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The Surface Waves Investigation and Monitoring instrument (SWIM) provides the directional wave spectrum within the wavelength range of 23–500 m, corresponding to a frequency range of 0.056–0.26 Hz in deep water. This frequency range is narrower than the 0.02–0.485 Hz frequency range of buoys used to validate the SWIM nadir Significant Wave Height (SWH). The modulation transfer function used in the current version of the SWIM data product normalizes the energy of the wave spectrum using the nadir SWH. A discrepancy in the cut-off frequency/wavelength ranges between the nadir and off-nadir beams can lead to an overestimation of off-nadir cut-off SWHs and, consequently, the spectral densities of SWIM wave spectra. This study investigates such errors in SWHs due to the wavelength cut-off effect using buoy data. Results show that this wavelength cut-off error of SWH is small in general thanks to the high-frequency extension of the resolved frequency range. The corresponding high-frequency cut-off errors are systematic errors amenable to statistical correction, and the low-frequency cut-off error can be significant under swell-dominated conditions. By leveraging the properties of these errors, we successfully corrected the high-frequency cut-off SWH error using an artificial neural network and mitigated the low-frequency cut-off SWH error with the help of a numerical wave hindcast. These corrections significantly reduced the error in the estimated cut-off SWH, improving the bias, root-mean-square error, and correlation coefficient from 0.086 m, 0.111 m, and 0.9976 to 0 m, 0.039 m, and 0.9994, respectively. [ABSTRACT FROM AUTHOR]

The sea surface is a complex superposition of various wave systems, thus, analysing their characteristics provides more meaningful and accurate information compared to conventional integrated wave parameter approaches. The concept of wave family—a population of wave systems within a specific region in spectral space—provides the foundation for investigating the long‐term climatology of wave systems. This study adopts a wave family approach to investigate the climatology of wave systems and their long‐term climate controllers at the location of a coastal buoy in the western North Atlantic Ocean. The frequency‐direction wave spectrum is constructed for a historical 20‐year period by applying the Maximum Entropy Method on directional buoy measurements acquired from the National Data Buoy Center station 44025, located in the New York Bight. The two‐dimensional wave spectrum is partitioned, using the watershed partitioning algorithm, and the occurrence distribution of spectral partitions is calculated to identify predominant wave families. Each of the four identified wave families carries unique characteristics based on spatial formation and duration of propagation prior to arrival at the study site. The study quantifies long‐term trends and variability in wave height of each wave family on a monthly, seasonal and annual level, and their relative importance to the bulk sea‐state climatology. The nexus between the bulk or wave family seasonal wave heights and the climate indices is quantified to identify the wave climate controllers in the study area. [ABSTRACT FROM AUTHOR]

The Surface Waves Investigation and Monitoring instrument (SWIM) provides the directional wave spectrum within the wavelength range of 23–500 m, corresponding to a frequency range of 0.056–0.26 Hz in deep water. This frequency range is narrower than the 0.02–0.485 Hz frequency range of buoys used to validate the SWIM nadir Significant Wave Height (SWH). The modulation transfer function used in the current version of the SWIM data product normalizes the energy of the wave spectrum using the nadir SWH. A discrepancy in the cut-off frequency/wavelength ranges between the nadir and off-nadir beams can lead to an overestimation of off-nadir cut-off SWHs and, consequently, the spectral densities of SWIM wave spectra. This study investigates such errors in SWHs due to the wavelength cut-off effect using buoy data. Results show that this wavelength cut-off error of SWH is small in general thanks to the high-frequency extension of the resolved frequency range. The corresponding high-frequency cut-off errors are systematic errors amenable to statistical correction, and the low-frequency cut-off error can be significant under swell-dominated conditions. By leveraging the properties of these errors, we successfully corrected the high-frequency cut-off SWH error using an artificial neural network and mitigated the low-frequency cut-off SWH error with the help of a numerical wave hindcast. These corrections significantly reduced the error in the estimated cut-off SWH, improving the bias, root-mean-square error, and correlation coefficient from 0.086 m, 0.111 m, and 0.9976 to 0 m, 0.039 m, and 0.9994, respectively.

Nonlinear energy transfer between wind waves in a gravity wave spectrum plays a pivotal role in the evolution of waves and was included as one of the source term (named nonlinear source term) in the third-generation (3G) wave models. The main objective of this paper is to compute the energy distribution due to nonlinear quadruplet wave–wave interactions for observed wave spectrum. This is achieved by utilizing cubic spline technique to fit and represent the theoretical as well as the measured spectra at given location. This technique is further incorporated into Gauss–Legendre Quadrature Method (GLQM) [1-2] for computing the nonlinear source term. Results were illustrated and validated for the theoretical as well as measured spectra (single- or multi-peaked spectrum) without compromising the accuracy of the method. The significance of this work includes an improvement in the computational efficiency of the method up to 65 % by employing optimal set of points of input spectrum (using a procedure discussed) without affecting the nonlinear results of the original one. GLQM (spline fitted spectra) is suitable for deep and finite water depths. Also, this work does not adhere to any assumptions for the tail factor, as the measured spectrum is directly fitted using splines. [ABSTRACT FROM AUTHOR]

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]

The theory and the performance of floating breakwaters have been widely researched and developed by researchers, both physical and numerical models. This study has tested the floating breakwater model with pontoon, saw, and saw-porous types. These models have been analyzed experimentally on irregular waves with JONSWAP spectra at various wave heights and periods and water depths of 35 cm, 40 cm, and 45 cm. This experiment has been carried out to know the change in the shape of the wave spectrum before and after passing the floating breakwater, indicating the occurrence of energy reduction (Δm0). This study has found out that the saw-type floating breakwater has an average reduction in wave spectrum energy of 25.75% greater than the pontoon type. The porous saw type has an average wave energy spectrum reduction of 1.78%, smaller than the pontoon type. The relationship between the transmission coefficient (Kt) and Δm0 on a floating breakwater is generally inversely related. The smaller Kt value indicates more effective attenuation than the floating breakwater, while at Δm0, the more significant value indicates more effective attenuation than the floating breakwater. [ABSTRACT FROM AUTHOR]

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Modeling a nonlinear ocean wave is one of the primary concerns in ocean engineering and naval architecture to perform an accurate numerical study of wave-structure interactions. The high-order spectral (HOS) method, which can simulate nonlinear waves accurately and efficiently, was investigated to see its capability for nonlinear wave generation. An open-source (distributed under the terms of GPLv3) project named "HOS-ocean" was used in the present study. A parametric study on the "HOS-ocean" was performed with three-hour simulations of long-crested ocean waves. The considered sea conditions ranged from sea state 3 to sea state 7. One hundred simulations with fixed computational parameters but different random seeds were conducted to obtain representative results. The influences of HOS computational parameters were investigated using spectral analysis and the distribution of wave crests. The probability distributions of the wave crest were compared with the Rayleigh (first-order), Forristall (second-order), and Huang (empirical formula) distributions. The results verified that the HOS method could simulate the nonlinearity of ocean waves. A set of HOS computational parameters was suggested for the long-crested irregular wave simulation in sea states 3 to 7.

Wave conditions around islands in the South China Sea (SCS) are of significant interest due to their importance for marine operations and coastal engineering. Understanding and accurately predicting wave characteristics in this region are crucial. In this study, the third-generation wave model WAVEWATCH III is employed to examine wave conditions around islands in the SCS. According to the water depth and significant wave height, the sea state around the island was classified into two categories: typhoon sea state and moderate sea state. Several popular wind input–dissipation source terms (ST2, ST4 and ST6) are used to assess the typhoon sea state and the moderate sea state separately. The results are validated by field wave data. ST4 and ST6 show good performance in significant wave height for moderate sea states, while ST2 is good at the mean wave period. For the typhoon sea state, ST2 gives the best results in significant wave height with larger correlation coefficients and a smaller RMSE. The above results provide valuable insights into the effects of different source terms on the accuracy of wave simulations for different sea states. The spatial distribution of the significant wave heights is also demonstrated with ST2, which may be useful for assessing the wave conditions of marine structures from the large scale of the SCS to the island scale of the Yongle Atoll. [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 present study highlights the wave–tide interactions in a tide-dominant coast Versova, along the west coast of India. Versova is a macro tidal area and is home to fisheries. Model simulations are carried out to investigate wave–tide interactions with and without incorporating water level (WL) variations in the model setup. The simulation results are compared with the observed data at Versova. Model comparison with wave observation shows that the simulated significant wave height (Hs) reproduced the observed wave heights with an accuracy of scatter index = 8% and correlation = 0.94 with the inclusion of WL variations. The incorporation of WL variations created the energy modulations in the low-frequency part of the wave spectra, raising the periodical modulations in wave height. This low-frequency wave energy modulation is absent in the without WL simulations, resulting in underestimation of energy density which causes underestimation of Hs by ~1 m. Hence this study strongly suggests that water level variations must be incorporated into the wave model to accurately represent wave modulations which are significant during monsoon and extreme events in the tide-dominant coastal areas. [ABSTRACT FROM AUTHOR]

The Pearl River Estuary is a typical estuary region in southern China, and the study of surface wave occurrence and characteristics is of great importance for shipping management, nearshore engineering, and monitoring shoreline changes and other human activities. Long-term and continuous observational data are critical for achieving a better understanding of waves. In this study, the wave measurements based on a high-precision wave gauge were analyzed and observation data over approximately two years at a sampling frequency of 2 Hz were obtained. The wave system in the Pearl River Estuary was found to deviate from the assumption of a stationary stochastic process similar to that in the open ocean, due to the effects of abnormal waves caused by human activities. Therefore, traditional distribution functions such as Rayleigh and Weibull were not suitable for accurately fitting the main wave parameters ( H s , T p , etc.), particularly in the tail. Consequently, abnormal wave signals were extracted from all wave sets, and through the comparison and analysis of the wave spectral features, it was determined that these abnormal waves are caused by the ship wakes. The spectral characterization of these waves was performed to determine the characteristics of different ship wake processes. Ship wakes in the Pearl River Estuary are an important part of the wave system, and their wave height is significantly larger than the normal wave. Based on the spectral characteristics of ship wakes, this study proposed some news characteristics of ship wakes in the main channel of the Pearl River Estuary. [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]

Spectral wave modelling is widely used to simulate large-scale wind–wave processes due to its low computation cost and relatively simpler formulation, in comparison to phase-resolving or hydrodynamic models. However, some applications require a time-domain representation of sea waves. This article proposes a methodology to transform the wave spectrum into a time series of water surface elevation for applications that require a time-domain representation of ocean waves. The proposed method uses a generated phase spectrum and the inverse Fourier transform to turn the wave spectrum into a time series of water surface elevation. The consistency of the methodology is then verified. The results show that it is capable of correctly transforming the wave spectrum, and the significant wave height of the resulting time series is within 5% of that of the input spectrum.

Ocean surface wind and wave information is important in a wide variety of areas, such as coastal disaster reduction, offshore structure design, and atmosphere‐ocean flux estimation. This study proposed a new method for ocean surface wind estimation from surface wave spectrum information measured by small global positioning system buoys. The concept of this method relies on the assumption that the high‐frequency part of the ocean‐wave spectrum is proportional to u∗f−4 ${u}_{\ast }{f}^{-4}$ where u∗ ${u}_{\ast }$ is the friction velocity and f $f$ is the frequency. The determination algorithm for the coefficient of f−4 ${f}^{-4}$ was optimized in this study. The wind direction was determined by the wave cross‐spectrum, assuming that the wind direction aligns the propagation direction of the high‐frequency part of the wave. The proposed wind estimation method was applied to bay and open ocean observations, and the performance of the proposed wind estimation method was similar between the bay and the open ocean. The proposed method improves the wind estimation especially in coastal areas and at high wind speeds in the open ocean compared with the previous method. The performance of the method of the previous study differs between the bay and open ocean due to their spectral shape differences. High‐quality wind and wave information can be obtained using the proposed method. If the mass deployment of small drifting buoys covered the global ocean, the information based on the proposed method could be considerably powerful, and could compensate for the weakness of satellite‐based wind and wave estimations. Plain Language Summary: Ocean observations are spatially sparse compared with on‐land observations because of the difficulty of observation platform development. However, ocean wind and wave information is important in a wide variety of areas, such as coastal disaster mitigation and offshore structure design. Recently, readily deployed small global positioning system (GPS)‐tracked buoys for wave observation have been developed that have the potential to fill gaps in observations through mass deployment. This study proposes a new ocean wind speed and direction estimation method using ocean wave information derived from a small GPS buoy. The performance of the proposed method was validated and compared with data of the observed wind. It was shown that the proposed method can be applied to any type of wave condition, whereas the applicability of the previous method was limited. The proposed method allows for high‐quality ocean wind and wave information to be simultaneously collected. Key Points: Ocean surface wind is estimated from ocean surface wave spectrum information measured by a small global positioning system buoyOcean surface wind is estimated from ocean surface waves for both bay and open ocean conditionsThe newly proposed method improves the accuracy of wind speed and direction estimations from ocean surface waves [ABSTRACT FROM AUTHOR]

Wave energy is a promising renewable resource for its reliability and power density, and many technological milestones have been achieved. Significant efforts are made to design and optimize Wave Energy Converters (WECs); however, analyses are often limited to simplified conditions. Among such restrictive assumptions, waves are frequently described utilizing monodirectional spectra, thus leading to approximate evaluations, also in terms of absorbed power. In real sea conditions, the waves are multidirectional, and the analysis as a 2D superposition of multiple wave components should be investigated. In particular, linear waves can be analyzed as a sum of sine waves characterized by different amplitudes, frequencies, phases and directions. The case study device analyzed in this paper is PeWEC (Pendulum Wave Energy Converter), a rotating mass device that converts energy based on pitch motion, moored through a spread catenary mooring system. The sea states investigated are those of the island of Cyprus. The spectrum is defined as the combination between the JONSWAP frequency spectrum and the cos-2s directional spectrum. To compute the sea elevation components the Deterministic Amplitude Scheme (DAS) method is used. The forcing acting on the device, the mooring loads and the device motions are examined and compared to quantify the error produced by the monodirectional approximations. The time domain solver OrcaFlex is employed to investigate the interaction of the waves with the moored hull. Compared with the multidirectional analysis, the monodirectional approximation generates an overestimation of the pitch by 5% and of the surge by 3%, highlighting the importance of taking spreading into account if the device is directional.

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]

Wave conditions around islands in the South China Sea (SCS) are of significant interest due to their importance for marine operations and coastal engineering. Understanding and accurately predicting wave characteristics in this region are crucial. In this study, the third-generation wave model WAVEWATCH III is employed to examine wave conditions around islands in the SCS. According to the water depth and significant wave height, the sea state around the island was classified into two categories: typhoon sea state and moderate sea state. Several popular wind input–dissipation source terms (ST2, ST4 and ST6) are used to assess the typhoon sea state and the moderate sea state separately. The results are validated by field wave data. ST4 and ST6 show good performance in significant wave height for moderate sea states, while ST2 is good at the mean wave period. For the typhoon sea state, ST2 gives the best results in significant wave height with larger correlation coefficients and a smaller RMSE. The above results provide valuable insights into the effects of different source terms on the accuracy of wave simulations for different sea states. The spatial distribution of the significant wave heights is also demonstrated with ST2, which may be useful for assessing the wave conditions of marine structures from the large scale of the SCS to the island scale of the Yongle Atoll.

Two approaches are considered for improving the profilometric data regarding machined surfaces: by digital or graphical analysis of the measurement results. [ABSTRACT FROM AUTHOR]

There is a wide consensus within the polar science, meteorology, and oceanography communities that more in situ observations of the ocean, atmosphere, and sea ice are required to further improve operational forecasting model skills. Traditionally, the volume of such measurements has been limited by the high cost of commercially available instruments. An increasingly attractive solution to this cost issue is to use instruments produced in-house from open-source hardware, firmware, and postprocessing building blocks. In the present work, we release the next iteration of our open-source drifter and wave-monitoring instrument, which follows these solution aspects. The new design is significantly less expensive (typically by a factor of 5 compared with our previous, already cost-effective instrument), much easier to build and assemble for people without specific microelectronics and programming competence, more easily extendable and customizable, and two orders of magnitude more power-efficient (to the point where solar panels are no longer needed even for long-term deployments). Improving performance and reducing noise levels and costs compared with our previous generation of instruments is possible in large part thanks to progress from the electronics component industry. As a result, we believe that this will allow scientists in geosciences to increase by an order of magnitude the amount of in situ data they can collect under a constant instrumentation budget. In the following, we offer (1) a detailed overview of our hardware and software solution, (2) in situ validation and benchmarking of our instrument, (3) a fully open-source release of both hardware and software blueprints. We hope that this work, and the associated open-source release, will be a milestone that will allow our scientific fields to transition towards open-source, community-driven instrumentation. We believe that this could have a considerable impact on many fields by making in situ instrumentation at least an order of magnitude less expensive and more customizable than it has been for the last 50 years, marking the start of a new paradigm in oceanography and polar science, where instrumentation is an inexpensive commodity and in situ data are easier and less expensive to collect. [ABSTRACT FROM AUTHOR]

The paper is devoted to further development of an accelerated method for simulation of the two-dimensional surface waves at infinite depth with the use of a two-dimensional model derived with simplifications of the three-dimensional equations for potential periodic deep-water waves. A 3D full wave model (FWM) is based on a numerical solution of a 3D Poisson equation written in the surface-fitted coordinates for a nonlinear component of the velocity potential. For sufficient vertical resolution used for the Poisson equation, the 3D model provides very high accuracy. The simplified model is based on the 2D Poisson equation written for a free surface. This exact equation contains both the first and second derivatives of the velocity potential, i.e., it is unclosed. The analysis of the accurate solutions for the 3D velocity potential obtained with the 3D model shows that those variables are linearly connected to each other. This property allows us to obtain a 2D equation for the first derivative of the velocity potential (i.e., vertical velocity on surface), which gives the closed 2D formulation for a 3D problem of two-dimensional waves. The previously developed scheme was not universal since the parameters of the closure scheme had to be adjusted to the specific setting. The current paper offers a new formulation of a closing scheme based on the integral parameters of wave field. The method of closing the equations, as well as the numerical parameters, were chosen on the basis of the multiple numerical experiments with the full nonlinear wave model (FWM) and selection of a suitable closing scheme. That is why the given model can be called Heuristic Wave Model (HWM). The connection between the first and second variables is not precise; hence, the method as a whole cannot be exact. However, the derived 2D model is able to reproduce different statistical characteristics of the 2D wave field with good accuracy. The main advantage of the model developed is its high performance exceeding that of 3D model by about two decimal orders. [ABSTRACT FROM AUTHOR]

Indonesian offshore and coastal areas are vulnerable to swells from Roaring Forties and cyclone disasters. However, the understanding of the characteristics and propagation mechanisms of local disastrous waves is insufficient, posing a threat to the construction, maintenance, and protection of coastal structures. This study establishes a multiple nested wave model based on the third-generation wave model WAVEWATCH III. This model includes sole forcing of Roaring Forties and combined forcing of Roaring Forties and cyclone Ernie to simulate the influence of disastrous waves under the Roaring Forties and tropical cyclones in the Indonesian offshore zone and coasts. The following results are obtained. The Indonesian offshore is prevailed by relatively stable southern to southwestern dominant swells and small wind waves under the impacts of the Roaring Forties without cyclone winds. Long propagating swells originated from the Roaring Forties dominate in nearshore coastal waters with deformed directions and strength because of the shoaling effect. [ABSTRACT FROM AUTHOR]

[Introduction] According to the measured wave data of one year in the deep water area of Eastern Guangdong, this paper mainly studies the basic characteristics of annual waves in the sea area. [Method] Firstly, the eigenvalues of wave height and period were counted month by month, get the basic distribution characteristics of the whole year; Then made statistics for the wave direction, obtain the seasonal characteristics of wave direction; Furthermore, the joint distribution of wave height and period and the relationship between wave height and period were explored; Finally, the characteristics of typical typhoon waves were studied. [Result] The results showed that: (1) The annual average Hs is 1.52 m, the Hmax is 15.97 m, the highest mean value of Hs in December, January and February, the Hmax is caused by Typhoon Mangkhut; (2) Affected by monsoon season and tropical cyclone, the normal wave direction and strong wave direction are ENE and SE respectively; (3) The main wave type in the whole year is wind wave component, the correlation between wave height and period is fitted; (4) According to the measured data of typhoon wave of Mangkhut, both wave height and period have a significant increase and decrease process. Through wave spectrum analysis during the typhoon, it experienced the evolution from double-peaked spectrum to single-peaked spectrum, it shows that the wave type during typhoon is mainly wind-surge mixed wave, the peak value reached 96.74 m2/Hz at 6:00 on September 16, peak frequency is 0.07 Hz. [Conclusion] The research results of this paper can provides technical reference for the design of related marine engineering.

We consider a method for calculating the natural wave spectra of round and rectangular shielded waveguides with arbitrary dielectric filling, which is a modification of the Galerkin method and based on the representation of the wave fields of the guiding structure in the form of an expansion in the eigenfunctions of the boundary value problem for uniformly filled waveguides. An algorithm for calculating the characteristics of symmetric waves of a circular waveguide with gradient dielectric filling and a rectangular shielded waveguide with arbitrary and angular dielectric filling has been compiled.

Spectral wave modelling is widely used to simulate large-scale wind--wave processes due to its low computation cost and relatively simpler formulation, in comparison to phase-resolving or hydrodynamic models. However, some applications require a time-domain representation of sea waves. This article proposes a methodology to transform the wave spectrum into a time series of water surface elevation for applications that require a time-domain representation of ocean waves. The proposed method uses a generated phase spectrum and the inverse Fourier transform to turn the wave spectrum into a time series of water surface elevation. The consistency of the methodology is then verified. The results show that it is capable of correctly transforming the wave spectrum, and the significant wave height of the resulting time series is within 5% of that of the input spectrum. [ABSTRACT FROM AUTHOR]

An approximate method of direct modeling of three-dimensional surface waves based on the complete equations of the potential motion of a liquid with a free surface in a curved non-stationary coordinate system is proposed. The separation of the velocity potential into nonlinear and linear components is used. The two-dimensional equations of the model are derived on the basis of an exact three-dimensional equation for the nonlinear component of the velocity potential written on the surface. The equation contains the first and second vertical derivatives of the potential on the surface; thus, the system of equations turns out to be unclosed. The analysis of the results of accurate three-dimensional modeling allowed us to establish that the first and second derivatives are linearly related to each other. This connection allows a closed two-dimensional (surface) formulation of the problem of three-dimensional waves. The first derivative of the potential (i.e., the vertical velocity on the surface) is calculated from the equation for the velocity potential on the surface using iterations. The relationship between the derivatives of the potential is not completely accurate, so in general, the method is approximate. Nevertheless, the model accurately reproduces the evolution of the wave field and its main statistical characteristics. The most obvious advantage of the model is its high efficiency: the speed of integration of a two-dimensional model is about two orders of magnitude higher than the speed of an equivalent three-dimensional model. The model is designed to quickly reproduce the dynamics of a two-dimensional wave field based on information about the wave spectrum. [ABSTRACT FROM AUTHOR]

Waves characteristics of the developing windfarm in the semi-enclosed Hangzhou Bay are distinctive due to the East Asian monsoon and frequent typhoons. In this paper, statistical analysis is performed to study the wave parameters in central Hangzhou Bay using 3-year-long wave datasets and the companion wind data. The monsoonal pattern has a significant impact on both annual and seasonal distribution of wave parameters. Compared with mild southeasterlies in summer, the NW-NE winds prevailing in winter tend to produce more extreme waves with large height and spectral energy, and especially in the south of the bay due to the extended fetch. Most waves are generated by local winds and have single-peak spectra. During extreme weather, most large waves had a peak frequency of around 0.2 Hz, i.e., the characteristic frequency. The wave generation processes observed during different extreme events had similar growth-decay tendencies and wave magnitudes. The occurrence probability of significant wave height and mean period can be well represented by both the Weibull and the Rayleigh distribution, and large waves ( H 1 / 3 > 1.0 m, T mean > 4 s) occur rarely (2.38% of the time). The correlations between key wave parameters are also examined. In general, this study highlights the typical wind wave patterns and provides practical guidance for future offshore development. [ABSTRACT FROM AUTHOR]

Spilled oil floats and travels across the water's surface under the influence of wind, currents, and wave action. Wave-induced Stokes drift is an important physical process that can affect surface water particles but that is currently absent from oil spill analyses. In this study, two methods are applied to determine the velocity of Stokes drift, the first calculates velocity from the wind-related formula based upon a one-dimensional frequency spectrum, while the second determines velocity directly from the wave model that was based on a two-dimensional spectrum. The experimental results of numerous models indicated that: (1) oil simulations that include the influence of Stokes drift are more accurate than that those do not; (2) for medium and long-term simulations longer than two days or more, Stokes drift is a significant factor that should not be ignored, and its magnitude can reach about 2% of the wind speed; (3) the velocity of Stokes drift is related to the wind but is not linear. Therefore, Stokes drift cannot simply be replaced or substituted by simply increasing the wind drift factor, which can cause errors in oil spill projections; (4) the Stokes drift velocity obtained from the two-dimensional wave spectrum makes the oil spill simulation more accurate. [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 vast majority of guiding structures are described [13] by non-self-adjoint electrodynamic operators, which are understood as the totality of the differential equation and the system of boundary conditions. In [15], the conditions for the non-self-adjointness of electrodynamic operators are formulated as applied to the method of separation of variables. The indicated operators can be put in accordance with [56] integral equations. The boundary problems for cylindrical guiding structures are assigned the Volterra integral equations, using asymptotic solutions of which an a priori determination of the spectra of solutions of boundary-value problems for two-layer open and shielded waveguides is carried out.

The paper describes the attempt to develop the accelerated method of simulation of 2-D surface waves with a use of 2-D model derived by simplifications of 3-D equations for potential periodic deep-water waves. The derivation is based on separation of velocity potential in surface-fitted coordinates into linear and non-linear components and analysis of exact Poisson equation for non-linear component of potential on a free surface. This equation contains both the first and second derivatives of velocity potential. The analysis of very accurate multiple solutions for velocity potential obtained with 3-D model shows that these variables are linearly connected to each other, what allows to obtain the 2-D equation for first derivative of potential (i.e., the vertical velocity on a surface), what gives the closed 2-D formulation for 3-D problem of 2-D waves. The connection between first and second variables is not precise; hence, the method as a whole cannot be exact. However, the 2-D model derived is able to reproduce different statistical characteristics of 2-D wave field with good accuracy. The most evident advantage of new model consists of absence of calculation of 3-D structure of velocity potential what increases a speed of calculations by about two orders. [ABSTRACT FROM AUTHOR]

The paper is devoted to further development of an accelerated method for simulation of the two-dimensional surface waves at infinite depth with the use of a two-dimensional model derived with simplifications of the three-dimensional equations for potential periodic deep-water waves. A 3D full wave model (FWM) is based on a numerical solution of a 3D Poisson equation written in the surface-fitted coordinates for a nonlinear component of the velocity potential. For sufficient vertical resolution used for the Poisson equation, the 3D model provides very high accuracy. The simplified model is based on the 2D Poisson equation written for a free surface. This exact equation contains both the first and second derivatives of the velocity potential, i.e., it is unclosed. The analysis of the accurate solutions for the 3D velocity potential obtained with the 3D model shows that those variables are linearly connected to each other. This property allows us to obtain a 2D equation for the first derivative of the velocity potential (i.e., vertical velocity on surface), which gives the closed 2D formulation for a 3D problem of two-dimensional waves. The previously developed scheme was not universal since the parameters of the closure scheme had to be adjusted to the specific setting. The current paper offers a new formulation of a closing scheme based on the integral parameters of wave field. The method of closing the equations, as well as the numerical parameters, were chosen on the basis of the multiple numerical experiments with the full nonlinear wave model (FWM) and selection of a suitable closing scheme. That is why the given model can be called Heuristic Wave Model (HWM). The connection between the first and second variables is not precise; hence, the method as a whole cannot be exact. However, the derived 2D model is able to reproduce different statistical characteristics of the 2D wave field with good accuracy. The main advantage of the model developed is its high performance exceeding that of 3D model by about two decimal orders.

Increasing problems due to supplying energy demand conveyed researchers to find a solution in renewable energy resources and consequently marine engineers drew attentions towards wave energy which has the merit of higher energy density than the other resources. Oscillating Water Column (OWC) is one of the most propitious devices for capturing wave energy. Researchers have studied the device under different wave height and period conditions and they investigated various geometric parameters such as front wall draft and the chamber length. However, the effects of wave spectrum type or shape has not been investigated deeply yet. Different wave spectra have been developed for different places around the world but the focus of this study is on the two well-known spectra called JONSWAP and Pierson-Moskowitz to see how the type of the spectrum can impact on inner chamber fluctuation, pressure variation and reflection response of an offshore OWC. To achieve this goal, a 1:15 scale model of an offshore OWC was constructed in National Iranian Marine Laboratory. The results show that inner chamber free surface spectrum is affected by the type of incident wave spectrum. In another word, energy content at peak frequency was approximately 50% higher when the incident wave spectrum is of JONSWAP type. However, energy corresponding to sloshing frequency and total energy content in the chamber were almost the same for both types of the spectra. Pressure spectra inside the chamber showed a similar trend as free surface elevation. Although there was a little difference in reflection response of an OWC influenced by the type of spectra, this discrepancy was more pronounced in high frequency waves.

Successful rescue action at sea is based on a. o. a correct choice of rescue means and their reliability. Operational characteristics of life-saving appliances determine their performance in a given water area. Therefore they affect duration time of rescue action and decide this way on survival time of shipwrecked persons. This paper presents impact of characteristics of circular inflatable life rafts on their dynamics in a given sea environment. Particular issues dealing with raft motion were analyzed and their solutions were then presented in the form of computer programs built into MATLAB environment. The programs operate on the open choice basis–the user is requested to introduce data of a raft to be investigated. The program clearly informs which units should be used for the data. The obtained results allow to limit survivours searching area and simultaneously form the basis for working out a model of searched object drift motion. In this work the use was made of the results obtained from the KBN research project No. 4T12C03827 in which an attempt was made to analyzing capsize probability of a raft at given sea states. The raft investigated in the project is also used as a reference raft in the computer programs developed in this work.

Container ships are becoming larger and larger in recent years, requiring more evident assurance of the structural safety. To achieve this, it is essential to grasp actual stress history experienced by the ship structures to facilitate efficient design and maintenance, and to use them for optimal operation of the ship. To perform accurate estimation of these stress histories, it is important to precisely estimate the sea state which the ship is actually encountering. In this study, the authors studied a new method to estimate directional wave spectra using measured ship responses and discussed the following three cases. The first one is the combination of two components, vertical bending stress and horizontal bending stress. The second one is the combination of three components, vertical bending stress, horizontal bending stress and double bottom bending stress. The last one is the combination of three components of ship motion (pitch, roll and heave). The estimated sea states are compared with the ocean wave hindcast database and radar data, and then, accuracy and selection of appropriate combination of the responses are discussed. [ABSTRACT FROM AUTHOR]