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Predicting extreme waves can foresee the hydrodynamic environment of marine engineering, critical for avoiding disaster risks. Till now, there are barely any available models that can rapidly and accurately predict the occurrence probability of freak waves in a given state. This paper develops a trained model based on the Back Propagation (BP) neural network, with wave parameters of unidirectional sea state fed into the model, such as significant wave height, wave period, spectral type, and the intermodal distance of the peak frequencies. A rapid and accurate model optimized for predicting the occurrence probability of freak waves in a unidirectional sea state, from unimodal to bimodal configuration, is achieved by iterating to reduce accumulation errors. Compared to the regression and least-squares boosting trees, the optimized model performs much better in accurately predicting the occurrence probability of freak waves. Irrespective of whether in unimodal or bimodal sea state, this optimized model is competitive in calculation accuracy compared to theoretical models such as Rayleigh prediction and MER prediction, improved by at least 41%. The established model based on the BP neural network can quickly predict the threshold of freak waves in a given sea state, guiding practical engineering applications. [ABSTRACT FROM AUTHOR]

The ubiquitous scattering of time-dependent waves in free-space exterior to bounded configurations is fundamental for numerous applications. Simulation of time-domain scattering in the unbounded exterior region, without artificial domain truncation, facilitates understanding of the wave propagation process in the entire exterior region. The space-time hyperbolic partial differential equation (PDE) for the unknown scalar scattered field in the free-space can be reformulated as a retarded surface integral equation (SIE) on the boundary of the configuration, using a retarded potential ansatz for the field. The unknown surface density in the ansatz satisfies the SIE, and hence the exterior scattering problem reduces to the SIE model. The weakly- or hyper-singular complexity of the SIE depends on the (Dirichlet/Neumann/Robin) condition on the boundary of the configuration in the PDE model. In this work, we develop a fully discrete high-order algorithm for efficient and stable simulation of the time-domain scattering weakly- and hyper-singular SIE models. Our algorithm is a hybrid of high-order convolution quadrature (CQ) discretization in time and spectrally accurate approximation in space. We demonstrate computational efficiency of the algorithm using a gallery of configurations with Dirichlet/Neumann/Robin boundary conditions, and compare with CQ-based benchmarks and recent results in the literature. [ABSTRACT FROM AUTHOR]

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.

Predicting extreme waves can foresee the hydrodynamic environment of marine engineering, critical for avoiding disaster risks. Till now, there are barely any available models that can rapidly and accurately predict the occurrence probability of freak waves in a given state. This paper develops a trained model based on the Back Propagation (BP) neural network, with wave parameters of unidirectional sea state fed into the model, such as significant wave height, wave period, spectral type, and the intermodal distance of the peak frequencies. A rapid and accurate model optimized for predicting the occurrence probability of freak waves in a unidirectional sea state, from unimodal to bimodal configuration, is achieved by iterating to reduce accumulation errors. Compared to the regression and least-squares boosting trees, the optimized model performs much better in accurately predicting the occurrence probability of freak waves. Irrespective of whether in unimodal or bimodal sea state, this optimized model is competitive in calculation accuracy compared to theoretical models such as Rayleigh prediction and MER prediction, improved by at least 41%. The established model based on the BP neural network can quickly predict the threshold of freak waves in a given sea state, guiding practical engineering applications.

The study of extreme ocean waves has gained considerable interest in recent years, due to their importance for offshore design and navigation safety, and several theoretical approaches have been developed for their statistical description. However, in the case of crossing seas, where two or more wave systems of different characteristics are present, a full understanding of the main physical mechanisms responsible for the occurrence of very high individual waves is still lacking. As a consequence, the prediction of extremes in such conditions currently relies on integrated parameters of the total sea state, such as the spectral wave steepness. In this study, to gain further insight into the role of the crossing wind sea and swell wave systems in producing extreme individual waves, we investigate realistic sea states during typhoon Kong-rey (2018) using an ensemble of numerical simulations obtained from a phase-resolving wave model based on the High-Order Spectral (HOS) method. The reliability of the numerical fields is assessed for the first time with stereo wave measurements of the sea surface elevation field collected from an offshore platform in the area of interest. We show that, in specific conditions, space-time extreme crest heights in crossing seas can be larger than in unimodal seas due to second-order bound wave interactions between the wind sea and the swell. To improve existing prediction capabilities, we propose a novel formulation for the wave steepness in crossing seas, which includes nonlinear effects up to the second order and accounts for the spectral parameters of the interacting wave systems.

The occurrence of rogue waves is closely related to the non-Gaussianity of sea states, and this non-Gaussianity can be estimated using corresponding two-dimensional wave spectra. This paper presents an approach to non-Gaussianity estimation based on a phase-resolving model called the high-order spectral method (HOSM). Based on numerous HOSM simulations, a set of precalculated non-Gaussianity indicators was established that could be applied to real sea states without any calibration of spectral shapes. With a newly developed extraction approach, the indicators for given two-dimensional wave spectra could then be conveniently extracted from the precalculated dataset. The feasibility of the newly developed approach in a real wave environment is verified. Using the estimation approach, phase-resolved non-Gaussianity can now be illustrated throughout the evolution of sea states of interest, not just at a few specific times; and the level of non-Gaussianity at any time in a duration can be identified according to the statistics (e.g., quantities) of the phase-resolved indicators, that are obtained throughout the duration concerned. [ABSTRACT FROM AUTHOR]

The accurate description of the complex genesis and evolution of ocean waves, as well as the associated kinematics and dynamics is indispensable for the design of offshore structures and the assessment of marine operations. In the majority of cases, the water-wave problem is reduced to potential flow theory on a somehow simplified level. However, the nonlinear terms in the surface boundary conditions and the fact that they must be fulfilled on the unknown water surface make the boundary value problem considerably complex. Hereby, the contrary objectives with respect to a very accurate representation of reality and numerical efficiency must be balanced wisely. This paper investigates the influence of characteristic sea state parameters on the accuracy of irregular wave field simulations of different complexity. For this purpose, the high-order spectral method was applied and the underlying Taylor series expansion was truncated at different orders so that numerical simulations of different complexity can be investigated. It is shown that, for specific characteristic sea state parameters, the boundary value problem can be significantly reduced while providing sufficient accuracy. [ABSTRACT FROM AUTHOR]

Accurate prediction of deep-water wave dynamics is essential for ocean engineering, meteorology, and maritime safety. Traditional physical models, though effective, face significant computational and time challenges with complex nonlinear dynamics. This study introduces an autoregressive prediction model using a one-dimensional adaptive Fourier Neural Operator-Residual Convolutional Neural Network (1D-FNO-ResNet) to enhance prediction accuracy. We developed a high-precision single-step prediction model capable of capturing wave characteristics such as height and fluid particle velocity. A fine-tuning training strategy based on multi-step prediction errors was proposed for autoregressive evolution. Performance comparisons between the ResNet and FNO-ResNet models were made under various fine-tuning steps. A correction model was also introduced to control error accumulation, improving autoregressive prediction steps. The model's generalization performance was validated with modulated and random wave trains under different conditions, optimizing predictive stability and accuracy. This approach demonstrates efficient 1D deep-water wave evolution prediction, offering a novel deep learning solution for wave dynamics prediction in ocean engineering, supporting wave energy conversion device design and optimization. • Introduced 1D-FNO-ResNet autoregressive prediction model for deep water wave evolution. • Proposed a fine-tuning training strategy based on multi-step prediction errors. • Validated the model's generalization performance under different carrier and sideband distance conditions. • Utilized the 1D-FNO-ResNet to predict modulated wave trains and random wave trains. [ABSTRACT FROM AUTHOR]

The phase-resolved wave prediction based on physical methods is difficult to ensure both accuracy and efficiency simultaneously. In recent years, Artificial Neural Network (ANN) has been successfully utilized for deterministic ocean wave prediction with efficiency and high precision. In this work, an ANN with the exponential linear unit (ELU) activation function is developed for deterministic wave prediction in unidirectional sea states. High-order Spectral method is used to generate the data on wave elevation. Instead of the traditional rectified linear unit (ReLU), we propose to use ELU as the activation function in the present ANN. Numerical results show that the ANN with the ELU activation function provides a more accurate prediction than the ANN with the ReLU activation function. Based on wave elevation measured at a fixed position, wave elevation prediction at another fixed position and wave elevation prediction in a fixed zone, are both studied by making use of the ANN with the ELU. Moreover, the factors including sea state and time length of wave elevation measured at a fixed position are considered to demonstrate the efficiency of the prediction results. • An enhanced artificial neural network model for deterministic wave prediction. • Point-to-point wave prediction and point-to-zone wave prediction. • Effects of sea-state levels, measuring time length on prediction performance. [ABSTRACT FROM AUTHOR]

The accurate description of the complex genesis and evolution of ocean waves, as well as the associated kinematics and dynamics is indispensable for the design of offshore structures and the assessment of marine operations. In the majority of cases, the water-wave problem is reduced to potential flow theory on a somehow simplified level. However, the nonlinear terms in the surface boundary conditions and the fact that they must be fulfilled on the unknown water surface make the boundary value problem considerably complex. Hereby, the contrary objectives with respect to a very accurate representation of reality and numerical efficiency must be balanced wisely. This paper investigates the influence of characteristic sea state parameters on the accuracy of irregular wave field simulations of different complexity. For this purpose, the high-order spectral method was applied and the underlying Taylor series expansion was truncated at different orders so that numerical simulations of different complexity can be investigated. It is shown that, for specific characteristic sea state parameters, the boundary value problem can be significantly reduced while providing sufficient accuracy.

Numerical simulations were performed to study the long-distance evolution of irregular waves in deep water. It was observed that some solitons, which are the theoretical solutions of the nonlinear Schrödinger equation, emerged spontaneously as irregular wave trains propagated in deep water. The solitons propagated approximately at a speed of the linear group velocity. All the solitons had a relatively large amplitude and one detected soliton’s height was two times larger than the significant wave height of the wave train, therefore satisfying the rogue wave definition. The numerical results showed that solitons can persist for a long distance, reaching about 65 times the peak wavelength. By analyzing the spatial variations of these solitons in both time and spectral domains, it is found that the third-and higher-order resonant interactions and dispersion effects played significant roles in the formation of solitons.

This paper examines the results in case of breaking wave groups reported in Sriram et al. (2015) against a wave breaking model called Tian–Barthelemy model (Seiffert and Ducrozet, 2017). In this paper, Tian–Barthelemy model is extended to incorporate (Schäffer, 1996) corrections to linear wave making signals for generating focused wave groups and implemented in an open source computer code for high order spectral (HOS) method based numerical wave tank (NWT) viz., HOS-NWT. The developed model is then studied in the context of wave breaking in dispersively focused intermediate water wave groups with particular focus on multiple wave breaking events. The adapted model performs well in conformity with experimental observations in Sriram et al. (2015). A range of kinematic thresholds are studied with this model to calibrate the right threshold for the model against the experiments. We find strong evidence of a non-breaking wave group in intermediate depths crossing the kinematic threshold of 0.85 (stated in Seiffert and Ducrozet (2017)), implying that this threshold is not universal for intermediate depths. It is also shown that the model does not interfere with the spurious free wave suppression. However, various dynamic and kinematical aspects of this study reveal that suppression of spurious free wave makes the short waves dominant in the lead up to breaking. Hence, the model detects numerous threshold exceedences implying plausibly more wave breaking instances. It is also shown that this model in general violates the spectral signature of breaking in a dispersively focused wave. • Tian–Barthelemy wave breaking model extended to second order wavemaking in HOS. • The model preserves suppression of spurious free waves with Schäffer correction. • Onset of wave breaking parameter studied in context of multiple wave breaking. • Extended model is calibrated for intermediate depth water wave groups. • The onset parameter shows considerable scatter in intermediate water depths. [ABSTRACT FROM AUTHOR]

As concluded from physical theory and laboratory experiment, it is widely accepted that nonlinearities of sea state play an important role in the formation of rogue waves; however, the sea states and corresponding nonlinearities of real-world rogue wave events remain poorly understood. Three rogue waves were recorded by a directional buoy located in the East China Sea during Typhoon Trami in August 2013. This study used the WAVEWATCH III model to simulate the sea state conditions pertaining to when and where those rogue waves were observed, based on which a comprehensive and full-scale analysis was performed. From the perspectives of wind and wave fields, wave system tracking, High-Order Spectral method simulation, and some characteristic sea state parameters, we concluded that the rogue waves occurred in sea states dominated by second-order nonlinearities. Moreover, third-order modulational instabilities were suppressed in these events because of the developed or fully developed sea state determined by the typhoon wave system. The method adopted in this study can provide comprehensive and full-scale analysis of rogue waves in the real world. The case studied in this paper is not considered unique, and rules could be found and confirmed in relation to other typhoon sea states through the application of our proposed method. [ABSTRACT FROM AUTHOR]

The water particle velocity of the wave peaks is closely related to the wave load borne by offshore structures. It is of great value for marine disaster prevention to study the water particle velocity of nonlinear extreme waves represented by Freak waves. This study applies the High-order Spectral Method (HOS) numerical model to analyze the characteristics and influencing factors of the water particle velocity of Freak wave peak with two different generation mechanisms under the initial condition of a weakly modulated Stokes wave train. Our results show that the water particle velocity of the wave peak increases linearly with wave height and initial wave steepness in the evolution stage of modulation instability. While in the later stage, the relationship becomes exponential. Under the condition of similar wave heights, the deformation degrees of Freak waves with different generation mechanisms are distinct, the deformation degree of modulation instability stage is smaller than that of the later stage. The water particle velocity of the wave peaks increases with the deformation degrees. Furthermore, the correlation between wave peak height and water particle velocity is a quadratic function. This provides a theoretical basis for further understanding of nonlinear waves and the prediction of marine disasters.

This paper discusses the potential of deterministic wave prediction as one basic module for decision support of offshore operations. Therefore, methods of different complexity—the linear wave solution, the non-linear Schrödinger equation (NLSE) of two different orders and the high-order spectral method (HOSM)—are presented in terms of applicability and limitations of use. For this purpose, irregular sea states with varying parameters are addressed by numerical simulations as well as model tests in the controlled environment of a seakeeping basin. The irregular sea state investigations focuses on JONSWAP spectra with varying wave steepness and enhancement factor. In addition, the influence of the propagation distance as well as the forecast horizon is discussed. For the evaluation of the accuracy of the prediction, the surface similarity parameter is used, allowing an exact, quantitative validation of the results. Based on the results, the pros and cons of the different deterministic wave prediction methods are discussed. In conclusion, this paper shows that the classical NLSE is not applicable for deterministic wave prediction of arbitrary irregular sea states compared to the linear solution. However, the application of the exact linear dispersion operator within the linear dispersive part of the NLSE increased the accuracy of the prediction for small wave steepness significantly. In addition, it is shown that non-linear deterministic wave prediction based on second-order NLSE as well as HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance, with the HOSM providing a high accuracy over a wider range of applications.

In this paper, we extend the non-breaking second-order corrected focused wave experimental results of Sriram et al. (2015) in a numerical wave tank based on HOS in the presence of wind. The wind is modelled using the modified Jeffrey's Sheltering Mechanism (Kharif et al., 2008). We take care to preserve the consistency of application of pressure terms in the hybrid Stokesian-HOS formulations when applying wind. We confirm the results of Kharif et al. (2008) i.e. the focusing points in presence of wind show an amplification of the measure wave heights although no discernible shifting of focusing location is observed. However, compared to Kharif et al. (2008), the sheltering mechanism is found to be very weak since it depends on exceedance of a threshold slope based on constant steepness or constant amplitude spectrum. The energy flux to local phase celerity ( B x ) both in absence and presence of the aforementioned wind model for the detection of onset of wave breaking (Barthelemy et al., 2015b; Saket et al., 2017b) are reported. Moreover, in the absence of wind, if B x is used as parameter the onset of wave breaking, then for intermediate water wave groups its threshold should be close to 0.9 (computations based on Kurnia and van Groesen (2014)). [ABSTRACT FROM AUTHOR]

We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech , submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642-658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation successfully for a wide range of breaking conditions. The model is also able to successfully calculate the transfer of energy between frequencies due to wave focusing and wave breaking. This study is limited to unidirectional waves but provides a valuable basis for future application of the wave-breaking model to a multidirectional wave field. By including parameters for removing energy due to wave-breaking into a nonlinear potential flow solver, the risk of developing numerical instabilities due to an overturning wave is decreased, thereby increasing the application range of the model, including calculating more extreme sea states. A computationally efficient and accurate model for the generation of a nonlinear random wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures, and in the study of open ocean wave generation and propagation in a realistic environment. [ABSTRACT FROM AUTHOR]

This study investigates a wave-breaking onset criteria to be implemented in the non-linear potential flow solver HOS-NWT. The model is a computationally efficient, open source code, which solves for the free surface in a numerical wave tank using the High-Order Spectral (HOS) method. The goal of this study is to determine the best method to identify the onset of random single and multiple breaking waves over a large domain at the exact time they occur. To identify breaking waves, a breaking onset criteria based on the ratio of local energy flux velocity to the local crest velocity, introduced by Barthelemy et al. (2017) is selected. The breaking parameter is uniquely applied in the numerical model in that calculations of the breaking onset criteria ratio are not made only at the location of the wave crest, but at every point in the domain and at every time step. This allows the model to calculate the onset of a breaking wave the moment it happens, and without knowing anything about the wave a priori . The application of the breaking criteria at every point in the domain and at every time step requires the phase velocity to be calculated instantaneously everywhere in the domain and at every time step. This is achieved by calculating the instantaneous phase velocity using the Hilbert transform and dispersion relation. A comparison between more traditional crest-tracking techniques shows the calculation of phase velocity using Hilbert transform at the location of the breaking wave crest provides a good approximation of crest velocity. The ability of the selected wave breaking criteria to predict single and multiple breaking events in two dimensions is validated by a series of large-scale experiments. Breaking waves are generated by energy focusing and modulational instability methods, with a wide range of primary frequencies. Steep irregular waves which lead to breaking waves, and irregular waves with an energy focusing wave superimposed are also generated. This set of waves provides a wide range of breaking-wave strengths, types and scales for validation of the model. A comparison of calculations made using HOS-NWT with experimental measurements show that the model is successful at predicting the occurrence of wave breaking, as well as accurately calculating breaking onset time and location. Although the current study is limited to a unidirectional wave field, the success of the wave-breaking model presented provides the basis for application of the model in a multidirectional wave field. By including wave breaking onset with the addition of an appropriate energy dissipation model into HOS-NWT, we can increase the application range of the model, as well as decrease the occurrence of numerical instabilities that are associated with breaking waves in a potential flow solver. An accurate description of the wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures and the general physics of ocean waves, for example. [ABSTRACT FROM AUTHOR]

Amplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and dispersion parameters of optical fibers are two orders of magnitude smaller than the hydrodynamic counterparts, and therefore, considered to better assure the slowly varying envelope approximation (SVEA) of the nonlinear Schrödinger equations (NLSE). While most optics experiment demonstrate an NLSE-like symmetric solutions, experimental studies by Dudley et al. (Optics Express, 2009, 17, 21497−21508) show an asymmetric spectral evolution in the dynamics of unstable electromagnetic waves with high intensities. Motivated by this result, the hydrodynamic Euler equation is numerically solved to study the long-term evolution of a water-wave modulated wave train in the optical regime, i.e., at small steepness and spectral bandwidth. As the initial steepness is increased, retaining the initial spectral bandwidth thereby increasing the Benjamin−Feir Index, the modulation localizes, and the asymmetric and broad spectrum appears. While the deviation of the evolution from the NLSE solution is a result of broadband dynamics of free wave interaction, the resulting asymmetry of the spectrum is a consequence of the violation of the SVEA.

This paper presents a general overview of the practical applicability of non-linear potential flow solvers for water wave propagation. Those numerical models are unable to describe explicitly the wave breaking phenomena, including free surface reconnexion, energy dissipation, etc. This reduces their range of application in real sea waves, which are in the most general context irregular and directional wave fields. This study covers the influence of discretization, water depth, directional spreading and spectral peakedness on the limitations in the use of such non-linear potential models. The approach at use relies on a highly non-linear model based on the High-Order Spectral method. [ABSTRACT FROM AUTHOR]

The scattering of nonlinear and non-breaking surface gravity waves propagating over a three-dimensional varying bathymetry is considered in this paper. In a recent study (Gouin et al., 2016) two numerical schemes for propagating waves over a variable bottom in an existing High-Order Spectral (HOS) model have been introduced. Both the computational effort and the accuracy of the model were shown to be conserved with the introduction of these new schemes. Moreover, they have been extensively validated in 2D, but the propagation of regular and irregular waves over 3D varying bottoms remains to be addressed with such spectral methods. In this paper, the three-dimensional formalism is introduced as well as the practical implementation of 3D configurations. Then the method is applied to a three-dimensional varying bathymetry consisting of an elliptical lens, as used in the Vincent and Briggs (1989) experiment. Incident waves passing across the lens are transformed and a strong convergence region is observed after the elliptical mound. The wave amplification depends on the incident wave. Numerical results for regular waves, unidirectional and directional irregular waves are analysed and compared with experimental data, demonstrating the efficiency and practical applicability of the present approach to treat the nonlinear propagation of various sea states over a varying bathymetry. [ABSTRACT FROM AUTHOR]

A series of laboratory experiments related to Kuznetsov-Ma breather solution have been performed in a seakeeping wave tank with different initial wave steepness and intermediate water depths. Analysis of the experimental results reveals that the maximum wave height in Kuznetsov-Ma breather solution is normally accompanied with a large crest amplitude, which can be largely reduced with the decreasing water depth due to the slower modulational process and the limited length of wave tank, regardless of the initial nonlinearity. The laboratory observations can be accurately simulated by the high-order spectral model (HOS) if the initial Benjamin-Feir index is not very large as a result of weak nonlinearity and/or decreased water depth. Numerical studies also indicate that in the evolutionary process the amplitude of carrier wave will decrease sharply and a peak frequency downshifting can be detected. If the evolutionary time scale is long enough, the spectrum will eventually evolve into a continuous one with the energy relocated in the lower wave frequency part. For Peregrine breather solution that is a particular case of Kuznetsov-Ma solution, it is found that in some cases a specific phase shift of the initial condition can lead to a longer distance for the wave group to travel to achieve the first maximum amplitude and a larger amplification factor than that predicted by the theoretical solution. [ABSTRACT FROM AUTHOR]

This study addresses the impact of nonlinear wave evolution on the resulting wave force values on a vertical wall. To this end, the problem of interaction between non-breaking water waves and a vertical wall over constant depth is investigated. The investigation is performed using a two-dimensional wave flume model which is based on the high-order spectral method. Wave generation is simulated at the flume entrance by means of the additional potential concept. This model enables to preserve full dispersivity. Therefore, the model enables to examine the role of nonlinear evolution in the formation of extreme wave force values on a vertical wall for a wide range of water depths. The results for the force exerted on a vertical wall are presented for shallow and deep water conditions. In shallow water, extreme wave force values occur due to the formation of an undular bore. In deep water, extreme wave forces have been obtained as a result of disintegration process of incident wave groups into envelope solitons. Multiple maximum force values have been detected for each of the highest run-up peaks. This phenomenon has been introduced in shallow water conditions and is extended here for deep water conditions. [ABSTRACT FROM AUTHOR]

In the present paper two numerical schemes for propagating waves over a variable bathymetry in an existing High-Order Spectral (HOS) model are introduced. The first scheme was first developed by Liu and Yue (1998), and the second one is an improved scheme which considers two independent orders of non-linearity: one for the bottom and one for the free-surface elevation. We investigate the numerical properties (accuracy, convergence rate, efficiency) of both schemes with respect to the numerical parameters on a simple configuration. To validate the proposed schemes, we first consider Bragg reflection from a sinusoidal bottom patch — as an example of a small bottom variation around a mean water depth. The second validation case focuses on a larger bottom variation with the study of the shoaling of linear waves. Finally, an application is performed to demonstrate the applicability of the proposed model to non-linear cases where the bottom variation is important. In this concern, the very well documented test case of a 2D underwater bar is studied in detail. Comparisons are provided with both experimental and numerical results. [ABSTRACT FROM AUTHOR]

This paper deals with the reproduction of unidirectional extreme events in a numerical wave basin. From a rogue wave measurement at a given location, experiments or numerical simulations are conducted with the same wave profiles using reproduction procedures. Although it is recognized that many different physical mechanisms may be at play in freak wave formation, reproduction procedures generally use frequency focusing to generate these high waves. This paper intends to assess the validity of this approach. In particular, it will focus on the relationship between an accurate reproduction of the free surface elevation and the accuracy of the corresponding wave kinematics inside the fluid domain. A highly nonlinear model is used to compute the occurrence of unidirectional freak waves in large periodic domain, which are reproduced in a 2-D numerical wave tank and compared. The study presents an advanced reproduction procedure that deals with rogue waves embedded in an irregular sea state. It shows that, using the appropriate reproduction procedure, it is possible to accurately reproduce free surface elevation as well as kinematics induced by this extreme event. [ABSTRACT FROM AUTHOR]

A fully nonlinear near-far fields coupling solver is proposed in this work. The target is to provide an efficient numerical tool for wave-current-structure interaction simulations. A GPU-accelerated high-order spectral (HOS) solver is developed to simulate the wave propagation and interaction with current in large far field and an incompressible flow solver with free surface capture scheme from the OpenFOAM library is adopted in the near field to solve the nonlinear wave loads and seakeeping response of the ship hull. The newly developed HOS solver is firstly validated by two wave-current interaction test cases, including a regular wave train travelling on collinear following and opposing current, and regular waves blocked by strong opposing current. Then, the near and far field coupling solver is applied to a simulation of the seakeeping response of a cruising ship hull in head wave condition. Lastly, The proposed method is applied to a more practical application, i.e. the self-propulsion of a hull in short crested spreading irregular waves. The numerical results are compared to the lab measurement data or numerical results, good agreements have been obtained. A fully nonlinear near-far field coupling method for marine-offshore applications is proposed in this work. The key features include: • The large far field is solved by the efficient high-order spectral (HOS) method. • The HOS code is further optimized by exploiting the GPU. • The wave-current interaction module is able to handle the wave-current-structure interaction simulations. • The near field domain is free to move within the far field domain, in order to support the ship towing or cruising simulations. • Finally yet importantly, the near and far field solvers are coupled in either runtime or file-based mode to suit different simulation needs. Four validation cases are presented: • Regular Waves on Collinear Current; • Regular Waves Blocking on Opposing Current • Seakeeping of Ship Hull in Head Waves • Ship hull self-propulsion in 3D spreading irregular waves The validation results suggest that the present method is superior to its precedent. [ABSTRACT FROM AUTHOR]

numerical approach was performed to predict the propagation and transformation of nonlinear water waves. A numerical wave flume was developed based on the non-periodic high-order spectral (HOS) method. The flume was applied to analyze the effect of wave steepness and wavelength on the propagation of nonlinear waves. The results show that for waves of low steepness, the wave profile and the wave energy spectrum are stable, and that the propagation can be predicted by the linear wave theory. For waves of moderate steepness and steep waves, the effects associated with the interactions between waves in a wave group become significant and a train of initially sinusoidal waves may drastically change its form within a short distance from its original position. [ABSTRACT FROM AUTHOR]

Numerical simulations were performed to study the long-distance evolution of irregular waves in deep water. It was observed that some solitons, which are the theoretical solutions of the nonlinear Schrödinger equation, emerged spontaneously as irregular wave trains propagated in deep water. The solitons propagated approximately at a speed of the linear group velocity. All the solitons had a relatively large amplitude and one detected soliton's height was two times larger than the significant wave height of the wave train, therefore satisfying the rogue wave definition. The numerical results showed that solitons can persist for a long distance, reaching about 65 times the peak wavelength. By analyzing the spatial variations of these solitons in both time and spectral domains, it is found that the third-and higher-order resonant interactions and dispersion effects played significant roles in the formation of solitons. [ABSTRACT FROM AUTHOR]

The water particle velocity of the wave peaks is closely related to the wave load borne by offshore structures. It is of great value for marine disaster prevention to study the water particle velocity of nonlinear extreme waves represented by Freak waves. This study applies the High-order Spectral Method (HOS) numerical model to analyze the characteristics and influencing factors of the water particle velocity of Freak wave peak with two different generation mechanisms under the initial condition of a weakly modulated Stokes wave train. Our results show that the water particle velocity of the wave peak increases linearly with wave height and initial wave steepness in the evolution stage of modulation instability. While in the later stage, the relationship becomes exponential. Under the condition of similar wave heights, the deformation degrees of Freak waves with different generation mechanisms are distinct, the deformation degree of modulation instability stage is smaller than that of the later stage. The water particle velocity of the wave peaks increases with the deformation degrees. Furthermore, the correlation between wave peak height and water particle velocity is a quadratic function. This provides a theoretical basis for further understanding of nonlinear waves and the prediction of marine disasters. [ABSTRACT FROM AUTHOR]

Optimizing the production of wave energy converters using Model Predictive Control (MPC) requires a real-time, deterministic prediction of the waves arriving at the device. This study presents a new method for deterministic sea wave prediction, using the horizontal velocity profile over the water column as a boundary condition for a dedicated nonlinear wave model. However, direct measurement of the horizontal velocity component over the whole vertical column is hardly achievable at sea. A method to reconstruct this profile from measurement devices currently at use, such as ADCPs, is thus presented and evaluated. The performance of the prediction method itself is then tested using synthetic numerical data. First, the reconstruction of the horizontal velocity profile as a boundary condition is evaluated. Then, the whole prediction procedure is assessed. In both these stages, the simulations are based on synthetic numerical data and the outcomes are compared with numerical reference solutions. The results show that the method is promising enough to justify further investigation through wave tank experiments. • A new method for deterministic sea wave prediction is proposed. • It is based on an efficient wave propagation model and uses velocity measurements. • The method is evaluated with realistic, synthetic numerical data as reference. • Prediction remains accurate even for high steepness wave cases. [ABSTRACT FROM AUTHOR]

In this work, numerical simulations of steady-state resonant wave system have been conducted by high-order spectral method (HOS) to study its evolution mechanism in deep water. Convergent high-order series solutions of steady-state resonant waves are first obtained by homotopy analysis method (HAM). Theoretical solutions together with disturbances of different orders of magnitude are then served as the initial solutions in HOS. It is found that as more accurate wave components are generated at the initial stage of the numerical simulation, the time that amplitude of the two largest wave components keeps unchanged increases. Steady-state resonant waves with time-independent spectra can be obtained if sufficient number of wave components are generated at the initial stage. At the end of simulation, additional new wave components that have not been considered at the initial stage appear in the spectra due to four-wave resonant interactions. For steady-state resonant waves with random disturbances, the numerical simulations confirm again the existence of steady-state resonant waves. Besides, energy transfer among different components is more remarkable for steady-state resonant waves with small disturbances before the wave breaking. • Evolution of steady-state resonant waves with disturbance has been considered numerically in a sufficiently long basin. • Steady-state resonant waves can be obtained numerically if accurate enough components are considered at the initial stage. • Energy transfers among different components due to the four-wave resonant interactions before the waves break. [ABSTRACT FROM AUTHOR]

• A high-order spectral method is developed for the simulation of capillary waves. • An order-consistent scheme is constructed to ensure complete energy conservation. • An integration factor scheme is applied to mitigate the time step restriction. • The method is benchmarked for accuracy, stability and long-term error evolution. • The capillary-wave thermal equilibrium spectrum is simulated for the first time. We develop the simulation capability for surface capillary waves based on the high-order spectral method, which solves the primitive Euler equations truncated to a prescribed nonlinearity order in wave steepness. The uniqueness in this development is to construct an order-consistent scheme to model the surface tension term, so that the simulation at arbitrary order forms a Hamiltonian system with complete energy conservation. The model equations are integrated in time using an integration factor scheme coupled with a 4th-order Runge-Kutta method (IF-RK4), where the linear terms are solved analytically (i.e., under machine precision in the numerical implementation), and nonlinear terms explicitly. The performance of the model is tested by simulation of a progressive Crapper wave and a broadband capillary wave spectrum. The property of order consistency as well as the enhanced accuracy and stability due to the IF-RK4 (compared to RK4 only) are clearly benchmarked. We finally show the effectiveness of the model to reproduce (for the first time) the thermal equilibrium spectrum of capillary waves when energy is injected at small scales of the wave field. [ABSTRACT FROM AUTHOR]