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This paper employs the third-generation simulating waves nearshore (SWAN) ocean wave model to estimate and analyze storm waves induced by Typhoon Bolaven, focusing on its impact along the west coast and Jeju Island of Korea. Utilizing reanalyzed meteorological data from the Japan Meteorological Agency meso scale model (JMA-MSM), the study simulated storm waves from Typhoon Bolaven, which maintained its intensity up to high latitudes as it approached the Korean Peninsula in 2012. Validation of the SWAN model against observed wave data demonstrated a strong correlation, particularly in regions where wind speeds exceeded 20 m/s and wave heights surpassed 5 m. Results indicate significant storm wave heights across Jeju Island and Korea's west and southwest seas, with coastal grid points near islands recording storm wave heights exceeding 90% of the 50-year return period design wave heights. Notably, specific grid points near islands in the northern West Sea and southwest Jeju Island estimated storm wave heights at 90.22% and 91.48% of the design values, respectively. The paper highlights the increased uncertainty and vulnerability in coastal disaster predictions due to event-driven typhoons and emphasizes the need for enhanced accuracy and speed in typhoon wave predictions amid the escalating climate crisis.

Coral reefs protect coastlines from inundation and flooding and serve over 200 million people globally. Wave transformation has previously been studied on coral reef flats with limited focus on forereef zones where wave transformation is greatest during high‐energy conditions. This study investigates the role of forereef spur and groove (SaG) morphology in wave energy dissipation and transmission at the reef crest. Using XBeach on LiDAR‐derived bathymetry from One Tree Island in the southern Great Barrier Reef, we reproduced dissipation rates comparable to SaG field studies. We examined how wave energy dissipation differs between realistic bathymetry and those with SaG features removed, demonstrating an up to 40% decrease in dissipation when SaG features are absent. We then investigated changes to wave energy dissipation and wave transmission at the reef crest based on IPCC AR5 emission scenarios (RCP2.6 and RCP8.5) and a total disaster scenario (TD) for the year 2100. For RCP2.6, an increase in wave heights of 0.8 m and an increase in water level of 0.3 m resulted in a two‐fold increase in dissipation rates. For RCP8.5 and TD, with no increase in incident wave height, dissipation rates were 29% and 395% lower than RCP2.6. This resulted in increased wave transmission at the reef crest by 1.8 and 2.7 m for the RCP8.5‐ and TD based models, respectively, when compared to the RCP2.6‐based model. The results from our novel modeling approach of using long‐shore varying accurate bathymetry on forereefs show increased wave energy dissipation rates with implications for reducing coastal flooding and island inundation on reef‐lined coasts. Plain Language Summary: Coral reefs protect coastlines from floods and waves, benefiting over 200 million people globally. We studied how waves change over coral reefs, focusing on the forereef zone where wave transformation is most significant during high‐energy conditions. The shape of the forereef, specifically the long comb‐like grooves that cut through coral reefs, known as spur and grooves (SaG), modify wave energy transformation. Utilizing digital representation of waves over accurate reef shapes (known at bathymetry), we simulated wave dissipation rates comparable to real‐world SaG studies. By comparing high resolution, accurate bathymetry to smoothed bathymetry with SaG removed, we demonstrate a 40% decrease in wave energy dissipation. Next, we investigated how wave energy dissipation changes in different forereef environments. We considered low and high emission scenarios (RCP2.6 and RCP8.5) from the IPCC AR5 report and a total disaster scenario (TD) for the year 2100, considering changes to wave power, and water‐level. We found that models based on high‐emission scenarios (RCP 8.5) had decreased dissipation rates, resulting in more water passing the reef crest. Our study highlights the benefits of using accurate reef shapes in simulating wave energy dissipation on coral reefs. Accurate bathymetry can incorporate features such as SaG of different shapes, which increase wave dissipation. Key Points: Accurate bathymetry (<1 m) in forereef wave energy dissipation models can include features such as spurs and grooves (SaG)SaG increases forereef wave energy dissipation when compared to similar bathymetry without SaGForereef dissipation shifts from bed friction to wave breaking in modeled environmental conditions based on future climate projections [ABSTRACT FROM AUTHOR]

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In this study, we aim to examine the influence of water entry velocity of a single and two tandem projectile(s) on the supercavitation flow and projectile loading under wave conditions using numerical simulation. The volume of fluid model, renormalization group (RNG) κ-ε turbulence model, and Schnerr-Sauer cavitation model are adopted to simulate the multiphase, turbulent, and cavitation flow, respectively. The projectile movement is considered using overlapping grids and a six-degree-of-freedom model. The results show that as the projectile velocity increases, both the dimensionless maximum radius and length of the cavity, as well as the yaw angle, also increase with the rising water entry velocity. For the two tandem projectiles, the cavity pattern on the second projectile varies as the projectile velocity changes. With a lower projectile velocity, the second projectile cannot directly access the front cavity, and there may be situations wherein the part of the second projectile is not enveloped by cavity. As the projectile velocity increases, the second one can directly enter the cavity of the first projectile without forming a separate cavity around itself. In all of the examined cases, the peak pressure on the first projectile is approximately an order of magnitude higher than that on the second one. Furthermore, with increasing projectile velocity, the pressure peak ratio between the first and second projectiles increases. [ABSTRACT FROM AUTHOR]

In this study, we aim to examine the influence of water entry velocity of a single and two tandem projectile(s) on the supercavitation flow and projectile loading under wave conditions using numerical simulation. The volume of fluid model, renormalization group (RNG) κ-ε turbulence model, and Schnerr–Sauer cavitation model are adopted to simulate the multiphase, turbulent, and cavitation flow, respectively. The projectile movement is considered using overlapping grids and a six-degree-of-freedom model. The results show that as the projectile velocity increases, both the dimensionless maximum radius and length of the cavity, as well as the yaw angle, also increase with the rising water entry velocity. For the two tandem projectiles, the cavity pattern on the second projectile varies as the projectile velocity changes. With a lower projectile velocity, the second projectile cannot directly access the front cavity, and there may be situations wherein the part of the second projectile is not enveloped by cavity. As the projectile velocity increases, the second one can directly enter the cavity of the first projectile without forming a separate cavity around itself. In all of the examined cases, the peak pressure on the first projectile is approximately an order of magnitude higher than that on the second one. Furthermore, with increasing projectile velocity, the pressure peak ratio between the first and second projectiles increases.

Coastal erosion is a normal process of nature. However, the rate of coastal erosion, and the frequency and intensity of coastal flooding events, are now on the rise around the world due to the changing climate. Current responses to coastal erosion are primarily determined by site-specific factors, such as coastal elevation, coastal slope, coastal features, and historical coastline change rate, without a systematic understanding of the coastal-change processes in the context of climate change, including spatiotemporal changes in sea level, regional changes in wave climate, and sea ice coverage. In the absence of a clear understanding of the coastal-change processes, most of the current coastal responses have been built upon a risky assumption (i.e., the present-day coastal change will persist) and are not resilient to future climate change. Here, we conduct a literature review to summarize the latest scientific understanding of the coastal-change processes under climate change and the potential research gaps towards the prediction of future coastal erosion. Our review suggests that a coupled coastal simulation system with a nearshore wave model (e.g., SWAN, MIKE21, etc.) can play a critical role in both the short-term and long-term coastal risk assessment and protective measure development. [ABSTRACT FROM AUTHOR]

The wave period is a wave parameter that is significantly influenced by factors such as wind speed and bottom topography. Previous research on wave period parameterization has primarily focused on wind-dominated sea areas and may not be applicable to certain regions, such as the equatorial calm or coastal areas dominated by swell waves. To address this limitation, this paper utilizes the third-generation wave numerical model SWAN to perform wave numerical simulations for a portion of the Northwest Pacific Ocean. The simulation incorporates observational data from nearshore stations, buoys, and satellite altimeters for error analysis. To develop a new wave parameterization scheme (WS-23), we employ extensive NDBC buoy data and incorporate the exponential rate and wave age characteristics that were previously established by predecessors. Our scheme introduces a judgement mechanism to distinguish between wind waves, swell waves, and mixed waves. The resulting ocean wave factor enhances the mean wave period values calculated using the model and other parameterization schemes. The experimental results demonstrate that our new parameterization scheme effectively improves the abnormal peak of the fitting data. Comparing the output values of the mean wave period element output of the SWAN model with our new parameterization scheme, we observe a reduction in the mean values of E a , E c , and R M S E by 0.231, 1.94%, and 0.162, respectively, while increasing the average r by 0.05. [ABSTRACT FROM AUTHOR]

This study estimates wave energy for the Moroccan Atlantic coast using SWAN, a third-generation wave model, covering a period of 30 years, from 1991 to 2020. The model is forced by the wind from the ERA-5 reanalysis dataset and uses boundary conditions generated by the WAVEWATCH III model. The significant wave height and period are used to obtain wave energy, which is analyzed at a regional scale. The mean wave energy density within the domain is assessed to be about 20 kW/m. Five specific locations are evaluated along the coast in order to determine the most energetic ones. The most energetic area of the Moroccan Atlantic coast is located at the center, between the cities of Agadir and Essaouira. Finally, the performance of six different wave energy converters is assessed through their power matrix for each of the five locations. [ABSTRACT FROM AUTHOR]

A numerical stochastic wave model was developed in this study based on the quasi-coherent theoretical framework proposed by Smit and Janssen in 2013. Subsequently, the model was implemented to reproduce and cross-confirm the findings of the quasi-coherent (QC) spectral wave modeling approach. The process included simulations of experiments conducted by Vincent and Briggs regarding waves propagating over a submerged shoal. The results of the simulations agree with the expected results of the QC theory, which can account for the spatial coherence of inhomogeneous wave fields and capture wave interference more accurately than conventional spectral wave models. In addition, extra insight was gained about aspects of the overall numerical implementation of the QC theory. [ABSTRACT FROM AUTHOR]

How should we write a history of mathematics education? To answer this question, we have to consider why we should want to study this history. For many mathematics teachers – as in the case of the author- it is simply necessary to explore your own profession to improve your teaching. But in the end it would be useful if some people took a more scientific approach and looked for mainlines in the development, tendencies, patterns or even explanations. To do so we have to consider the initial local history of mathematics education in a wider context both in a nationwide and in an international comparison as well in comparison with other school subjects and the history of pedagogy in general. In this paper we explore the possibility to make a wave model of the development of mathematics education in Denmark in the past two centuries, illustrating periodic changes between times with emphasis on understanding and times with emphasis on drill and skills. To which extent can a model like this be explained?

Authors researched the wave model of text representation which is one of the implementations of distributive semantics. This model takes into account not only the frequency of words occurrence in the text, but also their mutual location. The purpose of the study: to increase the accuracy of the analysis of the tonality of short texts based on the wave model. The method of determining the relationship between the text and the term is based on the calculation of the probability amplitude of the text and term proximity using a wave model. The term with the highest probability amplitude is considered to correspond most closely to the meaning of the text. The wave model allowed taking into account the fact that well-known methods define antonyms as semantically close lexical units. For the experimental study of this technique, a solution to the problem of sentiment analysis was chosen, exactly, finding the correspondence of user reviews about the product to the classes “positive” and “negative”. As a result, the accuracy of the text tonality defining was obtained up to 76.4 %, which exceeds the accuracy of the classical approach as well as the well-known methods of sentiment analysis for the Russian language. In addition, authors detected significant influence on classification accuracy of such model parameters as the choice of a basic distributive semantic model, the choice of a control point for calculating wave numbers, taking into account the influence of antonyms. The presented model has shown high accuracy in identifying the relationships of the text with concepts that are not explicitly present in it and can be successfully used as a mathematical basis for solving problems of sentiment analysis. In addition, the results obtained indicate the potential use of the wave model in other areas that require the classification of texts by indirect signs, for example, to determine the elements of author psychological portrait.

The influence of small-scale processes at the ocean–atmosphere boundary layer such as spray and foam on the surface waves prediction is studied. Estimates of the effect of including the exact number of specific fragmentation "parachute" type in the spray on the resulting drag coefficient is shown. For the estimates, the numerical simulations within WAVEWATCH III wave model are performed. The parameterizations of wind input are tested within WAVEWATCH III wave model: default ST4 and ST6 parameterizations and the ST1 and ST6 parameterizations used together with the implemented drag coefficient parameterization. The proposed parameterization takes into account the presence of foam and spay. The obtained results are compared with the NDBC buoys data. The importance of small-scale processes for waves at hurricane winds prediction and the prospects for their inclusion in modern numerical wave models is shown. [ABSTRACT FROM AUTHOR]

In response to record-breaking flooding on Lake Champlain in 2011, the International Joint Commission launched a 5-year study to explore solutions to flooding in the binational Lake Champlain-Richelieu River (LCRR) basin. As a component of the study, a real-time flood forecasting modeling system was developed to provide short-term (5 days) water level and wave forecast guidance, intended to enhance flood preparedness by providing advanced warning of flooding to residents and other stakeholders within the basin. The system consists of a hydrodynamic model built on the Finite Volume Community Ocean Model (FVCOM) with one-way coupling to a WAVEWATCH III wave model. The National Water Model stream network was expanded to include the entire LCRR domain and is used to inform river inflows into the system. Water level output from the hydrodynamic model shows strong agreement with gauge observations at annual and short-term time scales, with an increasing negative bias at longer forecast horizons. Modeled significant wave heights compared well with observations from a wave buoy deployed as part of the study and also have a negative bias in the latter portions of the forecast. The scale of the errors in modeled water levels and wave heights is consistent with an underestimation of river inflow and wind speed inputs, respectively, based on validation of this model forcing against available observations. The development and validation of the LCRR modeling system serve as a precursor for the first operational real-time 3D hydrodynamic-wave forecast system for Lake Champlain. [ABSTRACT FROM AUTHOR]

Quantum computing algorithms are actively developed and applied in the field of natural language processing. The authors of the paper proposed a new quantum-like method for classifying short texts. The basis of the method is the representation of the text as an ensemble of elementary particles. The value of the detection probability amplitude of a given ensemble at the selected points in space is chosen as a classification criterion. In this case, the space is understood as a vector space described using the distributive-semantic model of the language. The authors suggested one of the possible ways of interpreting the parameters of the wave function that describes the behavior of an elementary particle, as well as an algorithm for calculating the probability amplitude taking into account these parameters. For the experimental research of the described method, authors performed the classification of Internet communities by topics. For the analysis, the names and the “information” section of communities were used. In total, 100 groups of the social network “VKontakte” belonging to five various topics were taken. The proposed model showed rather high classification accuracy (91 % in general on the data set and from 75 % to 95 % within individual classes). The proposed model is supposed to be used to classify user comments about goods, services and events, as well as to determine some properties of the psychological portraits of users of online communities.

The modelling of coastal Directional Wave Spectra (DWSs) often requires downscaling techniques integrating DWSs from open ocean boundaries. Dynamic downscaling methods reliant on numerical wave models are often computationally expensive. In coastal areas, wave dynamics are strongly influenced by the bathymetry and coastal morphology, implying that once the DWSs at the open ocean boundary are known, the DWSs at various locations along the coast are almost determined. This property can be utilized for statistical downscaling of coastal DWSs. This study presents a deep learning approach to compute coastal DWSs from open ocean DWSs. The performance of the proposed downscaling model was evaluated using both numerical wave model data and buoy data in the Southern California Bight. The results show that the deep learning approach can effectively and efficiently downscale coastal DWSs without relying on any predefined spectral shapes, thereby showing potential for coastal spectral wave climate studies. • A data-driven method is presented to downscale directional spectra of coastal waves. • The model uses open ocean directional spectra as inputs and coastal ones as outputs. • The low computational cost makes it suited for coastal spectral wave climate studies. [ABSTRACT FROM AUTHOR]

This study estimates wave energy for the Moroccan Atlantic coast using SWAN, a third-generation wave model, covering a period of 30 years, from 1991 to 2020. The model is forced by the wind from the ERA-5 reanalysis dataset and uses boundary conditions generated by the WAVEWATCH III model. The significant wave height and period are used to obtain wave energy, which is analyzed at a regional scale. The mean wave energy density within the domain is assessed to be about 20 kW/m. Five specific locations are evaluated along the coast in order to determine the most energetic ones. The most energetic area of the Moroccan Atlantic coast is located at the center, between the cities of Agadir and Essaouira. Finally, the performance of six different wave energy converters is assessed through their power matrix for each of the five locations.

The wave period is a wave parameter that is significantly influenced by factors such as wind speed and bottom topography. Previous research on wave period parameterization has primarily focused on wind-dominated sea areas and may not be applicable to certain regions, such as the equatorial calm or coastal areas dominated by swell waves. To address this limitation, this paper utilizes the third-generation wave numerical model SWAN to perform wave numerical simulations for a portion of the Northwest Pacific Ocean. The simulation incorporates observational data from nearshore stations, buoys, and satellite altimeters for error analysis. To develop a new wave parameterization scheme (WS-23), we employ extensive NDBC buoy data and incorporate the exponential rate and wave age characteristics that were previously established by predecessors. Our scheme introduces a judgement mechanism to distinguish between wind waves, swell waves, and mixed waves. The resulting ocean wave factor enhances the mean wave period values calculated using the model and other parameterization schemes. The experimental results demonstrate that our new parameterization scheme effectively improves the abnormal peak of the fitting data. Comparing the output values of the mean wave period element output of the SWAN model with our new parameterization scheme, we observe a reduction in the mean values of Ea, Ec, and RMSE by 0.231, 1.94%, and 0.162, respectively, while increasing the average r by 0.05.

A numerical stochastic wave model was developed in this study based on the quasi-coherent theoretical framework proposed by Smit and Janssen in 2013. Subsequently, the model was implemented to reproduce and cross-confirm the findings of the quasi-coherent (QC) spectral wave modeling approach. The process included simulations of experiments conducted by Vincent and Briggs regarding waves propagating over a submerged shoal. The results of the simulations agree with the expected results of the QC theory, which can account for the spatial coherence of inhomogeneous wave fields and capture wave interference more accurately than conventional spectral wave models. In addition, extra insight was gained about aspects of the overall numerical implementation of the QC theory.

A longitudinal impact against a rigid barrier is considered for a system of homogeneous and stepped rods, one of which has a defect in the form of an initial curvature. Using the method of initial parameters and the wave model of a longitudinal impact, the initial bending moment and the angle of rotation of the section of a curved rod interacting with a rigid barrier are calculated, and the longitudinal dynamic force and the time of its impact are calculated. The maximum amplitude of the transverse oscillations of the curved rod of the system under consideration and its average impulse are calculated, which are the most important characteristics of the vibrational effect of the resulting oscillatory process. The universality of the application of the proposed technique to the calculation of rod systems with an arbitrary initial state is noted. In the article, the average value of the vibration impulse was modeled for rod systems with different ratios of the lengths of homogeneous sections with the same ratio of their thickness and the same pre-shock velocity. As shown by the simulation results, there is no clear pattern between the magnitude of the average impulse and any ratio of the lengths of the sections of the considered rod system, which is of considerable scientific interest. This is due to the chaotic nature of the interference pattern of longitudinal deformation waves during their propagation and transformation along homogeneous sections and when passing through their boundaries. As a result, for each specific configuration of the rod system, in the process of impact interaction, longitudinal waves of different magnitude and duration are formed, on which the average value of the simulated impulse depends. [ABSTRACT FROM AUTHOR]

The influence of small-scale processes at the ocean–atmosphere boundary layer such as spray and foam on the surface waves prediction is studied. Estimates of the effect of including the exact number of specific fragmentation “parachute” type in the spray on the resulting drag coefficient is shown. For the estimates, the numerical simulations within WAVEWATCH III wave model are performed. The parameterizations of wind input are tested within WAVEWATCH III wave model: default ST4 and ST6 parameterizations and the ST1 and ST6 parameterizations used together with the implemented drag coefficient parameterization. The proposed parameterization takes into account the presence of foam and spay. The obtained results are compared with the NDBC buoys data. The importance of small-scale processes for waves at hurricane winds prediction and the prospects for their inclusion in modern numerical wave models is shown.

In this paper, a calibration algorithm for forecasting the significant wave height (SWH) in nearshore areas is proposed, based on artificial neural networks. The algorithm has two features: first, it is based on SOM−BRFnn (self−organizing map–radial basis function neural network) to better reflect the clustering characteristics of the input parameters regarding wind and wave. In addition, the high-frequency variation part and the low-frequency variation part of SWH are separated by a threshold of 24 h to better describe the diurnal variation of SWH under the influence of tidal current. The algorithm is applied to the nearshore region of Nan-ao Island in the northeastern South China Sea. The results show that the algorithm can effectively correct the modeling results of nearshore SWH. Compared with the original outputs of the ERA5 model, the correlation coefficient is increased from 0.472 to 0.774, the root mean square error is reduced from 0.252 m to 0.103 m, and the mean relative error is reduced from 41% to 17.6%, respectively. Further analysis indicates that the frequency division is crucial in realizing the correction of the high-frequency variation of SWH. The results have reference significance for the application of wave numerical models in coastal areas. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithm for generating a spherical multiple-cell (SMC) grid. The algorithm adopts a recursive loop structure and provides two refinement methods: (1) an arbitrary area refinement method and (2) a nearshore refinement method. Numerical experiments are carried out, and the results show that compared with the existing grid generation algorithm, this algorithm is more flexible and operable. [ABSTRACT FROM AUTHOR]

Intense atmospheric disturbances, which impact directly on the sea surface causing a significant increase in wave height and sometimes strong storm surges, have become increasingly frequent in recent years in the Mediterranean Sea, producing extreme concern in highly populated coastal areas, such as the Gulf of Naples (Western Mediterranean Sea, Central Tyrrhenian Sea). In this work, fifty-six months of wave parameters retrieved by an HF radar network are integrated with numerical outputs to analyze the seasonality of extreme events in the study area and to investigate the performance of HF radars while increasing their distances from the coast. The model employed is the MWM (Mediterranean Wind-Wave Model), providing a wind-wave dataset based on numerical models (the hindcast approach) and implemented in the study area with a 0.03° spatial resolution. The integration and comparison with the MWM dataset, carried out using wave parameters and spectral information, allowed us to analyze the availability and accuracy of HF sampling during the investigated period. The statistical comparisons highlight agreement between the model and the HF radars during episodes of sea storms. The results confirm the potential of HF radar systems as long-term monitoring observation platforms, and allow us to give further indications on the seasonality of sea storms under different meteorological conditions and on their energy content in semi-enclosed coastal areas, such as the Gulf of Naples. [ABSTRACT FROM AUTHOR]

The aim of the work - to research changes in the dynamic stiffness of pile foundations from the distance between the piles during vertical vibrations using experimental data from literature sources and solving wave models describing the vertical vibrations of a thin plate with round cuts. Methods. To verify the reliability of solutions of wave models describing changes in dynamic stiffness during vertical vibrations of pile foundations, it is used data obtained in experiments to determine the eigenfrequencies of 33 groups of friction piles with different distances between them. Also the data obtained from forced vertical oscillations of 22 groups of friction piles connected by pile-caps at different loads and distances between piles was used. In the processing of available amplitude-frequency curves for determining the dynamic stiffness the inverse problem is solved using the theory of nonlinear oscillations. The correspondence between the measured and predicted data is evaluated, when describing the behavior of the pile-ground system. Results. It is established that the relations that take into account the mutual influence of piles in the group, obtained in the framework of wave models solutions and used for calculating dynamic stiffness in vertical vibrations of pile foundations, allow us to obtain satisfactory results in accuracy. The deviation of the calculation results from the experimental data does not exceed 15%.

Analysis of the applicability of wave model solution to evaluate the variation of the dynamic stiffness in the pile foundation versus the distance between piles at the vertical vibrations; both experimental data from references and our own measurements in field are involved. To justify the reliability of the solutions of the wave models used to determine the dynamic stiffness values of the pile foundations at the vertical vibrations, we use the data obtained experimentally for the determination of natural frequencies in the cap-bound groups. The data obtained for the natural frequencies of 3×3 floating piles with different distances between them are considered. In addition, the data found at the forced vertical vibrations of the cap-bound groups of 2×2 piles under different loads and at different distances between the piles are involved. Processing of available amplitude-frequency curves involves the solution of the inverse problem with the theory of nonlinear vibrations to determine the parameters of the “pile group – soil” system, namely the effective mass, stiffness, and damping. The correlation between the measured and predicted data is evaluated by using the data obtained at the description of the pile groups in soil behavior. It has been found that the relations obtained at the solution of wave models and used to calculate the dynamic stiffness at the vertical vibrations of pile foundations consider the mutual effect of the piles in the group and permit satisfactory accuracy of the results. The maximum discrepancy between the results and experimental data is 15 %.

The paper aims to obtain exact analytical solution of nonlinear nonhomogeneous space-time fractional order partial differential equations in Gas dynamics model, Advection model, Wave model and Klein-Gordon model by improved Adomian decomposition method coupled with fractional Taylor expansion series. The solution of these equations are in series form may have rapid convergence to a closed-form solution. The effectiveness and sharpness of this method is shown by obtaining the exact solution of these equations with suitable initial conditions(ICs). With the help of this method, it is possible to investigate nature of solutions when we vary order of the fractional derivative. Behaviour of the solution of these equations are represented by graphs using MATHEMATICA software. [ABSTRACT FROM AUTHOR]

Aims of research. Studies to determine the effect of the distance between the piles in group with vertical oscillations of pile foundations on the value of dynamic stiffness are carried out and the results obtained in full-scale tests, within the wave model and according to SP 26.13330.2012 are compared. Methods. The eigenfrequency changes of the foundation of nine piles with a diameter ( d ) with a high pile cap are calculated depending on the distances between the piles - 2 d , 3 d and 5 d . The obtained results are compared with the data obtained after a series of pulse dynamic loads performed under semi-natural conditions on foundation models. The values of the transverse wave velocities were determined directly at the test site. Results. It is found that the reduction of the distance between the piles in the bush leads to a decrease in the natural vibration frequencies of pile foundations. Reducing the distance between piles from 5 to 2 diameters of piles leads to reduce the frequency of vertical vibrations of pile foundations by 1. times. It is shown the advantage of the results of calculations in the frame-work of the wave model in comparison with the method of SP 26.13330.2012. Also shown their high coincidence with the values obtained in the course of experiments, which allows to accurately determine the amplitude-frequency characteristics of the foundations. The results determined according to SP 26.13330.2012 have significantly lower values of natural frequencies and do not fully reflect the change in the distance between the piles. The maximum discrepancy with the experimental data is 2.7 times for the vertical oscillations of the pile foundation.

In this study, the wave conditions in the Arabian Sea induced by tropical cyclone Kyarr (2019) have been simulated by employing the 3rd generation wave model MIKE 21 SW. The model was run from 24 October to 1 November 2019, a total of 8 days. The MIKE 21 SW model was forced by reanalyzed ERA5 wind data from the European Centre for Medium-Range Weather Forecasts (ECMWF). The results are compared with buoy data from the Indian National Centre for Ocean Information Services (INCOIS), which is located at 67.44° E, 18.50° N. In addition, the satellite altimeter data (CryoSat-2, SARAL and Jason-3 satellite altimeter data) was utilized for validation. Three wave parameters are considered for the validation: the significant wave height; the peak wave period; and the mean wave direction. The validation results showed that the significant wave height, the peak wave period, and the mean wave direction could be reasonably predicted by the model with reanalysis wind data as input. The maximum significant wave height reached to 10.7 m (with an associated peak wave period of 12.5 s) on 28 October 2019 at 23:00:00 in the middle of the Arabian Sea. For coastal areas, the significant wave height along the Iran and Pakistan (north Arabian Sea) coasts increased to a range of 1.4–2.8 m when tropical cyclone Kyarr moved northward. This wave height along with elevated sea level may cause severe coastal erosion and nearshore inland flooding. Impacts of cyclones on coastal zones critical facilities and infrastructure can be reduced by timely and suitable action before the event, so coastal managers should understand the effect of cyclones and their destructive consequences. The validated model developed in this study may be utilized as input data of evaluating the risk to life and infrastructure in this area.

Ocean surface waves tend to be attenuated by interaction with sea ice. In this study, six sea ice models in the third-generation wave model WAVEWATCH III® (WW3) were used to estimate wave fields over the Sea of Okhotsk (SO). The significant wave height (Hs) and mean wave period (Tm) derived from the models were evaluated with open ocean and ice-covered conditions, using SO coastal area buoy observations. The models were validated for a period of 3 years, 2008–2010. Additionally, the impact of sea ice on wave fields was demonstrated by model experiments with and without sea ice. In the open ocean condition, the root-mean square error (RMSE) and correlation coefficient for hourly Hs are 0.3 m and 0.92, and for hourly Tm 0.97 s and 0.8. In contrast, for the ice-covered condition, the averaged RMSE and correlation coefficient from all models are 0.44 m (1.6 s) and 0.8 (0.6) for Hs (Tm), respectively. Therefore, except for the bias, the accuracy of model results for the ice-covered condition is lower than for the open water condition. However, there is a significant difference between the six sea ice models. For Hs, the empirical formula whereby attenuation depends on the frequency relatively agrees with the buoy observation. For Tm, the empirical formula that is a function of Hs is better than those of other simulations. In addition, the simulations with sea ice drastically improved the wave field bias in coastal areas compared to the simulations without sea ice. Moreover, sea ice changed the monthly Hs (Tm) by more than 1 m (3 s) in the northwestern part of the SO, which has a high ice concentration.

In a perspective of impoverishment of the fossil fuel and preservation of the natural environment, the sea wave energy is being increasingly regarded as alternative and promising resource. A key aspect to take in consideration for the deployment of Wave Energy Converters is the local characterization of the wave climate. In this contribute, a methodology for the calculation and validation of a site-specific Test Reference Year (TRY), from a multiyear dataset such ERA-Interim and ERA-5, to be used in wave energy conversion studies is proposed. Comparison of the two datasets with observed data gives ERA-5 as the best dataset. The methodology applied for the TRY generation has proven to be very effective, with the daily sum of H s and T m being the most effective indices for the TRY generation and in general H s about twice more important than T m. Once obtained, the TRY is applied in order to force an implementation of the Simulating WAves Nearshore (SWAN) model in an area of the central Adriatic Sea to characterize the area. • Generation and Validation of a Test Reference Year for wave energy studies from a multiyear dataset. • Comparison of the wave field of ERA-Interim and ERA-5. • Propagation of the Test Reference Year toward the coast with the wave driver SWAN. [ABSTRACT FROM AUTHOR]

The aim of work. To determine the dynamic stiffness at considering vertical and horizontal vibrations of embedded foundations on a conventional and pile base, the possibility of using formulas obtained within the framework of the wave model and SP 26.13330.2012 is considered. Solution technique. Depending on deepening changes, the natural-vibration frequencies of the system oscillations are calculated. The obtained results are compared with the experimental data obtained in a series of impulse dynamic loads performed on foundation models in semi-real conditions. The values of the transverse wave velocities were determined directly on the experimental range from the results of measurements. Results. It is determined that deepening leads to an increase in the frequencies of natural oscillations, both pile foundations and shallow foundations. Full penetration helps to increase natural-vibration frequencies. For horizontal oscillations more than 1.6 times, for vertical oscillations up to 1.4 times. The influence of deepening on shallow foundations is more significant. The advantage of the calculations results and their high agreement with the values obtained during the experiments in the framework of the wave model in comparison with the method from SP 26.13330.2012 is shown. It allows to reliably determining the amplitude-frequency characteristics of the foundations. The results determined in accordance with SP 26.13330.2012, have significantly lower values of the natural-vibration frequencies and do not fully take into account the influence of deepening. The maximum difference with the experimental data for vertical vibrations for a foundation on piles and for a shallow foundation is 33 %. In case of horizontal fluctuations, the maximum differences are from 20 % for a shallow foundation and up to 27 % for a pile foundation.

The solution of dynamic problems on longitudinal impact of a system of homogeneous rods in a nonlinear formulation presents, as is known, significant mathematical difficulties. The existing approaches have a rather limited application, mainly due to the significant approximation of the solution of the problem. In addition, such approaches involve an extensive mathematical apparatus, which makes it difficult to use them in engineering calculations. In practice, it is of considerable interest to model the amplitude of transverse vibrations of a system of homogeneous rods having different lengths and thicknesses under longitudinal impact. The solution of the problem posed is complicated by the chaotic nature of the interference pattern of longitudinal waves when they pass through the impact cross-section of the rods, which is the boundary of the homogeneous sections for the rod system under consideration. In this regard, deformations and longitudinal forces along the length of the rods change rapidly over time. This study deals with the mathematical modeling of the amplitude of transverse vibrations of physically and geometrically homogeneous rods, one of which is stationary and interacts with an absolutely rigid obstacle, and the another, moving with a pre-impact speed, collides with the first rod. In the first case, the collision is considered by taking into account the eccentricity in the impact cross-section of the rods. In the second case, the initial curvature of one of the rods is taken into account. Modeling is carried out using the method of initial parameters and a wave model of longitudinal impact. The results of modeling the maximum deflection are obtained for various values of the initial curvature and eccentricity depending on the pre-impact velocity. The analysis of the results revealed the so-called "zone of maximum deflections", namely, the interval of change in the pre-impact velocity, at which the maximum amplitude of transverse vibrations of homogeneous rods is observed. Additionally, a number of regularities are noted that have been identified when comparing the results for both cases. The relevance of using this calculation method in solving dynamic problems arising in the design of engineering structures with dynamically loaded rod systems is pointed out. [ABSTRACT FROM AUTHOR]

In this paper, a calibration algorithm for forecasting the significant wave height (SWH) in nearshore areas is proposed, based on artificial neural networks. The algorithm has two features: first, it is based on SOM−BRFnn (self−organizing map–radial basis function neural network) to better reflect the clustering characteristics of the input parameters regarding wind and wave. In addition, the high-frequency variation part and the low-frequency variation part of SWH are separated by a threshold of 24 h to better describe the diurnal variation of SWH under the influence of tidal current. The algorithm is applied to the nearshore region of Nan-ao Island in the northeastern South China Sea. The results show that the algorithm can effectively correct the modeling results of nearshore SWH. Compared with the original outputs of the ERA5 model, the correlation coefficient is increased from 0.472 to 0.774, the root mean square error is reduced from 0.252 m to 0.103 m, and the mean relative error is reduced from 41% to 17.6%, respectively. Further analysis indicates that the frequency division is crucial in realizing the correction of the high-frequency variation of SWH. The results have reference significance for the application of wave numerical models in coastal areas.

Intense atmospheric disturbances, which impact directly on the sea surface causing a significant increase in wave height and sometimes strong storm surges, have become increasingly frequent in recent years in the Mediterranean Sea, producing extreme concern in highly populated coastal areas, such as the Gulf of Naples (Western Mediterranean Sea, Central Tyrrhenian Sea). In this work, fifty-six months of wave parameters retrieved by an HF radar network are integrated with numerical outputs to analyze the seasonality of extreme events in the study area and to investigate the performance of HF radars while increasing their distances from the coast. The model employed is the MWM (Mediterranean Wind-Wave Model), providing a wind-wave dataset based on numerical models (the hindcast approach) and implemented in the study area with a 0.03° spatial resolution. The integration and comparison with the MWM dataset, carried out using wave parameters and spectral information, allowed us to analyze the availability and accuracy of HF sampling during the investigated period. The statistical comparisons highlight agreement between the model and the HF radars during episodes of sea storms. The results confirm the potential of HF radar systems as long-term monitoring observation platforms, and allow us to give further indications on the seasonality of sea storms under different meteorological conditions and on their energy content in semi-enclosed coastal areas, such as the Gulf of Naples.