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In this note, a wave simulation method based on the wave spectrum is proposed, and the wave simulation is transformed into external interference to verify the necessity of using variable encounter angle real wave interference. Firstly, A wave simulation method based on wave spectrum and equidistant method is proposed and demonstrated. Secondly, wave modeling is transformed into interference force related to the encounter angle by fully considering the real marine environment. Furthermore, a trajectory tracking controller with variable encounter angles and the actual sea state is designed using the disturbance modeling method. Finally, the necessity and authenticity of considering varying encounter angles and real sea conditions in the motion control of unmanned surface vehicles (USVs) are proved by simulation. [ABSTRACT FROM AUTHOR]

Wave energy resource characterization investigations have been hindered because frequency-directional wave spectra are not broadly available for many coastal regions due to the insufficient spatial coverage of buoy observation networks and spectral wave model hindcast outputs. We address this problem by developing and validating a practical method for approximating temporally-averaged frequency-directional wave spectra averaged over periods of months or years from bulk wave parameters, which are available at a much greater coverage and resolution than frequency-directional wave spectra. While the temporally averaged frequency-directional wave spectrum over these periods cannot be used for analyzing a single sea state, it aggregates multiple sea states, identifies dominant wave energy systems representing wave climate, and resolves their spectral characteristics. Therefore, modelling temporally averaged frequency-directional wave spectra is of great value for planning and designing wave energy projects, e.g., resource characterization, site assessment, and conceptual design of wave energy converters. Temporally-averaged frequency-directional wave spectra and related important wave energy parameters approximated using this method are found to be more accurate than commonly used parametric wave spectrum models. This method can be applied to a wide range of wave climates given its universality and high accuracy. Also, the availability of bulk wave parameters from multi-decade high-resolution wave model hindcasts is increasing. • A practical method for modeling temporally averaged 2D wave spectra using bulk wave parameters. • Simple but highly accurate method compared to existing parametric spectrum models. • Consistent performance with great accuracy across a broad spectrum of wave climates. • The results and accuracy are independent of the data period of record. [ABSTRACT FROM AUTHOR]

The utilization of digital twin technology, which integrates real-world measurement data with a digital representation of the vessel, is garnering increasing attention within the realm of structural integrity management. Due to limitations in sensor deployment on ships, the integration of the digital twin framework, which merges measurement data with the ship's digital design model, becomes crucial for ensuring the effectiveness of structural integrity management. This investigation introduces a methodological approach for estimating localized responses at unmeasured locations, leveraging both measurement and design datasets. To approximate the response at unobserved sites, the directional wave spectrum is initially determined utilizing the least squares method, thereby, minimizing the disparity between the estimated and measured response spectra. The methodology notably incorporates cubic B-spline interpolation specifically to smooth the directional wave spectrum deployed on the heading-frequency domain. This deliberate choice of employing cubic B-spline interpolation underscores the emphasis on achieving a refined and continuous representation of the directional wave spectrum, thus enhancing the accuracy and reliability of the estimation process. To validate the proposed methodology, synthetic pseudo-measurement data derived from the wave spectrum and RAO of a 13,000 TEU container ship are employed. Subsequently, the directional wave spectrum is estimated utilizing the pseudo-measurement data, and the estimated directional wave spectrum, in conjunction with the Response Amplitude Operator (RAO), is harnessed to approximate the response spectrum at the location where sensors are not installed. • A numerical methodology was proposed to estimate directional wave spectrum around vessels using onboard measurement data. • Directional wave spectrum was discretized with B-spline, and the non-parametric quadratic programming problem was solved • Proposed method was validated with pseudo measurement data of 13,000TEU container carrier model and accuracy was confirmed. [ABSTRACT FROM AUTHOR]

In the realm of ocean engineering and environmental research, the accuracy of the wave spectrum is paramount. Traditional models, constrained by the number of parameters, often struggle to accurately capture the intricacies of real-world wave spectra, especially when confronting the complexities of multi-peak spectral shapes shaped by wind-sea and swell systems. This research develops a novel multi-parameter wave spectrum model that substantially amplifies the capacity to describe the diversity of wave spectra by introducing more shape parameters. The proposed model includes more shape parameters than its predecessors. These parameters can be directly optimized and obtained through the Heterogeneous Comprehensive Learning Particle Swarm Optimizer (HCLPSO). This sophisticated algorithm leverages its robust global search capabilities and swift convergence to fine-tune the model's parameters, ensuring a high degree of precision in fitting the measured wave spectra. Furthermore, the proposed model also shows great potential in wave spectrum prediction, even when there are fewer training samples, it can still yield relatively accurate predictive results. This research not only improves the applicability and accuracy of the wave spectrum model but also offers a new tool for ocean wave research and real-world applications, thereby contributing important research and practical value to the field. • A multi-parameter wave spectrum is proposed. • Optimization method HCLPSO was used to fit the parameters. • Measured wave spectra are used to verify the proposed wave spectrum. • Compared with other wave spectrum model, the advantages of the proposed model are verified. [ABSTRACT FROM AUTHOR]

This paper presents a neural network model to estimate wave spectra from wave parameters by the zero-crossing analysis, maximum, significant, and average wave heights and their corresponding wave periods. The present model was trained with the wave data in the JES (Japan/East Sea), and then applied to wave measurements in the Yellow Sea and the South Sea for its feasibility at other seas. According to the present study, the predicted wave spectra well agree with the measurements, even the wave data not in model training. This comparison shows that the accuracy of the present model is comparable to that of JONSWAP wave spectrum. Furthermore, the present model was employed to the wave hindcasting to see its applicability, while JONSWAP wave spectrum also being applied. The significant wave heights from both numerical simulations well agree with the measured ones. However, the average RMSE of significant wave period with the present neural network was 7.08 % smaller than the other, and its Pearson's correlation coefficient is 6.33 % larger on average. From this, it can be seen that the present model was well applied to the wave hindcasting without considering the local wave measurements. • This paper presents a neural network model to estimate wave spectra from wave parameters by the zero-crossing analysis, maximum, significant, and average heights and the corresponding wave periods. • The wave spectra predicted by the present model well agree with the measured ones. The accuracy of present model is comparable to that of JONSWAP wave spectrum with Hwang et al.'s (2021) peak enhancement factor, comparing them. • The present model was employed to the wave hindcasting in Young-il bay to see its applicability. The numerical simulation with incident waves by JONSWAP wave spectrum was also carried out to compare the applicability of both models. • The numerical results show that the significant wave heights from both models are similar to each other. However, the significant wave period with the present model is more accurate than the other. [ABSTRACT FROM AUTHOR]

Frequency spectra obtained from the wave height and period joint probability distribution function (H-T JPDF) yields results that differ from the widely used empirical frequency spectrum. Thus, Accordingly, this study proposed a method to obtain H-T JPDF by combining the wave height distribution for each period adopted from the theoretical equations of Longuet-Higgins and Cavanie et al. and the empirical frequency spectrum. Consequently, waveforms were generated from the empirical spectrum and then compared with the H-T JPDF obtained by zero-up crossing method to validate the proposed methodology. The validity of the proposed JPDF was evaluated through comparisons of wave data observed in shallow coastal areas at Gonghyunjin in the eastern coast and Heukdo in the western coast of Korea having completely different wave environments. In addition, the validity of the theoretical probability distribution of wave height was investigated by comparing it with observed wave data. • To investigate the distribution characteristics of existing H-T JPDFs of narrow and broad-banded random processes. • To present a method of obtaining H-T JDPF by combining the wave height distribution by period and the period spectrum. • To compare the proposed H-T JPDF with the joint probability distribution obtained from wave series randomly generated. • To examine the validity of the proposed H-T JPDF by comparison with field observed results. [ABSTRACT FROM AUTHOR]

Assimilating observation data into wave models can significantly improve the numerical simulation accuracy of ocean waves. Traditionally, assimilation efforts have predominantly focused on significant wave height (SWH). However, the launch of the China-France Oceanography SATellite (CFOSAT)has facilitated the acquisition to obtain global-scale wave spectrum data, introducing a transformative dimension to assimilation methodologies. This novel wave spectrum data holds substantial potential for refining global wave data assimilation results. In our study, a series of numerical experiments were conducted employing CFOSAT data to systematically contrast the impact of wave spectrum assimilation with that of SWH assimilation on global wave simulations. The assimilating impacts of SWH assimilation and spectrum assimilation were validated against wave data retrieved from the National Data Buoy Center (NDBC) buoys and Jason-3 altimeter. The validation included SWH, mean wave period (MWP), dominant wave period (DWP), the direction from which the waves at the DWP are coming (DWD), and the wave spectrum. When comparing with the buoy measurements, spectrum assimilation demonstrated superior effectiveness in improving mean wave period (MWP) compared to SWH assimilation. The assimilation index for spectrum assimilation reached 12.21%, escalating to 15.78% when MWP exceeded or equaled 8 s. In contrast, for SWH, DWP and DWD, SWH assimilation performed better. Validation against Jason-3 altimeter data revealed that spectrum assimilation surpassed SWH assimilation in terms of overall improvement. Notably, SWH assimilation exhibited a more favorable impact when SWH values were <2.5 m. However, for SWH values greater than or equal to 2.5 m, spectrum assimilation outperformed SWH assimilation, yielding assimilation indices of 8.10% and 6.18% compared to buoys and Jason-3, respectively. Overall, this work illustrates that utilizing CFOSAT data for spectrum assimilation and SWH assimilation can enhance wave simulation accuracy under different conditions, which may point to promising applications in hurricane forecasting and disaster reduction research. • Assimilating CFOSAT data enhances ocean wave simulation accuracy. • Spectrum assimilation improves MWP and spectrum more than SWH assimilation. • SWH assimilation surpasses spectrum assimilation in improving SWH, DWP, and DWD. • Under high sea state, spectrum assimilation simulates SWH and MWP better. [ABSTRACT FROM AUTHOR]

The intertidal beach profile provides coastal engineers and managers with a good indication of the current state of a sandy coastline, however regular beach profile measurements are time consuming and expensive to obtain using conventional surveying methods. The potential to reconstruct the intertidal beach profile from measurements of reflected waves is tested here using three field datasets covering a different range of hydro-morphological conditions from dissipative, to reflective. The swash is found to behave as a low-pass filter on reflected waves, with a cut-off frequency that primarily depends on the swash slope. An agreement is found between video-derived swash spectrum saturation tail and the shortest reflected waves, computed from deep water directional wave measurements. By integrating this swash slope over a tidal cycle, the shape of the intertidal beach profile can be reconstructed. Our results clearly show the potential of such method to estimate complex intertidal beach profile, such as double-slope beaches. • The intertidal beach profile can be reconstructed by integrating the swash slope over a tidal cycle. • The swash behaves as a low-pass filter, with a cut-off frequency that primarily depends on the swash slope. • A good agreement is found between video-derived swash spectrum saturation tail and the shortest reflected waves. [ABSTRACT FROM AUTHOR]

Abstract Oscillating Water Column (OWC) is one of the pioneer devices in harnessing wave energy; however, it is not fully commercialized perhaps due to the complicated hydrodynamic behavior. Previous studies are significantly devoted to OWC devices located in nearshore and coastal regions where incident wave energy would experience dissipation more than offshore. In this paper, a 1:15 scaled fixed offshore OWC model is tested in a large towing tank of National Iranian Marine Laboratory. Wave spectrum shape effect on the efficiency of the OWC model is addressed. Moreover, the paper investigates the effects of the geometric and hydrodynamic factors on OWC device efficiency and uncovers new points in nonlinear interaction occurring inside the chamber; i.e. sloshing. The results indicate that shape of the spectrum inside the chamber is affected by the type of incident wave spectrum, especially for long waves. Pierson–Moskowitz spectrum leaded to higher efficiency rather than JONSWAP spectrum at longer incident wave periods. According to efficiency analysis, increasing wave height may lead to air leakage from the chamber followed by vortex generation, which is a reason for decreasing the efficiency of the OWC device. Furthermore, no shift in the resonant period of the OWC model, due to wave height increase, was observed at the opening ratios equal or smaller than 1.28%. Spectral analysis of water fluctuation inside the OWC chamber illustrates two modes of sloshing. The first mode can be seen at short period waves while the second mode is visible at long period waves. The sloshing modes approximately vanish by increasing draft value. [ABSTRACT FROM AUTHOR]

Highlights • A hurricane risk assessment framework is introduced to identify vulnerable bridges. • The maximum sustained wind speed is selected as the intensity measure. • Uncertainties in both demand and capacity variables are considered. • The proposed framework is highly effective in assessing risk of bridge failures. Abstract Coastal bridges sustained severe damage during hurricanes Ike, Katrina, and Ivan. Reducing the impact of future hurricane events to coastal bridges requires conducting a comprehensive risk analysis. A comprehensive risk analysis of bridges enables owners to assign limited resources to the most critical bridges in the inventory through a risk-informed decision making process. This study presents a computationally efficient methodology for structural fragility analysis and risk assessment of simply supported coastal bridges vulnerable to hurricane hazard. Various sources of uncertainty associated with hurricane hazard and bridge response are identified, and thereby establishing probability distributions. The novelty of the proposed method includes the consideration of uncertainties in extreme wave heights and wave period by means of a wave spectral density distribution in the calculation of wave forces. The proposed hurricane risk analysis method was successfully applied to coastal bridges located in the state of Georgia (U.S.A). The application presents the derivation of probabilistic models of demand, capacity and hazard; and highlights the potential of the proposed framework for identification and ranking of the most vulnerable bridges. [ABSTRACT FROM AUTHOR]

Abstract The safety aspect of the airgap question is discussed. Thereafter uncertainties related to airgap assessments will be discussed both for fixed platforms and semi-submersibles. The various sources are discussed and illustrated with examples. Results are discussed both for 10−2 – annual probability scenario (ULS) and an ALS scenario (10−4 annual probability). This because the most important difference between the two possible rule regimes for Norwegian Continental Shelf is the way ALS is introduced regarding airgap. Highlights • Discussion of rule regimes applied at the Norwegian Continental Shelf. • Sources of uncertainties regarding determining airgap for fixed platforms. • Uncertainties in predicting proper airgaps for semi-submersibles. • Discussion of assumptions that must be made for a proper airgap assessment. [ABSTRACT FROM AUTHOR]

The wave characteristics of the eastern Guangdong offshore water were quantified based on 1-year wave observations at a water depth of 60 m. This study statistically analyzed the observed wave characteristics and quantified the variations of the wave parameters and spectrum due to Super Typhoon Mangkhut. Results showed that the dominant and strong wave directions in the northeastern South China Sea were north-eastern and eastern, respectively. The average significant wave height was in the range of 0.7–2.4 m. During Super Typhoon Mangkhut, the maximum wave height and period were 11.3 m and 10–12 s, respectively, and peak spectral density mainly varied between 0.06 and 0.1 Hz. Results of this study can provide a basis for offshore engineering design and are of great significance for marine forecasting and disaster prevention and reduction. • The wave characteristics of the eastern Guangdong offshore water were quantified based on 1-year wave observations. • The significant wave height (H 1/3) was 1.7 - 3.5 m, and maximum wave height (H max) was 11.3 m during Super Typhoon Mangkhut. • Both Jonswap and Wenshengchang spectrum can fit the measured wave spectrum well in this region during Super Typhoon Mangkhut. [ABSTRACT FROM AUTHOR]

A mathematical model is developed to estimate the amplification of multidirectional random waves in the Paradip port, Odisha, India under the resonance conditions. A 3-D boundary element method with the consideration of variable bathymetry is utilized for solving Laplace equation in an irregular domain including the partial reflection boundary condition. The current numerical scheme is validated through the comparison of simulation results with previous well-defined studies along with measurement data for the rectangular harbor. Six key recorder stations are chosen as port location of moored ship to analyze the wave response in the Paradip port for multidirectional random waves. Further, wave spectrum is also estimated based on Fast Fourier Transformation (FFT) with respect to wave period at six recorder stations. Actual bathymetry of Paradip port is utilized to estimate the wave height ratio at each record station for the incident waves with different directions. Further, the resonance frequencies are determined for each directional incident wave and safe locations in Paradip port is also identified based on the simulation results. Thus, the proposed numerical scheme can be utilized to foster the prediction of wave profile in the realistic ports or harbors with complex geometries for the safe navigation. [ABSTRACT FROM AUTHOR]

Based on the linear random wave solutions of water wave equations in finite water depth, a theoretical statistical distribution of the wave-induced drift is derived. The parameters involved in the distribution can be determined by the water depth and the wave spectrum of ocean waves. As an illustrative example, we consider a simple wind-generated sea and the parameters are calculated for typical wind speeds and water depths by using Phillips spectrum. The behaviours of the distribution and the effects of wind speed and water depth on the distribution are investigated. [ABSTRACT FROM AUTHOR]

This paper presents an innovative methodology to assimilate peak period into wave models at a local scale. The proposed methodology estimates the peak period by processing time stack images from a video monitoring system for assimilation into a wave energy balance spectral model. Assimilation of the wave peak period is performed by correcting the boundary conditions and replacing the directional spectra prescribed by SWAN when using a nesting scheme. This methodology represents a new procedure for assimilating wave peak periods in coastal areas with video system infrastructures. The wave modelling is performed using a three-mesh nesting scheme where the finer domain coincides with the local scale and the proposed assimilation methodology is applied. The results show that the model improves the estimation of the peak period across the whole domain. The shape of the spectrum obtained changes significantly in the inner domain, mainly for low frequencies. • Peak period from time stack image processing was assimilated into the wave models using a new novel method. • Assimilation of peak period in coastal arear was achieved with a low computational cost. • The proposed methodology is a very useful tool for hindcast modelling in swell dominated coastal areas. • The methodology proposed allow to increase the quality of Peak period in local wave numerical models. [ABSTRACT FROM AUTHOR]

The article presents a practical approach to transform a wave energy spectrum from encounter domain to absolute domain. This problem has its specific relevance, when shipboard sea state estimation is conducted by the wave buoy analogy; notably for some particular implementation solving for the sea state directly in the encounter domain. In this context, the encounter domain is that observed from a ship when it advances in a seaway, whereas the absolute domain is that corresponding to making observations from a fixed point in the inertial frame. Spectrum transformation can be uniquely carried out if the ship sails “against” the waves (beam to head sea) but in following sea conditions there exists no unique solution to the problem. Instead, a reasonable approach valid for practical engineering must be applied, and the article outlines one viable solution that can be used to transform a wave spectrum from encounter to absolute domain. Specifically, two pseudo algorithms are presented, and good performance is achieved with both algorithms when they are tested at different operational scenarios. [ABSTRACT FROM AUTHOR]

The substructures of offshore wind turbines are subjected to different types of hydrodynamic loads from sea states. The wave forces exerted by irregular breaking waves are one of the serious concerns because of the uncertainties involved in defining the breaking wave and the resulting force calculations. In the present study, irregular breaking wave forces on a vertical pile structure are investigated using an open-source Computational Fluid Dynamics (CFD) model REEF3D. The Level Set Method (LSM) is used for modelling the free surface. The Bretschneider spectrum is used for the irregular wave generation. This is validated in the numerical wave tank by comparing the numerical wave spectrum with the experimental wave spectrum. The wave free surface is calculated at three wave gauge locations and compared with experiments. It is observed that the peak of spectral wave density is higher for the wave gauge located besides the cylinder due to shoaling, wave run up and reflections from the cylinder and the peak of spectral wave density is lower for the wave gauge located behind the cylinder due to wave breaking. Further, simulations are performed to study the wave forces on a monopile due to the depth-limited breaking waves. A good match is observed with the experimental and numerical results. Numerical wave energy spectra at different locations along the tank are compared to study the changes in the wave surface elevations due to the interaction of irregular breaking waves with a monopile. The statistical parameters for free surface elevation and wave forces are further investigated. The free surface features around the monopile during its interaction with waves are also studied. [ABSTRACT FROM AUTHOR]

The waves measured in the eastern Arabian Sea during the fall inter-monsoon period (October) are examined at 4 locations during 2010–2015. Multi-modal features have been observed in measured wave spectra due to independent wave systems corresponding to long-period swells generated by remote storms, swells generated by nearby storms and locally generated wind waves. In October, the long-period waves (peak wave period>18 s) appeared 5–7 times in different years and the significant wave height of these long-period waves are less than 1.4 m. The spatial distribution of peak wave period based on the numerical wave model shows that the presence of long-period swells along the 350 km stretch of the eastern Arabian Sea is almost in the same day. It is observed that the high waves (significant wave height >4 m) generated in an area bounded by 40–60°S and 20–40°E in the south Indian Ocean reached the measurement locations in 5–6 days and resulted in the long-period waves. Relatively high percentage of long-period waves are observed in 2011 and 2015 compared to other years due to the reduction in short-period waves at the study location due to the influence of Indian Ocean Dipole. [ABSTRACT FROM AUTHOR]

Climate change has necessitated the development of modular floating structures (MFS) as a sustainable solution to enhance the resiliency of coastal cities against flooding and sea level rise. Hence, it is imperative that simplified methods of analysis are introduced to the design community. This technical note presents closed-form expressions parameterizing the response amplitude operators (RAO) of rectangular pontoons subject to yaw (rotation about the vertical z axis) to complement solutions derived by Wang (2022) for the five remaining degrees of freedom. Following validation, a parametric investigation was implemented to assess the influence of pontoon geometry on the yaw response of an idealized MFS exposed to realistic sea states. It was identified that pontoons exhibiting a characteristic width smaller than the wavelength are generally more resistant to yaw excitation as they become squarer in shape. Conversely, while larger pontoons are less sensitive to geometric effects, they exhibit heightened sensitivity to changes in wave conditions. The simplified analytical approach thus provides an accessible pathway towards the structural or architectural design of floating structures as a precursor to detailed computational modeling. • Closed-form RAO equations derived for yaw validated against numerical results. • Yaw response parametrized against pontoon size, geometry, and wave conditions. • Larger MFS dampen yaw accelerations but more sensitive to changing sea states. • Analytical method facilitates the preliminary design of MFS prior to CFD modeling. [ABSTRACT FROM AUTHOR]

The present study investigates the hydrodynamic performance of a hybrid wave energy converter device consisting of a piezoelectric plate and the oscillating water column wave energy converter device placed over an undulated seabed. Primary emphasis is given to analyze the power extraction of the hybrid wave energy converter device, piezoelectric plate, and the OWC devices for various values of incident wave parameters and shape parameters associated with the hybrid wave energy converter device and undulated seabed. Moreover, the time-domain analysis is carried out by considering the Bretschneider spectrum as the incident wave spectrum for irregular incident waves. A multi-parameter optimization based on the Taguchi method is provided. The study reveals that the power extraction by the hybrid wave energy converter device consisting of a piezoelectric plate and the oscillating water column device is significantly higher than the power extraction by the standalone piezoelectric plate and the OWC device for a wider range of frequencies. Further, the present study shows that the power extraction by the hybrid wave energy converter device is higher when the piezoelectric plate is placed in the close proximity of the OWC device. Moreover, the time-domain simulation reveals that the piezoelectric plate is able to capture the incident wave energy for a longer period of time in real sea conditions. • Hybrid WEC is suited at locations having broadband incident wave spectrum. • Power extracted by the hybrid WEC is significantly higher than isolated devices. • System 1 is best suited for Bretschneider spectrum with ω m = 0. 837 , H 1 / 3 = 0. 875 m. • Lower gap between piezoelectric plate and OWC device increases power extraction. • Piezoelectric plate can capture the incident wave energy for a long period of time. [ABSTRACT FROM AUTHOR]

Estimates of directional wave spectra and related parameters can be obtained from ship motion data through the wave-buoy analogy approach. The fundamental input is the response amplitude operator (RAO), which translates ship response into a wave energy spectrum. While ship motion is routinely measured on ocean going vessels, the RAO is not directly available and it is approximated using ship hydrodynamic models. The lack of publicly available details of hull geometry and loading conditions can results in significant inaccuracy of this operator. Considering the reliability of remotely sensed wave height, here we propose an assimilation technique that uses satellite altimeter observations to calibrate the RAO and minimise its uncertainties. The method is applied to estimate sea state conditions during the Antarctic Circumnavigation Expedition by converting motion response of the icebreaker Akademik Tryoshnikov as recorded by the on-board inertial measurement unit. Comparison against concurrent sea state observations obtained from a marine radar device shows a good agreement for a variety of parameters including significant wave height, wave periods and mean wave direction. • Sea state properties and wave spectrum, are estimated from ship motion response. • Satellite observations are used in the estimation of the response amplitude operator. • Estimated sea state conditions from ship motion match well radar measurements. [ABSTRACT FROM AUTHOR]

The accurate assessment of the dynamic response of the offshore wind turbine is fundamental to its economical and safe design, where the precise characterization of the incident wind and waves is essential. While reliable aerodynamic models can accurately reproduce wind characteristics, the widely-used empirical JONSWAP spectrum in wave field simulation may not capture the multi-modal feature of the mixed wave field near the wind farm. In this study, the stochastic structural responses based on an integrated FE model of the soil-pile-structure system are assessed employing the empirical and actual wave spectra, along with discussions on the impacts of wave theory and wave-structure interaction. The main conclusions are: (1) The empirical wave spectrum can overestimate the dynamic responses compared with the measured swell-dominant one, but the dominant wind load weakens its influence on displacement. (2) When the wave serves as the decisive loading, using the empirical spectrum overestimates the dynamic performance for the swell-dominant wave spectrum while underestimating it for the wind-induced-wave-dominant one. The approximation of the actual wave spectrum to the JONSWAP spectrum is only recommended when the coupling effect of wind and wave is inapparent. (3) The wave theory imposes an evident effect on the dynamic behavior of the offshore wind turbine subject to joint wind and wave loading, where the JONSWAP wave spectrum is more sensitive. (4) The influence of water-monopile interaction is negligible when using the JONSWAP wave spectrum but prominent for the simulation's actual wave spectrum. • An integrated FE model considering soil-pile-structure interaction is developed. • Response discrepancies induced by JONSWAP and actual wave spectra are analyzed. • Influence of spectral disparities induced by inhomogeneous wave field is discussed. • Sensitivities of spectrum influence to wave theory and wave-structure interaction are studied. [ABSTRACT FROM AUTHOR]

Full-scale measurements taken during a naval vessel sea trial are compared to calculated stress spectra and associated fatigue damage estimates using linear frequency-domain hydrodynamic and finite element analysis codes. Results were generated using four different wave spectrum models to better understand their influence on fatigue damage estimates. The results using measured two-dimensional wave spectra were most similar to measurements, but the agreement with measurements for each of the spectrum models was acceptable. Significant improvement in calculation accuracy was observed when adding a spreading function to longcrested wave spectra. The use of ±90° as the extent of wave spreading gave results with minimal differences from the use of measured spreading angles. The agreement between measurements and calculations using longcrested wave spectra with a constant spreading function is fortunate because available seaway data are commonly limited to wave height and period combinations. The results of this study suggest the spectral fatigue analysis method can be used to generate reasonable estimates of stress spectra and resulting fatigue damage for a naval vessel. [ABSTRACT FROM AUTHOR]

Three different packages describing the white capping dissipation process, and the corresponding energy input from wind to wave were used to study the surface wave dynamics in South Atlantic Ocean, close to the Brazilian coast. A host of statistical parameters were computed to evaluate the performance of wave model in terms of simulated bulk wave parameters. Wave measurements from a buoy deployed off Santa Catarina Island, Southern Brazil and data along the tracks of Synthetic Aperture Radars were compared with simulated bulk wave parameters; especially significant wave height, for skill assessment of different packages. It has been shown that using a single parameter representing the performance of source and sink terms in the wave model, or relying on data from only one period of simulations for model validation and skill assessment would be misleading. The model sensitivity to input parameters such as time step and grid size were addressed using multiple datasets. The wind data used for the simulation were obtained from two different sources, and provided the opportunity to evaluate the importance of input data quality. The wind speed extracted from remote sensing satellites was compared to wind datasets used for wave modeling. The simulation results showed that the wind quality and its spatial resolution is highly correlated to the quality of model output. Two different sources of wave information along the open boundaries of the model domain were used for skill assessment of a high resolution wave model for the study area. It has been shown, based on the sensitivity analysis, that the effect of using different boundary conditions would decrease as the distance from the open boundary increases; however, the difference were still noticeable at the buoy location which was located 200–300 km away from the model boundaries; but restricted to the narrow band of the low frequency wave spectrum. [ABSTRACT FROM AUTHOR]

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. • Waves and seakeeping responses are measured for two research vessels in moderate sea states in the Adriatic Sea. • Measured time series are subjected to the statistical and spectral analysis. • Seakeeping calculations are performed for both vessels and calculated responses are compared to the measurements. • Comparison for heave and pitch motion shows fair agreement with measurements except for response periods in following seas. [ABSTRACT FROM AUTHOR]

Ocean wave simulations must be conducted in real-time and are more complicated than other natural scenery simulations. This study proposes a novel ocean wave simulation method that inputs the spatiotemporal sequences of the wave height field obtained by a wave spectrum formula and the fast Fourier transform (FFT) algorithm into a convolutional long short-term memory (ConvLSTM) training model. The method resolves the problems of poor real-time performance and authenticity in the traditional ocean wave simulation process. The ocean wave simulation method calculates the wave height field rapidly using the ConvLSTM-based model rather than the traditional FFT method. Finally, it accelerates the wave simulation process and predicts the height field at a future time. The model was evaluated in a simulation experiment on two kinds of wave spectra. The experimental results confirmed the realism of the waves simulated by the proposed model. The computational speed of the ConvLSTM model exceeds that of the FFT method, especially as the sample size and length of the prediction sequence increase, indicating the effectiveness and feasibility of the ConvLSTM model in accelerating the FFT algorithm. [Display omitted] • The wave height fields obtained by FFT algorithm can be regarded as a sequence of height maps with spatiotemporal features. • A deep learning model for spatiotemporal prediction named ConvLSTM can replace FFT algorithm in predicting height fields. • The ConvLSTM model can output one or more height maps in a single execution and outperforms FFT in real-time performance. [ABSTRACT FROM AUTHOR]

Commercial ships frequently operate under irregular sea conditions; hence, their performance must be estimated through simulations in a more realistic environment. To date, a number of experiments and numerical studies have been conducted using regular waves to estimate added resistance. In this study, the performance of the KVLCC2 hull considering the added resistance in various regular and irregular waves was evaluated using an unsteady Reynolds-averaged Navier–Stokes solver. Resistance and motion responses were observed for regular waves with various wavelengths, regular waves with various wave steepness, and bichromatic waves superposed with regular waves. The change in resistance performance and damping with respect to motion response based on wave height was analyzed. An irregular wave corresponding to the joint North Sea wave project spectrum under sea state 6 was derived; based on this derived wave, the added resistance in irregular waves was estimated. The added resistance was compared with the estimated value using the spectral method, which was also employed to derive the added resistance under the target sea state using regular wave results. The estimated values differ from the direct calculation results owing to the nonlinearity of resistance in the irregular wave. However, the motion responses showed a similar tendency to those of the regular wave (except for those in the proximity of natural frequency that were relatively large and could be influenced by the wave height), as observed when various wave steepness values were used. • Comparison of resistance and motion responses in regular waves with various steepness and length as well as bichromatic waves. • Comparison of added resistance between the spectral method in regular waves and the direct simulation in irregular wave. • Investigation on the nonlinearity of resistance and motion in the irregular wave. • Investigation on the flow structure around a hull according to wave period. [ABSTRACT FROM AUTHOR]

Wave data are required in many engineering applications. At locations where measured records are not available or are too short for design purposes, estimates of wave properties from numerical wave models are often used to characterise the expected wave climate. Typically, model predictions are validated against observations of the sea-state parameters, such as significant wave height, peak wave period, mean wave period and mean wave direction. However, while agreement between observed and predicted sea-state parameters can be good, in some cases the measured and predicted wave spectra can diverge significantly. In these circumstances, simple sea state parameters alone are not sufficient to describe the range of wave conditions that could arise at a given site. In this paper we present a new, alternative approach for assessing wave model performance by applying new parameterisation to the frequency wave spectrum. Seven parameters (significant wave height, peak frequency, peak energy density, squared Euclidean distance, skewness, kurtosis and mean width deviation) are used to better define the characteristics of unimodal wave spectra. Sensitivity tests are undertaken to analyse the performance and sensitivity of these parameters in identifying differences between observed and predicted wave spectra, using a range of idealised JONSWAP wave spectra. We demonstrate that comparing multiple parameters is a better method to distinguish differences between spectra than the results obtained using individual parameters in isolation. As such, application of two-dimensional validation matrices are proposed to provide a better, qualitative overview of the goodness of fit between observed and predicted wave spectra. The advantages of the new approach are demonstrated through validation of a hindcast spectral wave model at Hastings, southeast England. We believe that we have achieved our purpose here to start a discussion on alternative validation techniques that could be enhanced in the future. [ABSTRACT FROM AUTHOR]

In-situ wave measurement data are mainly used to validate the bulk wave parameters predicted by numerical models. Although the frequently used third-generation wave models are spectral models, determination of various spectral parameters and validation with the observed data are not common. This study covers the spectral analysis of selected storm records of a nearshore wave measurement campaign carried out at Filyos coasts with the complex bottom topography in Turkey, Southwestern Black Sea. The bulk wave and the spectral parameters are also calculated by a third-generation nearshore wave model, SWAN (Simulating Waves Nearshore), forced by the ERA5 offshore wave data, which is the newest re-analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) for the selected storms. Before using ERA5 offshore wave data, they are calibrated by the wave data of the satellite radar altimeter. In-situ measured bathymetry data are used in the SWAN model. Observed and predicted bulk wave and spectral parameters are compared, and the statistical error measures are calculated not only for the significant wave height, the peak period, and the peak wave direction but also for the three different spectral periods, three different frequency width parameters, a directional width and, a spectral peakedness parameter for the first time. Low values of statistical error measures show that the current wave predictions have a good agreement with the observed ones in terms of the significant wave height, H s, and the peak period, T p. However, the SWAN model predicts a slightly narrower frequency and directional spectrum with higher peaks, although the error measures are low. Moreover, SWAN can not predict the wide range of spectral shape occurrences that the observed spectra have. The development of the various spectral parameters during the storms is also investigated for the first time. It is found that the frequency and directional spreading of the observed spectra become wider and unsharpened in the late stages of the storm compared to the early stages. However, the same tendency is not observed clearly in the predicted directional spreading. • Sea surface elevation data analysis of one of the limited numbers of nearshore wave measurement campaigns in the Black Sea. • Spectral shape parameters are predicted by a third-generation wave prediction model, SWAN, and validated for the first time. • SWAN is forced by the recently released latest model re-analysis deep water wave dataset called ERA5 after calibration. • Considering the complex bottom topography in Filyos coasts, in-situ measured bathymetry data are used in the SWAN model. • The development of spectral parameters during a storm is investigated for the first time by identifying three storm stages. [ABSTRACT FROM AUTHOR]

The evolution of the wave spectrum is important, because often initial wave parameters necessary for modeling and coastal engineering tasks are obtained on the basis of spectral characteristics. The wave spectra evolution over mild sloping bottom was studied. The data of laboratory experiments were used for spectral and bispectral analysis. The spectrum maximum frequency downshifting with discrete step (i.e. the cascade downshifting) was revealed. Its peculiarities depending on initial wave parameters and spectrum width were investigated. The cascade frequency downshifting occurs due to nonlinear processes and difference triad interactions between a) main frequencies of wave spectrum and infragravity frequencies and b) the frequencies of second harmonics and the new forming low-frequency peak in the main frequency range. According to laboratory experimental data the initial spectrum width determines the frequency step of downshifting and the number of cascades. The wider the initial wave spectrum, the less numbers of cascades are observed. It was shown that wave energy dissipation due to wave breaking is not a main reason for peak frequency downshifting and it has no direct influence on this process. The variability of the main wave period due to the cascade peak frequency downshifting can be important for engineering models because many calculations assume a constant wave period in the coastal zone. • During the transformation of waves over a mild slope bottom the peak spectrum frequency is not constant and the frequency downshifting is observed. • The main mechanism of peak frequency downshifting is the difference nonlinear triad interactions between them and infragravity frequencies. • The difference nonlinear interactions between the peak frequency and higher harmonics also contribute in frequency downshifting process. • Discrete multi-step frequency downshifting revealed or by other words - cascade downshifting. • The features of cascade downshifting depending on the wave's parameters are discussed. [ABSTRACT FROM AUTHOR]

In this paper, an active optimization method of a wave energy converter (WEC) array that focuses on the characteristics of the random sea condition is proposed. Physical model tests were conducted in both regular and irregular wave conditions. Three representative regular wave cases were determined from the target wave spectrum using the method. A rigid cylindrical heaving buoy model with different constant power take-off (PTO) damping forces and drafts was applied to find the optimal isolated WEC parameter under each regular wave condition. Three equal buoys with respective optimized parameters were arranged rectilinearly into a WEC array for irregular wave tests. The power output of arrays with different settings are compared, indicating the advantages of the different optimized array and the significance of unit order. To amplify the optimization effect, a supplementary numerical investigation of a 5-body WEC array was carried out using the boundary element method (BEM). The results demonstrate the method and show the influence of the number of different units. • An optimization method of WEC array that based on the target wave spectrum is proposed. • Model tests for isolated buoy and array were conducted in regular and irregular waves. • Supplementary simulations of a 5-body array were executed using BEM to validate the method. [ABSTRACT FROM AUTHOR]

Through assessment of wind-wave directional spectra, we provide a comprehensive explanation of the projected 21st Century changes in the global wind-wave climatology under a high green-house emissions scenario. Using a seven-member wave climate projection ensemble, we estimate wave climate changes by comparing present and projected climatologies. Clustering techniques are applied to define regional patterns of change with homogenous behavior. The underlying mechanisms behind the changes are also explored by exploiting the relationship between the wave generation area and the effective energy flux propagating toward a target location. A robust transition from positive to negative trends in Southern Ocean westerly swells is observed around 45°S. The increasing signal found in the southernmost swells propagates north beyond 30°N, contributing significantly to the projected changes in tropical regions such as the tropical southern Atlantic and tropical southeastern Pacific. Results highlight the great complexity of the Pacific Ocean due to the convergence of multiple wave systems with different geneses. In the northern basins, the combined effect of the ice melting and a poleward shift of the storm track drives an increase of the northernmost westerly swells. This is countered by a decreasing trend projected in the main wave systems propagating in the North Atlantic Ocean. A poleward shift of trade-induced waves due to the Hadley cell expansion can also be observed globally, causing a clear dipole change pattern in the tropical southern Atlantic and tropical Indian oceans. • The effect of climate change on wave climate is assessed based on directional spectra. • The climate change signals of the main swell systems are described. • Sixteen ocean regions with a similar pattern of change are found. [ABSTRACT FROM AUTHOR]

Highlights: [•] This study is the first to assimilate partitioned HF radar wave data. [•] Relative advantages of assimilating partitions over mean parameters are discussed. [•] Independent buoy data is used to validate the assimilation experiments. [•] Background error covariances are specifically designed for the coastal region. [•] Correlations are specified to reflect the complex coastline and bathymetry. [Copyright &y& Elsevier]

Abstract: Seasonal and annual variations in wave characteristics are studied based on measurements during 2009–2011 using wave rider buoy. Presence of swells generated by the south Indian Ocean cyclones are found over the south western Bay of Bengal during pre-monsoon season. Maximum significant wave height is measured 6m during Thane cyclone in December, 2011. Long period waves are observed mostly during the summer (SW) monsoon and are negligible in the winter (NE) monsoon period. Short period waves dominate (63%) the wave climate during the NE monsoon. Wave spectra during the SW monsoon are multi peaked whereas during the post monsoon season single peaked spectra are found. Single peaked spectra observed during SW monsoon of 2011 coincides with the presence of positive Indian Ocean Dipole. Waves during the pre monsoon and SW monsoon season are influenced by sea breeze. Analysis indicates that directional width is minimum for waves from the NE since they are wind waves and maximum for waves from SE since they are swells. Study indicates that wave climate of the south western Bay of Bengal is in contrast to that in eastern Arabian Sea during the SW monsoon. [Copyright &y& Elsevier]

Abstract: The importance of wave evolution and necessity for reliable prediction in coastal environments is widely recognized in many ocean engineering applications. Numerical wave models developed for limited area forecast can predict ocean waves fairly well upon imposing realistic boundary conditions from measurements. The forecast quality wherein depends on the number of measured data from various platforms specified along model boundary, which is undoubtedly very expensive. In a highly dynamic coastal environment, non-linear interaction from distant long period swells can essentially modulate the local wind-waves. This effect is more pronounced when local wind waves are opposed by distant swells reaching the coast. In addition, small scale convective phenomena like land and sea breeze create localized wind-sea having wide degree of directional behavior, thereby resulting in a more complex non-linear interaction process. For operational scenario, multi-scale modeling approach could be recommended as the best choice. The present work investigates influence of distant swells generated from Southern Ocean, and their role in modifying local wind-waves at coastal Kalpakkam located at south-east coast of India. Numerical experiments were performed to understand the influence of distant swells in modulating the local wind-waves which resulted in enhancing the wave energy by almost double off Kalpakkam coast. [Copyright &y& Elsevier]

Abstract: Two well-known third generation wave models, SWAN and WAVEWATCH-III, with different assumptions for high cut-off frequency were used to evaluate the interaction of low and high frequency components in wave spectral evolution. The results showed that WAM cycle 3 formulation overestimates the energy content in frequency band of 0.5–1Hz for Gulf of Mexico, which suggests using cut-off frequency close to 0.5Hz rather than 1Hz would improve the simulated bulk wave parameters. The evaluation of WAM cycle 4 and a newer nonlinear formulation implemented recently for white capping in SWAN also showed the better performance of wave model in oceanic scale with cut-off frequency close to 0.5Hz. However, WAM cycle 3 was more sensitive to cut-off frequency as well as to the exponent used in the expression for the frequency tail, than other formulations in SWAN. The use of f −5tail shape, rather than the f −4 form for the frequency spectrum beyond both cut-off frequencies used in this study, resulted in better agreement between simulated and observed wave parameters for most of the formulations implemented in these models. Also, it was demonstrated that WAM cycle 3 with dynamic cut-off frequency outperformed the corresponding configuration with static cut-off frequency. The suggested modifications for cut-off frequency and the expression for high frequency tail in SWAN substantially ameliorates the widely known underestimation of the average wave period associated with the WAM cycle 3 formulation, and reduces the amount of calculations needed for other formulations. [Copyright &y& Elsevier]

Abstract: If a swell propagating over a long distance is dominant, existing spectral wave models will produce unphysical oscillations in the model-predicted wave height field as a result of finite spectral resolution. This is called the Garden Sprinkler Effect (GSE), which is more apparent with high-accuracy propagation schemes. Here, an interpolation method to remove the GSE is developed. This method involves retrieving the higher-resolution wave spectra from lower-resolution wave spectra that are predicted not from a GSE-alleviating scheme but from a shape-preserving advection scheme, by considering the spatial distribution of spectra. Using this method both the removal of the GSE and the preservation of the spatial distribution of spectral values can be attained almost completely. [Copyright &y& Elsevier]

Abstract: Waves at 15m water depth in the northern Arabian Sea are measured during the summer monsoon for a period of 45 days and the characteristics are described. The significant wave height varied from 1.1 to 4.5m with an average value of 2.5m. 75% of the wave height at the measurement location is due to the swells arriving from the south-west and the remaining is due to the seas from south-west to north-west. Wave age of the measured data indicates that the waves in the nearshore waters of northern Arabian Sea during the summer monsoon are swells with young sea. [ABSTRACT FROM AUTHOR]

Abstract: The relationship between significant wave height and period, the variability of significant wave period, the spectral peak enhancement factor, and the directional spreading parameter of large deepwater waves around the Korean Peninsula have been investigated using various sources of wave measurement and hindcasting data. For very large waves comparable to design waves, it is recommended to use the average value of the empirical formulas proposed by Shore Protection Manual in 1977 and by Goda in 2003 for the relationship between significant wave height and period. The standard deviation of significant wave periods non-dimensionalized with respect to the mean value for a certain significant wave height varies between 0.04 and 0.21 with a typical value of 0.1 depending upon different regions and different ranges of significant wave heights. The probability density function of the peak enhancement factor is expressed as a lognormal distribution, with its mean value of 2.14, which is somewhat smaller than the value in the North Sea. For relatively large waves, the probability density function of the directional spreading parameter at peak frequency is also expressed as a lognormal distribution. [Copyright &y& Elsevier]

Abstract: The directional spreading of both the wavenumber and frequency spectra of finite-depth wind generated waves at the asymptotic depth limit are examined. The analysis uses the Wavelet Directional Method, removing the need to assume a form for the dispersion relationship. The paper shows that both the wavenumber and frequency forms are narrowest at the spectral peak and broaden at wavenumbers (frequencies) both above and below the peak. The directional spreading of the wavenumber spectrum is bi-modal above the spectral peak. In contrast, the frequency spectrum is uni-modal. This difference is shown to be the result of energy in the wind direction being displaced from the linear dispersion shell. A full parametric relationship for the directional spreading of the wavenumber spectrum is developed. The analysis clearly shows that typical dispersion relationships are questionable at high frequencies and that such effects can be significant. This result supports greater attention being focussed on the routine recording of wavenumber spectra, rather than frequency spectra. [Copyright &y& Elsevier]

Power spectral density and frequency-dependent directional spreading functions are developed for describing extreme sea state spectra in the Danish sector of the North Sea. The input to the spectral models are the significant wave height, the spectral peak period, the spectral second-moment period, and the circular root-mean-square spreading at the spectral peak frequency. The new spectral functions have been developed from measurements of large sea states, made with a Directional Waverider buoy, at two sites in the Danish sector of the North Sea. This paper describes the new directional spreading function; a companion paper describes the new power spectral density function. The new directional spreading function is based on a simple parameterisation of measured frequency-dependent spreading derived from the Directional Waverider buoys. It is defined in terms of the peak period and significant wave height, with different expressions depending on whether the dominant component in the spectrum is a wind-sea or a swell. A form for a combined wind-sea and swell sea state is also defined. The new spreading function is compared against measurements for the location and found to provide an accurate representation of the spreading estimated from the measurements. • Extreme sea state spectra in the North Sea. • Bimodal frequency-dependent directional spreading function. • Spreading function validation against North Sea measurements. [ABSTRACT FROM AUTHOR]

A power spectral density function that describes extreme sea states in the Danish sector of the North Sea is developed. The power spectrum is specified in terms of the parameters: significant wave height, spectral peak period, and spectral second-moment period. The power spectral density function is a modified Torsethaugen spectrum, involving an expression for the peak enhancement factor that is dependent on the inverse of the square root of wave steepness and a high-frequency tail that decays at a rate which is dependent on the significant wave height and the ratio of the peak and second-moment periods. The new function was developed from Directional Waverider data measured at two sites in the Danish sector of the North Sea and validated with data from other sites offshore Denmark, primarily recorded with Saab WaveRadars. A companion paper describes a new directional spreading function, which together with the power spectral density function, provides a description of the complete frequency-direction spectrum of extreme sea states in the Danish sector of the North Sea. • Modified Torsethaugen wave spectrum for extreme sea states in the North Sea. • Sea state steepness-dependent JONSWAP peak enhancement factor formulation. • Sea state severity-dependent high-frequency spectrum tail decay formulation. • Comprehensive validation against a large data set of wave measurements. [ABSTRACT FROM AUTHOR]

Abstract: Because traditional frequency domain analysis can hardly properly handle nonlinear effects induced from many sources, based on a nonlinear time domain dynamic analysis approach, the current paper presents a general calculation procedure and comparison for wave induced fatigue damage of a typical jacket structure under two hydrodynamic coefficient specification systems. Compared with the previous version of Norsok Standard N-003 [Norsok Standard. Actions and action effects, N-003. Oslo: Norwegian Technology Standards Institution; 1999], the inertia coefficients adopted by the latest Norsok Standard [Norsok Standard. Actions and action effects, N-003. Oslo: Norwegian Technology Standards Institution; 2007] released in 2007 are significantly decreased while the drag coefficients are slightly increased. The current paper shows that, for fixed offshore structures such as jackets, this change may result in a significantly increased calculated fatigue life. This may indicate that offshore jacket structures currently in service may be allowed a significant life time extension with regard to fatigue. In addition, the influence of the bottom support conditions of the jacket structure on the fatigue life is also investigated. The investigation indicates that, in cases where the pile-soil and conductor soil stiffness data are not available and the structure is high enough, for a rough estimation of the fatigue life on the upper part of a jacket, the jacket’s bottom support condition may be simply modelled as fully fixed. By comparing the fatigue life from dynamic analysis with that from static analysis without taking the inertia effects of the structure, equipment mass and other non-structural installations into account, it also shows the significance of the contribution from the structure’s dynamic response. The nonlinear dynamic analysis method presented in the current paper has been successfully applied in several industry projects for the life time extension of offshore installations subject to wave and wind loads. [Copyright &y& Elsevier]

Abstract: A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications. [Copyright &y& Elsevier]

Abstract: An overview is given of the WRT method for the computation of weakly resonant non-linear four-wave interactions in a gravity wave spectrum and its application in discrete spectral wave models. The WRT method is based on Webb''s [Webb, D.J., 1978. Nonlinear transfer between sea waves. Deep-Sea Res., 25, 279–298.] transformation of the Boltzmann integral and the numerical method introduced by Tracy and Resio [Tracy, B.A., Resio, D.T., 1982. Theory and calculation of the nonlinear energy transfer between sea waves in deep water. WIS technical report 11. US Army Engineer Waterways Experiment Station, Vicksburg, Mississippi, USA, 47 pp.]. It is shown that Webb''s method produces an attractive set of integrable equations. Moreover, the Jacobian term arising from the integration over the frequency delta-function in the Boltzmann integral has a singularity well outside the energy containing part of the wave spectrum. A description is given of methods for computing the integration space for a given discrete spectral grid, both for deep and finite depth water. Thereafter, the application of Webb''s method to discrete spectral wave models is described, followed by a summary of techniques reducing the computational workload while retaining sufficient accuracy. Finally, some methods are presented for the optimal inclusion of the WRT method in operational discrete spectral wave prediction models. [Copyright &y& Elsevier]

Abstract: Stochastic surface wind waves are considered as an intermediate physical phenomenon responsible for the state of upper layer of the water column. Mathematical formulation of the problem is done by using the wind wave spectral evolution model. It is shown that parameters of the air boundary layer are controlled by input evolution mechanism of wind waves, while dissipation mechanism is important for description of energy and momentum transfer into upper layer of the water column. Estimations of the wave energy dissipation rate are found utilizing the optimized numerical model for wind waves derived earlier. Such estimations can be used for better description of numerous important phenomena at the air–sea surface, including air bubbles entrainment, vertical mixing of oil slicks, near surface shear flow and many others. Three applications of the theory are presented. [Copyright &y& Elsevier]

Abstract: Bed load is a type of sand drift and accumulation on the sea-bed. Sand drift is a very important index to survey the erosion or deposition of coastal zone. The change of water depths indicates the change of bed load in shallow waters. The conventional method for measuring water depth uses the shipboard echo sounder, which is accurate for point-measurement, but is a time-consuming and labor-intensive task. For periodic survey of bathymetry as synoptic scale, the remote sensing method may be a viable alternative. Wave spectrum bathymetric (WSB) method takes advantages of remote sensing to obtain the bathymetry of shallow waters safely, economically and quickly. The WSB method is feasible to detect the change of water depths over coastal zones where water depths are less than about 12m. This remote sensing method is worthy to be well developed and efficiently applied to change detection of water depths and bed load in shallow waters. [Copyright &y& Elsevier]

The Hilbert Huang Transform method is applied to identify different components of the spectra of real sea waves. Field data collected at the Portuguese coast are used in this study. The ability of Empirical Mode Decomposition to extract the different oscillation modes, embedded in the sea surface elevation records, is demonstrated. The contribution of different Intrinsic Mode Functions to the wave data is examined. [Copyright &y& Elsevier]

The Huang–Hilbert transformation (HHT, composed of empirical mode decomposition and Hilbert transformation) can be applied to calculate the spectrum of nonlinear and nonstationary signals. The superior temporal and frequency resolutions of the HHT spectrum are illustrated by several examples in this article. The HHT analysis interprets wave nonlinearity in terms of frequency modulation instead of harmonic generation. The resulting spectrum contains much higher spectral energy at low frequency and sharper drop off at high frequency in comparison with the spectra derived from Fourier-based analysis methods (e.g. FFT and wavelet techniques). For wind generated waves, the spectral level of the Fourier spectrum is about two orders of magnitude smaller than that of the HHT spectrum at the first subharmonic of the peak frequency. The resulting average frequency as defined by the normalized first momentum of the spectrum is about 1.2 times higher in the Fourier-based spectra than that of the HHT spectrum. [Copyright &y& Elsevier]

The characteristics of surface wave fields in the eastern Arabian Sea under tropical cyclone Tauktae were investigated using buoy data. On May 16, 2021, the cyclone passed within 96 km of the buoy location, and a maximum wave height of 9.7 m with a significant wave height of 5.6 m was recorded by the buoy, moored at 23.5 m water depth off Goa. As the cyclone approached the buoy location, a shift in the frequency caused waves to turn into unimodal spectra with high wave energy and spectral peak parameter. Further, the evolution of cyclone-induced waves and their spatial variation have been investigated using the ERA5 reanalysis data. The results suggest that for distances of ∼400 km spatial extend from the cyclone's eyewall, the cyclone induced waves to have a high impact with significant wave height above 3 m for a cyclone sustained wind speed of around 100–120 knots. The dominance of wind-seas over swells and the directional shift are noticeable, specifically along the west coast of India during the tropical cyclone passage. • Wave field in Arabian Sea during cyclone Tauktae examined with buoy and ERA5 data. • Cyclone induced waves have high impact up to ∼400 km spatial extend. • Dominance of wind-seas over swells during tropical cyclone. • 4.5% of the records during 11–21 May 2021 contained freak waves. • Wave heights are higher on the east side of cyclone track than on the west. [ABSTRACT FROM AUTHOR]