for coastal waters of the United States. The result shows that the coefficients (C) of wind sea, swell, and total sea vary geographically and range from 0.84 to 0.90, 0.92 to 0.98, and 0.79 to 0.85. This approach derives consistent coefficients with different periods of record and results in better agreements in Te estimation compared to those of the approach relying on parametric spectrum models. Frequency distributions of dominant wave systems reaching different coastal regions, e.g., Pacific northwest swell in the Pacific Ocean, nor'easter swell and trade wind swell in the Atlantic Ocean, explain the observed spatial trends in the coefficient.

Non-stationary extreme value analysis of sea states based on linear trends. Analysis of annual maxima series of significant wave height and peak period in the Mediterranean Sea

Non-stationary Extreme Value Analysis (NEVA) allows to determine the probability of exceedance of extreme sea states taking into account trends in the time series of data at hand. In this work, we analyse the reliability of NEVA of significant wave height (Hs) and peak period (Tp) under the assumption of linear trend for time series of annual maxima (AM) Hs in the Mediterranean Sea. A methodology to assess the significance of the results of the non-stationary model employed is proposed. Both the univariate long-term extreme value distribution of Hs and the bivariate distribution of Hs and Tp are considered. For the former, a non-stationary Generalized Extreme Value (GEV) probability is used, and a methodology to compute the parameters of the distribution based on the use of a penalty function is explored. Then, non-stationary GEV is taken as a reference to compute the Environmental Countours of Hs and Tp, assuming a conditional model for the latter parameter. Several methods to compute linear trends are analysed and cross-validated on the series of AM Hs at more than 20,000 hindcast nodes. Results show that the non-stationary analysis provides advantages over the stationary analysis only when all the considered metrics are consistent in indicating the presence of a trend. Moreover, both the univariate return levels of Hs and bivariate return levels of Hs and Tp show a marked dependence to the time window considered in the GEV distribution formulation. Therefore, when applying NEVA for coastal and marine applications, the hypothesis of linear trend and the length of the reference data used for the non-stationary distribution should be carefully considered.

Comparative wave measurements at a wave energy site with a recently developed low-cost wave buoy (Spotter), ADCP and pressure loggers

AbstractWave measurements from a new, low-cost, real-time wave buoy (Spotter) are investigated in a comparative study as part of a site characterization study at a wave energy candidate site at King Island, Tasmania, Australia. Measurements from the Sofar Ocean Spotter buoy are compared with concurrent measurements from a Teledyne RD Instrument (RDI) 1200 kHz Work Horse ADCP and two RBRsolo3 D wave16 pressure loggers. The comparison period between 8th August – 12th October 2019 provides both the shallowest and longest continuous published comparison undertaken with the Spotter buoy.Strong agreement was evident between the Spotter buoy and RDI ADCP of key wave parameters including the significant wave height, peak wave period, and mean wave direction, with the mean values of those parameters across the full deployment period agreeing within 3%. Surface wave spectra and directional spectra are also analyzed with good agreement observed over the majority of the frequency domain, although the Spotter buoy records approximately 17% less energy within a narrow frequency band near the peak frequency when compared to the RDI ADCP. Measurements derived from the pressure loggers routinely underestimated the significant wave height and overestimated the mean wave period over the deployment period. The comparison highlights the suitability of the Spotter buoy for low-cost wave resource studies, with accurate measurements of key parameters and spectra observed.

Physical Modelling of the Effect on the Wave Field of the WaveCat Wave Energy Converter

The WaveCat is a moored Wave Energy Converter design which uses wave overtopping discharge into a variable v-shaped hull, to generate electricity through low head turbines. Physical model tests of WaveCat WEC were carried out to determine the device reflection, transmission, absorption and capture coefficients based on selected wave conditions. The model scale was 1:30, with hulls of 3 m in length, 0.4 m in height and a freeboard of 0.2 m. Wave gauges monitored the surface elevation at discrete points around the experimental area, and level sensors and flowmeters recorded the amount of water captured and released by the model. Random waves of significant wave height between 0.03 m and 0.12 m and peak wave periods of 0.91 s to 2.37 s at model scale were tested. The wedge angle of the device was set to 60°. A reflection analysis was carried out using a revised three probe method and spectral analysis of the surface elevation to determine the incident, reflected and transmitted energy. The results show that the reflection coefficient is highest (0.79) at low significant wave height and low peak wave period, the transmission coefficient is highest (0.98) at low significant wave height and high peak wave period, and absorption coefficient is highest (0.78) when significant wave height is high and peak wave period is low. The model also shows the highest Capture Width Ratio (0.015) at wavelengths on the order of model length. The results have particular implications for wave energy conversion prediction potential using this design of device.

Comparison of Sea Wave Measurement Systems Based on Marine Radar and Microseismic Technologies

Sea state affects the coasts of all maritime regions, and it impacts anthropic infrastructures and influences the activities carried out in the sea as well as in its proximity. Sea-state monitoring is therefore important for a number of reasons, including the need to validate weather forecast models and study the impact of sea waves on anthropic infrastructures such as ports. In this letter, we combined the measurements of sea state collected with Ocean Seismic Integrated System (OS-IS), a seismic-based system developed by AGI (Assist in Gravitation and Instrumentation) srl and INGV (National Institute for Geophysics and Volcanology), with those obtained using a Wave Radar system. The aim was to prove that this combination could enhance the efficacy and reliability of sea monitoring, thanks to the complementarity of the two types of measurements in terms of area covered and spatial resolution. More specifically, the sea-state parameters provided by OS-IS were compared with those provided by a Wave Radar system. OS-IS data were collected from three microseismic stations installed near the Gulf of La Spezia, on the Ligurian Coast, whereas the Wave Radar system was installed at the center of the Cinque Terre National Park at about 12 km from the OS-IS system. The comparison between the measurements of significant wave height ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{s}$ </tex-math></inline-formula> ) and peak period ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{p}$ </tex-math></inline-formula> ) showed a good agreement, with a correlation index close to 0.9. The residual difference highlights the complementarity of the two systems and the potential of an integrated system that includes both. In particular, OS-IS provides measurements over large, offshore areas, whereas the Wave Radar System provides high spatial-resolution measurements over areas near the coast.

Sea State Monitoring by Ship Motion Measurements Onboard a Research Ship in the Antarctic Waters

A parametric wave spectrum resembling procedure is applied to detect the sea state parameters, namely the wave peak period and significant wave height, based on the measurement and analysis of the heave and pitch motions of a vessel in a seaway, recorded by a smartphone located onboard the ship. The measurement system makes it possible to determine the heave and pitch acceleration spectra of the reference ship in the encounter frequency domain and, subsequently, the absolute sea spectra once the ship motion transfer functions are provided. The measurements have been carried out onboard the research ship “Laura Bassi”, during the oceanographic campaign in the Antarctic Ocean carried out in January and February 2020. The resembled sea spectra are compared with the weather forecast data, provided by the global-WAM (GWAM) model, in order to validate the sea spectrum resembling procedure.

Projected wave climate temporal variability due to climate change

This work proposes a new general procedure to stochastically analyze multi-model multivariate wave climate time series projections at different temporal scales. For every projection, it characterizes significant wave height, peak period and mean direction by means of univariate non-stationary distributions capable of capturing cyclic climate behavior over a reference time interval duration. The temporal dependence between the values at a given sea state and previous short-term wave climate is described with a vector autoregressive model (VAR). The multi-model ensemble wave climate characterization is based on a compound distribution of the individual non-stationary distributions and a weighted averaged VAR model. The methodology is applied to bias-adjusted wave climate projections derived using WaveWatch III forced by wind field data from EURO-CORDEX models at a location close to the Mediterranean Spanish coast. Results are compared to hindcast data which shows a clear bi-seasonal behavior. Different temporal references were considered, starting with a 1-year reference period to analyze overall changes in wave climate at scales ranging from days, months and seasons with respect to historic conditions. The results show that the projected wave climate has a very different temporal behavior than hindcast data, delaying and widening/shortening the start and duration of the two main seasons and including shorter term variations. Regarding the energetic content of the sea states, the compound variable highest percentiles of the significant wave height present lower values than the hindcast (≈3−10%) during the traditionally more severe period (November–March) but higher values (≈10−35%) during the calmer months. The projected peak period presents a similar temporal pattern to the hindcast data, while the mean wave direction shows a significant change from the historical bi-modal behavior towards more likely easterly waves throughout the year. Additionally, a 10-year analysis is done to find larger temporal variabilities such as decadal variations associated with the North Atlantic Oscillation. The observed temporal variability in the yearly seasonal pattern throughout the century is addressed by analysing 20-year rolling windows in all the model projections and in the compound variable. The compound distribution shows significant temporal variabilities throughout the century with the most severe periods and more likely severe waves during summer at the end of the century.

On the Nile Fan's Wave Power Potential and Controlling Factors Integrating Spectral and Geostatistical Techniques

Wave energy is foreseen to contribute to the 20 % renewable energy supply of Egypt’s electricity budget to meet burgeoning energy demand. This research analyses the Nile Fan wave energy forcasted from numerical modeling for 2020 of the Copernicus Marine Environment Monitoring Service (CMEMS) database, hourly sampled at 0.042° as the finest remotely-sensed data available. Wave power spatial distribution is analyzed using data from 259 points proposed as Wave Energy Converters (WECs). Spectral analyses techniques were appraised for disclosing the frequency and power return periods of the significant wave height and peak periods and to understand the similarity among selected WECs of varied conditions. K-means clustering was used to distinguish energy classes with large inter-class variances. The obtained wave power resources ( av . 5.32 kW/m; maximum of 112.9 kW/m; annual mean of 46.96 MW/m) are among the largest found in the Mediterranean Sea. More than 98 % of the wave power variance is controlled, in decreasing order of influence, by the depth, distance to shore, significant wave height, wave peak period, and the wave principal direction. Deepest water and near shore classes attained the largest wave power. Detailed environmental factors induced the wave shape and power is concluded.

The effects of geometrical buoy shape with nonlinear Froude-Krylov force on a heaving buoy point absorber

This study examined the effects of buoy shape and Nonlinear Froude-Krylov force (NFK) on a heaving-buoy-type Wave Energy Converter (WEC). Based on the Maclaurin expansion, the theoretical solutions of the NFK were derived for three different buoy shapes; hemispheric buoy, circular vertical cylinder, and truncated conical cylinder. A hydraulic power take-off system was adopted, and the latching control strategy was applied to maximize the extracted power from the WEC. The nonlinear effects of the Froude-Krylov force and restoring force on the heaving point absorber were investigated by comparing the heave Response Amplitude Operator (RAO) and time-averaged power extraction. The results showed that the conventional linear analyses were overestimated by up to 50% under the high amplitude wave condition. The latching control strategy was the most effective when peak wave period of regular or irregular wave was 0.4–0.45 times the heave natural period of the buoy.

Experimental investigations on wave induced dynamic pressures over slotted vertical barriers in random wave fields

Experimental investigations were carried out to assess the wave induced pressures on slotted vertical barriers. Thirty six different wave barrier configurations (10%, 20%, 30%, 40%, 50% and 60% porosities and 1 to 6 numbers of slotted walls) were tested in random wave fields of JONSWAP spectra for different combinations of significant wave heights and peak periods. It is found that on the dynamic pressure on vertical slotted wave barrier reduces progressively from the seaside to the rear side. In general, the dynamic pressure coefficient Ps/(ρgHis/2) reduces with an increase in relative water depth, d/Lp. where Ps is the significant dynamic pressure, ρg is the weight density of water, His is the significant incident wave height, d is the water depth and Lp is the wave length corresponds to peak wave period. It is also found that the highest value of measured Ps/(ρgHis/2) is about 1.5. The barrier with 3 walls and 10% porosity and for d/Lp of 0.3, the seaside wall panel experience dynamic pressure coefficient of 1.44, the first rear wall with 0.82 and the lee side porous wall with 0.58. The results can be used for the optimal design of the panels of multiple slotted vertical wave barriers.

Assessment of inhomogeneity in environmental conditions in a Norwegian fjord for design of floating bridges

Environmental conditions along a very large floating bridge are inhomogeneous due to complex topography and hydrography. Evaluating the inhomogeneity in environment conditions is important for safety design of floating bridges but challenging because of their large size. This study addresses the assessment of long-term spatial inhomogeneity in wind and wave parameters for environmental conditions in a Norwegian fjord for design of floating bridges based on 16-year hindcast data. The wind and wave data are numerically simulated by using the Weather Research and Forecasting (WRF) model and Simulating Waves Nearshore (SWAN) model, respectively. The accuracy of hindcast wave data is validated by comparison against field measurements. Inhomogeneity in wind and wave parameters are revealed by contour maps by considering two dominant wave directions. Significant wave height and peak period are fairly close in the south part and decrease gradually towards the north end. Mean wave direction decreases from south end to north end. Mean wind speed has a relatively small variation in the south part and a great variation in the north part, so do the mean wind direction. Correlation of wind and wave parameters along a potential bridge route is analyzed. Wind parameters are less correlated than the wave parameters.

Calibration and skill assessment of two input and dissipation parameterizations in WAVEWATCH-III model forced with ERA5 winds with application to Persian Gulf and Gulf of Oman

The wind energy input and whitecap dissipation terms in the third generation wave models have been improved over the time. In this research, the well-known WAM-Cycle4, known as ST3, and the newest ST6 package in WAVEWATCH-III model were employed combined with ERA5 wind data over the Persian Gulf and Gulf of Oman. In order to model the wave height appropriately over the study area in comparison with both in-situ and satellite observations, new combined error parameters were introduced leading to two major calibration values: (1) the local calibration values relating to either Persian Gulf (PGc) or Gulf of Oman (GOc); (2) the global calibration values over the entire computational domain (PGGOc). Considerably different model performance was appeared in the Persian Gulf (PG) compared to either the Gulf of Oman (GO) or entire computational domain (PGGO) when ST3 package was employed, while obtained results using ST6 package showed negligible sensitivity to the domain. Both ST3 and ST6 packages with default tuning values significantly underestimated the wave height and peak period in PG; however, slight underestimation (~0.03 m) for wave height and overestimation (~0.1 s) for mean wave period were obtained in GO. During the time period the cyclone Phet has traversed across the study area, the model overestimated the wave height in comparison with altimeter dataset. Mean bias distribution over the study area indicates that calibrated ST6 outperforms calibrated ST3 over GO; however, both packages provide similar results over PG. Considering different methods for nonlinear interaction term led to similar directional wave spectrums over the study area and negligible changes in bulk wave parameters.

Multi-Step-Ahead Forecasting of Wave Conditions Based on a Physics-Based Machine Learning (PBML) Model for Marine Operations

Short-term wave forecasts are essential for the execution of marine operations. In this paper, an efficient and reliable physics-based machine learning (PBML) model is proposed to realize the multi-step-ahead forecasting of wave conditions (e.g., significant wave height Hs and peak wave period Tp). In the model, the primary variables in physics-based wave models (i.e., the wind forcing and initial wave boundary condition) are considered as inputs. Meanwhile, a machine learning algorithm (artificial neural network, ANN) is adopted to build an implicit relation between inputs and forecasted outputs of wave conditions. The computational cost of this data-driven model is obviously much lower than that of the differential-equation based physical model. A ten-year (from 2001 to 2010) dataset of every three hours at the North Sea center was used to assess the model performance in a small domain. The result reveals high reliability for one-day-ahead Hs forecasts, while that of Tp is slightly lower due to the weaker implicit relationships between the data. Overall, the PBML model can be conceived as an efficient tool for the multi-step-ahead forecasting of wave conditions, and thus has great potential for furthering assist decision-making during the execution of marine operations.

Wave Forecasting Dependent from Bottom Roughness: The Case of the Marano and Grado Lagoon

Several forecasting curves have been developed in order to provide a useful estimation of the wind wave field generated on shallow depths. In particular, these equations can be successfully applied in confined and sheltered basins, such as lakes, or even lagoons and semi – enclosed estuarine in coastal environments. The important role of the bottom friction dissipation in the generation process has been deeply recognized, leading to a reformulation of the available curves in terms of the equivalent bed roughness. In the present study, the recent new set of equations is considered and applied to a coastal lagoon. The results in terms of significant wave height and peak period are compared to those derived from a complete numerical model and other previous curves. The performed application corroborates and further validate the forecasting equations.

Operability study of walk-to-work for floating wind turbine and service operation vessel in the time domain

The operability of walk-to-work operation through gangway regarding floating wind turbine and service operation vessel is studied. An attempt has been made to investigate the limiting wave height in particular by the numerical modeling of multi-body configuration in the time domain. Special attention has been paid to the impact of second-order drift motion which is traditionally not taken into account in operability analysis. Meanwhile, the fluctuation of RAO and shielding effect due to the hydrodynamic interaction are discussed in depth. The failure mode that interrupts the operation, asymmetry of the polar diagram, and the effect of drift motion are emphasized and discussed in detail. The operational failure in the short wave peak period is caused by the horizontal displacement or velocity depending on whether the drift motion is considered. For a longer period, the vertical motion is the dominant the failure mode. Walk-to-work operation is checked against the obtained limiting wave height using two actual onsite wave conditions. With drift motion, the curves of allowable wave height show the declining trend as peak period increases; however, they present a growing trend if drift motion was considered.

Seasonal variation in longshore sediment transport rate and its impact on sediment budget along the wave-dominated Karnataka coast, India

The Karnataka coast is subjected to high wave activity during the southwest monsoon when most of the sandy beaches undergo erosion. Based on the littoral cell concept, the Karnataka coast is broadly divided into 14 major littoral cells and 26 stations are selected in the present study. WaveWatch III global wave model data at 0.5° interval were used to derive the nearshore wave characteristics from XBeach numerical model. The model results were validated with the measured wave rider buoy data of the Indian National Centre for Ocean Information Services. The beach orientation, nearshore slope, median sediment size, significant wave height, mean wave direction, and the peak wave period were used in the estimation of longshore sediment transport rate. The mean significant wave height along the Karnataka coast was about 0.86 m, wave direction was about 210° and peak wave period was about 13 sec. The wave height during southwest monsoon (June–September) was higher, post-monsoon (October–December) was moderate and pre-monsoon (January–May) was the calmest period. Direction of longshore sediment transport was southwards during pre- and post-monsoons when waves were from the south–southwest. Whereas, northwards during monsoon when the wave approach from west–southwest to west. The annual net longshore sediment transport rate estimated was about 0.65×106 m3 towards the south and the sediment budget investigation depicts the loss of 0.067×106 m3 during the study period.