Mean Zero-crossing Period Research Articles

Error analysis of wave intercomparison based on sampling variability

Quantitative analysis of error sources in wave measurement intercomparison under real-world conditions remains challenging due to various factors such as spatial and temporal offsets in the field, diverse configurations of wave sensors and platforms, and distinct measurement algorithms. This study introduces a modified error analysis method based on sampling variability. Measurements from two co-deployed Datawell Waverider buoys at the National Marine Test Site (Weihai) in China offer an opportunity to assess the spatial variability error. The results reveal that for non-directional wave parameters, like significant wave height and mean zero-crossing period, the wave conditions in the field can be considered stationary, with random errors primarily arising from inherent sampling variability. Spatial offsets significantly impact directional wave parameters at peak frequencies, with large deviations (greater than 20°) in peak wave direction primarily attributed to bimodal distribution. For data with significant wave heights exceeding 0.5 m, random errors in the mean wave direction at the same frequency can be mainly attributed to sampling variability. The bulk directional wave parameters weighted by the energy spectrum demonstrate lower sensitivity to spatial offsets, and there is excellent agreement between the bulk mean directions when considering only the unimodal distribution data.

Comparison of full-scale measurements and seakeeping calculations for two research vessels in the Adriatic Sea

The paper describes two experimental campaigns of seakeeping measurements for two research vessels in the Adriatic Sea and comparison of the experimental results with the seakeeping calculations. The waves and vessel motions are simultaneously measured at seas. Sea surface elevation of wind waves is measured using a wave buoy, freely floating near the vessel. Measurements of vessel motions are performed using motion sensors mounted on the bridge deck. Measurements are performed for different heading angles between the prevailing wave direction and the vessel. Time signals of the measured waves and resulting heave and pitch motions are treated statistically and subjected to spectral analysis. Wave-induced vessel responses are also calculated by the spectral analysis, employing the 3D panel method for transfer functions. Measured wave spectra are approximated by the standard JONSWAP spectra for that purpose. Statistical properties of the measured and calculated wave-induced motions are then compared. The results of the seakeeping calculations are in fair agreement with the measurements, except for mean zero-crossing period of the responses in following seas, where considerable discrepancies are found.

Analysis on statistical uncertainties of wave loads and structural fatigue reliability for a semi-submersible platform

The statistical uncertainties of wave loads have large proportions in the structural fatigue strength analysis of offshore platforms. To investigate the uncertainties of wave loads during predicting fatigue loads, the assessing methods and formulas are proposed involving the wave spectrum, sea wave height, wave loading transfer function, zero-crossing period, possibility of sea state occurrence and wave direction; meanwhile, the model test of the wave loads is carried out in a see-keeping basin for studying the uncertainty of the wave loading transfer function. The corrected formulas of the significant wave height and mean zero-crossing period are statistically regressed by calculating the sea states in the Northwest Pacific and South China Sea. Furthermore, the influence factors of the sea states of difference seasons are analysed, and the distribution law of the wave direction of the wave loads and fatigue life of a semi-submersible platform are investigated. Finally, the fatigue reliability index of typical structures for a semi-submersible platform is assessed on the basis of uncertainties of wave loads and the other uncertainties of structural factors.

Statistics of long-crested extreme waves in single and mixed sea states

Most of the studies on extreme waves are focused on the systems with single-peak wave spectra. However, according to the statistics of occurrence, the bimodal spectral system is also frequent in real sea conditions. In order to summarize the statistics of extreme waves, irregular wave trains under single-peak and bimodal spectra for long durations are simulated in this paper, based on a two-dimensional High Order Spectral (HOS) numerical wave tank. A large number of configurations have been tested under unimodal and bimodal spectra. The investigation on the wave trains under single-peak spectrum indicates that although in conditions often referred as deep water (kph > π), the relative water depth has a significant influence on the probabilities of occurrence of extreme waves. A detailed analysis of the combined effect of Benjamin-Feir Index (BFI) and relative water depth is provided. However, the situation is more complex in real sea conditions, which may exhibit multimodal spectra. We focus in this study on long-crested bimodal spectra characterized by the same significant wave height Hs and mean zero-crossing period Tz of the sea states as the single-peak spectrum. The wave conditions under bimodal spectrum present milder extreme wave statistics than those under single-peak spectrum. In addition, mixed ocean systems with equivalent energy distribution (i.e., Sea-Swell Energy Ratio (SSER) is close to 1.0) and larger separation between partitions (i.e., Intermodal Distance (ID) > 0.10) are the less prominent to extreme waves appearance. The comparison of the mixed sea states and the corresponding single independent systems demonstrates that the complexity of the underlying physics of a given sea state (for instance the presence of modulational instability or other nonlinear process) cannot be deduced by an analysis limited to the statistical content of the combined sea state. The wave energy being distributed among frequencies plays a major role. Additionally, Gram-Charlier distribution can accurately predict the probability of large waves (1.5 < H/Hs < 2.0) compared to the MER distribution, but it underestimates the statistics of the wave height distribution when H/Hs is larger than 2.0 for both single-peak and bimodal states.

A statistical simulation method for joint time series of non-stationary hourly wave parameters

Statistically simulated time series of wave parameters are required for many coastal and offshore engineering applications, often at the resolution of approximately 1 h. Various studies have relied on autoregressive moving-average (ARMA) processes to simulate synthetic series of wave parameters in a Monte Carlo sense. However, accurately representing inter-series dependencies has remained a challenge. In particular, the relationship between wave height and period statistics is complex, due to the limiting steepness condition. Here, we present a new simulation method for joint time series of significant wave height, mean zero-crossing periods and a directional regime variable. The latter distinguishes between northern and southwestern waves. The method rests on several model components which include renewal processes, Fourier series with random coefficients, ARMA processes, copulas and regime-switching. A particular feature is a data-driven estimate for a wave height-dependent limiting wave steepness condition which is used to facilitate copula-based dependence modeling. The method was developed for and applied to a data set in the Southern North Sea. For this site, the method could simulate time series with realistic annual cycles and inter-annual variability. In the time series data, the bivariate distribution of significant wave height and mean zero-crossing period was well represented. An influence of the directional regime on the bivariate distribution could also be modeled. However, the influence was not as strong in simulated data as in observed data. Finally, simulated series captured duration and inter-arrival time of storm events well. Potential applications for output of the simulation method range from the assessment of risks to the planning and budgeting of operations in coastal and offshore environments.

Study of the foundation design for a linear generator wave energy converter using stochastic methods

This paper presents design studies of the gravity-based foundation for a linear generator wave energy converter. The wave energy converter is based on a direct driven generator mounted on the gravity-based foundation located at the seabed. The linear generator is connected to a point absorbing buoy on the sea surface via a connection rope. Such a device, developed at Uppsala University, has been in operation on the Swedish west coast since 2006. Study is focused on the analysis of the impact from undesirable motions of the gravity-based foundation, particularly the study of the tip and lifts phenomena with regard to the heave and surge forces. Long-term extreme significant wave heights are extrapolated from the statistical analysis of the measured wave climate data in the test site where the wave energy converter is deployed. The joint distribution of the significant wave height and the zero-crossing period from the measured wave climate is also analyzed to estimate the associated periods with respect to the long-term extreme significant wave height. The 25 years return extreme significant wave height 4.8 m which is associated with its mean zero-crossing period 8.25 s from the joint distribution is chosen to determine the characteristics of the possible maximum wave for the Lysekil test site. The estimated maximum wave 9.2 m is used to estimate the extreme values of the heave and surge forces on the wave energy converter and the gravity-based foundation. The results with respect to the foundation of a new generation wave energy converter about 35 tons with the presented methodology indicate that a heavier foundation which is about 70 tons needs to be designed in terms of considering the stability of the mooring foundation for long term real sea operation. The purpose of this paper is to propose a reliable approach to estimate the appropriate dimensions for gravity-based foundation of the linear generator wave energy converter and provides a theoretical reference to the construction of the gravity-based foundation.

Bivariate distributions of significant wave height and mean wave period of combined sea states

This work presents the results of the fit of three bivariate models to twelve years of significant wave height and mean zero-crossing period data of swell, wind sea components, and combined sea states from Australia. The Conditional Modelling Approach defines the joint distribution from a marginal distribution of significant wave height and a set of distributions of mean zero-crossing period conditional on significant wave height. The second model fits the Plackett model to the data, and the last one applies the Box–Cox transformations to the data with the aim of making it approximately normal to fit a bivariate normal distribution to the transformed data. The conditional model with a lognormal distribution for the significant wave height and lognormal distributions for the zero-crossing period gave the best fit for the total sea states and for the wind component. In case of the swell component the conditional model with a Weibull distribution to the significant wave height and a lognormal distribution to the mean zero-crossing period gave a relatively close fit to the data.

English

Ocean wave energy is considered to be one of the important potential renewable energy resources for sustainable development. Various wave energy converter technologies have been proposed to harvest the energy from ocean waves. This thesis is based on the linear generator wave energy converter developed at Uppsala University. The research in this thesis focuses on the foundation optimization and the power absorption optimization of the wave energy converters and on the wave climate modelling at the Lysekil wave converter test site.The foundation optimization study of the gravity-based foundation of the linear wave energy converter is based on statistical analysis of wave climate data measured at the Lysekil test site. The 25 years return extreme significant wave height and its associated mean zero-crossing period are chosen as the maximum wave for the maximum heave and surge forces evaluation.The power absorption optimization study on the linear generator wave energy converter is based on the wave climate at the Lysekil test site. A frequency-domain simplified numerical model is used with the power take-off damping coefficient chosen as the control parameter for optimizing the power absorption. The results show a large improvement with an optimized power take-off damping coefficient adjusted to the characteristics of the wave climate at the test site.The wave climate modelling studies are based on the wave climate data measured at the Lysekil test site. A new mixed distribution method is proposed for modelling the significant wave height. This method gives impressive goodness of fit with the measured wave data. A copula method is applied to the bivariate joint distribution of the significant wave height and the wave period. The results show an excellent goodness of fit for the Gumbel model. The general applicability of the proposed mixed-distribution method and the copula method are illustrated with wave climate data from four other sites. The results confirm the good performance of the mixed-distribution and the Gumbel copula model for the modelling of significant wave height and bivariate wave climate.

A new empirically-based correction procedure for shipborne wave recorder data

A new correction procedure for Shipborne Wave Recorder (SBWR) wave height data is describedThe method is based on a new assessment of the available measurements of the frequency response of the SBWR using a Froude-type frequency scaling. Spectral data from the SBWR are corrected using this method and values of Hs, the significant wave height and Tz, the mean zero-crossing period are derived. The spectra appear to be reasonable while the Hs and Tz values are consistent with independent data which were also derived from spectral analysis. However, when the spectral the so-called Tucker-Draper method, the latter are found to be higher on average. For installations with deep pressure sensors, such as the Seven Stones lightvessels, the differences are substantial. It is argued that the differences are due to the use of an inappropriate frequency response correction. A method is derived for applying the new frequency response correction to historical Hs, Tzdata. The results of this procedure are compared with the simultaneous spectral values of Hs and with independent data from the Geostat altimeter. Finally, the changes in the 50-year design wave heights brought about by the use of the newcorrection procedure are evaluated. These calculations are done for a number of SBWR installations whose data contribute to the U K Department of Energy's Guidance Notes.

Long-term wave height distributions at seven stations around the British Isles

Long-term instrumental measurements of significant wave height and mean zero-crossing period at 7 stations are analysed. The marginal distribution of significant heights is well described by a Weibull law. The long-term distribution of individual wave heights is calculated from the joint distribution of significant wave height and mean wave period. It is found to be nearly exponential.

Waves Off Land's End

Since January 1962, waves have been recorded by a shipborne wave recorder (Tucker, 1956) on the Sevenstones light-vessel which is stationed about 20 miles south-west of Land's End in about 200 ft. of water. Records were taken at three-hourly intervals and were mostly of 12 minutes’ duration. The analysis presented here is based on 2920 records taken in the first year of operation; the method of analysis which has been used is that described by Tucker (1961). This gives for each record:(a) H1 = The sum of the distances of the highest crest and the lowest trough from the mean water level.(b) Tz = The mean zero-crossing period.(c) Tc = The mean crest period.