Generation Of Extreme Waves Research Articles

Extreme dynamics of wave groups on jet currents

Rogue waves are known to be much more common on jet currents. A possible explanation was put forward in Shrira and Slunyaev [“Nonlinear dynamics of trapped waves on jet currents and rogue waves,” Phys. Rev. E 89, 041002(R) (2014)] for the waves trapped on current robust long-lived envelope solitary waves localized in both horizontal directions become possible, such wave patterns cannot exist in the absence of the current. In this work, we investigate interactions between envelope solitons of essentially nonlinear trapped waves by means of the direct numerical simulation of the Euler equations. The solitary waves remain localized in both horizontal directions for hundreds of wave periods. We also demonstrate a high efficiency of the developed analytic nonlinear mode theory for description of the long-lived solitary patterns up to remarkably steep waves. We show robustness of the solitons in the course of interactions and the possibility of extreme wave generation as a result of solitons' collisions. Their collisions are shown to be nearly elastic. These robust solitary waves obtained from the Euler equations without weak nonlinearity assumptions are viewed as a plausible model of rogue waves on jet currents.

Experimental investigation on the hydrodynamic characteristics of extreme wave groups over unidirectional sloping bathymetry

A series of physical experiments were conducted to investigate the characteristics of extreme wave groups over a shoal. An improved method for detecting wave groups based on instantaneous energy was verified, which can identify wave groups reasonably and effectively. As a result, it was found that a linear relationship exists between the wave group energy and group time length on the logarithmic coordinate diagram, and the same tendency holds for extreme wave groups. Moreover, a steeper slope of the linear curve was observed for larger significant wave heights, indicating that the significant wave height significantly affects the wave heights and energy levels of extreme wave groups. The research also found that the average energy of the identified extreme wave group is approximately twice the average energy of the recorded data, thereby supporting the hypothesis that the wave group plays an important role in the generation of extreme waves.

Numerical study of the effect of current on waves in the Agulhas Current Retroflection

The generation of extreme waves in the Agulhas Current Retroflection as the result of strong wave-current interaction is examined. High-resolution simulations with two third-generation wave models are performed considering ocean surface currents for two years and six months. The study is made with high-resolution SWAN (Simulating Waves Nearshore) nested grids which use the boundary conditions from the outer WAM (Wave Advanced Modeling) grid. Surface current velocities of mesoscale eddies influence surface wave properties and wave energy. The effects of the current speed on the wave spectral shapes are explored inside the eddies and in their vicinity. The numerical results show that in the interior of the eddies the extreme wave parameters can reach high values as well as the probability of occurrence of abnormal waves.

Distribution of energy in propagation for ocean extreme wave generation in hydrodynamics laboratory

BACKGROUND AND OBJECTIVES: The hydrodynamic uncertainty of the ocean is the reason for testing marine structures as an initial consideration. This uncertainty has an impact on the natural structure of the topography as well as marine habitats. In the hydrodynamics laboratory, ships and offshore structures are tested using mathematical models as input to the wave marker. For large wavenumbers, Benjamin Bona Mahony's equation has a stable direction and position in the wave tank. During their propagation, the generated waves exhibit modulation instability and phase singularity phenomena. These two factors refer to Benjamin Bona Mahony as a promising candidate for generating extreme waves in the laboratory. The aim of this research is to investigate the distribution of energy in each modulation frequency change. The Hamiltonian formula that describes the phenomenon of phase singularity is used to observe energy. This data is critical in determining the parameters used to generate extreme waves.METHODS: The envelope of the Benjamin Bona Mahony wave group can be used to study the Benjamin Bona Mahony wave. The Benjamin Bona Mahony wave group is known to evolve according to the Nonlinear Schrodinger equation. The Hamiltonian governs the dynamics of the phase amplitude and proves the Nonlinear Schrodinger equation's singularity for finite time. The Hamiltonian is derived from the appropriate Lagrangian for Nonlinear Schrodinger and then transformed into the Hamiltonian with the displaced phase-amplitude variable.FINDINGS: Potential energy is related to wave amplitude and kinetic energy is related to wave steepness in the study of surface water waves. When , the maximum wave amplitude and steepness are obtained. When , extreme waves cannot be formed due to steepness. This is due to the possibility of breaking waves into smaller waves on the shore. In terms of position, the energy curve is symmetrical.CONCLUSION: According to Hamiltonian's description of the energy distribution, the smaller the modulation frequency, the greater the potential and kinetic energy involved in wave propagation, and vice versa. While the wave's amplitude and steepness will be greatest for a low modulation frequency, and vice versa. The modulation frequency considered as an extreme wave generator is , because the resulting amplitude is quite high and the energy in the envelope is also quite large.

On the extreme value statistics of spatio-temporal maximum sea waves under cyclone winds

Principles of the spatio-temporal statistics are used to investigate the characteristics of short-term/range extreme sea waves and related sea-state parameters under cyclone winds (northern hemisphere). We base our analysis upon consistent stereo-imaging observations of the 3D (2D space + time) sea surface elevation field, and spectral wave model results in the Northwestern Pacific during tropical storm Kong-rey (2018). The focus is on the extreme value analysis of individual maximum sea surface elevations (crest heights) and maximum crest-to-trough wave heights. Results highlight the sea areas around the storm centre where the spatio-temporal highest waves are more likely, and, via scale analysis, the principal mechanisms responsible for the occurrence of extreme conditions in bimodal (composed of wind-sea and swell) and short-crested storm seas. We find that individual waves are the highest to the north-east of the translating cyclone, where sea states are more energetic. However, in the south/south-west of the centre, where opposing wind-sea/swell sea states dominate, directional spread and bound nonlinear interactions are enhanced. In this area, more extreme waves may occur, having the maximum crest and wave heights mean values in excess of 1.3 and 2.1 times the significant wave height, respectively. This set of results provides insights into the role of the dispersive and directional focusing enhanced by nonlinearities up to the second order as an effective mechanism for the formation of extreme waves under cyclone winds. To examine what physical mechanism is behind the generation of extreme waves in different regions around the cyclone, we also explore for comparison areas where nonlinear four-wave interactions are more likely to occur.

Controlled extreme wave generation using an improved focusing method

Dispersive focusing technology is one of the most widely used methods to simulate extreme waves in the laboratory. However, such methods that are based on the linear dispersion relation are not robust. The focusing waves are always generated at unexpected positions owing to nonlinear effects. Hence, in this paper, an improved focusing method named the All Phase Correction Method (APCM) is developed to produce accurate focusing waves at a predefined position. An improved phase estimation algorithm and second-order wavemaker theory is employed to iteratively correct the phases and amplitudes of the generated waves. Different types of experiments were conducted in a wave flume using this method. The results indicate that the present method works well for accurately generating extreme events. Both the component phases and the focal positions match well with the target values. The influences of wave steepness, spectral bandwidth and spectral type on the correction procedure were investigated extensively. The analysis revealed that with the increase in wave steepness and narrowness of spectral width, the phase deviation increased. Thus, more correction iterations are needed to achieve convergence of iteration. In addition, the spectral type also influences the wave correction procedure. The focal position deviations for the constant-steepness spectrum and the constant-amplitude spectrum are significantly smaller than that of the JONSWAP spectrum, and the correlation coefficient converges faster.

Extreme Wave Generation, Breaking, and Impact Simulations Using Wave Packets in REEF3D

On several occasions, freak waves have been observed in the past, some causing severe damage. In order to model such extreme wave conditions, one possibility is to use focused waves of first- or second-order based on irregular sea-state wave spectra. The wave phase is chosen such that the waves focus at a predetermined location and time, but the individual wave components become steep and start breaking before the focus location for large amplitudes. In this study, transient wave packets are used for extreme wave generation. Extreme waves are generated that are higher and only break at the concentration point using the transient wave packets method implemented in the open-source CFD model REEF3D. Model validation is performed by comparison to experimental results. The generation of wave packets with an 8.3 times shorter focus distance is investigated and the wave is replicated in a shorter domain with a 9% higher crest. The method is further used to generate a steepness induced-breaking wave and calculation of extreme wave forces on an offshore structure is demonstrated.

Mathematical model of snake-type multi-directional wave generation

Research on extreme wave generation is one intensive research on water wave study because the fact that the occurrence of this wave in the ocean can cause serious damage to the ships and offshore structures. One method to be used to generate the wave is self-correcting. This method controls the signal on the wavemakers in a wave tank. Some studies also consider the nonlinear wave generation in a wave tank by using numerical approach. Study on wave generation is essential in the effectiveness and efficiency of offshore structure model testing before it can be operated in the ocean. Generally, there are two types of wavemakers implemented in the hydrodynamic laboratory, piston-type and flap-type. The flap-type is preferred to conduct a testing to a ship in deep water. Single flap wavemaker has been explained in many studies yet snake-type wavemaker (has more than one flap) is still a case needed to be examined. Hence, the formulation in controlling the wavemaker need to be precisely analyzed such that the given input can generate the desired wave in the space-limited wave tank. By applying the same analogy and methodhology as the previous study, this article represents multi-directional wave generation by implementing snake-type wavemakers.

Linear and nonlinear statistics of extreme waves

Abstract The probability of extremely high waves is calculated by two methods. The first method is based on the direct numerical simulation of two-dimensional wave field using a three-dimensional nonlinear model. The second method consists in calculation of the probability of wave heights over ensemble of fields representing a superposition of linear waves with random phases and a spectrum similar to that obtained in the nonlinear model. It is shown that the integral probability of extreme waves are very close to each other in both cases. This implies that the role of nonlinearity in the generation of extreme waves is probably not so important as it was assumed in most papers considering this phenomenon.

Numerical modeling of 3D fully nonlinear potential periodic waves

A simple and exact numerical scheme for long-term simulations of 3D potential fully nonlinear periodic gravity waves is suggested. The scheme is based on the surface-following nonorthogonal curvilinear coordinate system. Velocity potential is represented as a sum of analytical and nonlinear components. The Poisson equation for the nonlinear component of velocity potential is solved iteratively. Fourier transform method, the second-order accuracy approximation of vertical derivatives on a stretched vertical grid and the fourth-order Runge–Kutta time stepping are used. The scheme is validated by simulation of steep Stokes waves. A one-processor version of the model for PC allows us to simulate evolution of a wave field with thousands degrees of freedom for hundreds of wave periods. The scheme is designed for investigation of nonlinear 2D surface waves, generation of extreme waves, and direct calculations of nonlinear interactions.

Validation of a CIP-based tank for numerical simulation of free surface flows

A constrained interpolation profile CIP-based numerical tank is developed to simulate violent free surface flows. The numerical simulation is performed by the CIP-based Cartesian grid method, which is described in the present paper. The tangent of hyperbola for interface capturing (THINC) scheme is applied for capturing complex free surfaces. The new model is capable of simulating a flow with violently varied free surface. A series of computations are conducted to assess the developed algorithm and its versatility. These tests include the collapse of water column with and without an obstacle, sloshing in a fixed tank, the generation of regular waves in a tank, the generation of extreme waves in a tank. Excellent agreements are obtained when numerical results are compared with available analytical, experimental, and other numerical results.

Numerical Simulation of Extreme Wave Generation Using VOF Method

Numerical simulations of extreme wave generation are carried out by using the Volume Of Fluid (VOF) method. Extreme waves are generated based on wave focusing in a 2-D numerical model. To validate the capability of the VOF-based model described in this article, the propagation of regular waves is computed and compared with the theoretical results. By adjusting the phases of wave components, extreme waves are formed at given time and given position in the computation. The numerical results are compared with theoretical solutions and experimental data. It is concluded that the present model based on the VOF technique can provide acceptably accurate numerical results to serve practical purposes.

Freak waves: Their occurrence and probability

This paper describes the results of more than 4000 long-term (up to thousands of peak wave periods) numerical simulations of nonlinear gravity surface waves performed for the investigation of properties and estimation of statistics of extreme (“freak”) waves. The method of solution of two-dimensional potential wave equations based on conformal mapping is applied to the simulation of wave behavior assigned by different initial conditions, defined by the Joint North Sea Wave Observation Project and Pierson–Moskowitz spectra. It is shown that nonlinear wave evolution sometimes results in the appearance of very big waves. There are no predictors for the appearance of extreme waves; however, the height of dimensional waves is proportional to the significant wave height. The initial generation of extreme waves can occur simply as a result of linear group effects, but in some cases the largest wave suddenly starts to grow. It is followed sometimes by a strong concentration of wave energy around a peak vertical. It takes place typically for one peak wave period. It happens to an individual wave in physical space, with no energy exchange with surrounding waves taking place. A probability function for steep waves has been constructed. Such type of function can be used for the development of operational forecast of freak waves based on a standard forecast provided by a three-dimensional generation wave prediction model (WAVEWATCH or wave modeling).

Rogue Waves: Results of the MaxWave Project

Safety of shipping is an ever growing concern. In a summary, Faulkner investigated the causes of shipping casualties (2002, “Shipping Safety: A Matter of Concern,” Ingenia, The Royal Academy of Engineering, Marine Matters, pp. 13–20) and concluded that the numbers of unexplained accidents are far too high in comparison to other means of transport. From various sources, including insurers data over 30% of the casualties are due to bad weather (a fact that ships should be able to cope with) and a further 25% remain completely unexplained. The European project MaxWave aimed at investigating ship and platform accidents due to severe weather conditions using different radars and in situ sensors and at suggesting improved design and new safety measures. Heavy sea states and severe weather conditions have caused the loss of more than 200 large cargo vessels within the 20years between 1981 and 2000 (Table 1 in Faulkner). In many cases, single “rogue waves” of abnormal height as well as groups of extreme waves have been reported by crew members of such ships. The European Project MaxWave deals with both theoretical aspects of extreme waves and new techniques to observe these waves using different remote sensing techniques. The final goal is to improve the understanding of the physical processes responsible for the generation of extreme waves and to identify geophysical conditions in which such waves are most likely to occur. Two-dimensional sea surface elevation fields are derived from marine radar and space borne synthetic aperture radar data. Individual wave parameters such as maximum to significant wave height ratios and wave steepness, are derived from the sea surface topography. Several ship and offshore platform accidents are analyzed and the impact on ship and offshore design is discussed. Tank experiments are performed to test the impact of designed extreme waves on ships and offshore structures. This article gives an overview of the different work packages on observation of rogue waves, explanations, and consequences for design.

Numerical modeling of extreme rogue waves generated by directional energy focusing

Three-dimensional (3D) directional wave focusing is one of the mechanisms that contributes to the generation of extreme waves, also known as rogue waves, in the ocean. To simulate and analyze this phenomenon, we generate extreme waves in a 3D numerical wave tank (NWT), by specifying the motion of a snake wavemaker. The NWT solves fully non-linear potential flow equations with a free surface, using a high-order boundary element method and a mixed Eulerian–Lagrangian time updating. Some numerical aspects of the NWT were recently improved, such as the accurate computation of higher-order derivatives on the free surface and the implementation of a fast multipole algorithm in the spatial solver. The former has allowed the accurate simulation of 3D overturning waves and the latter has led to at least a one-order of magnitude increase in the NWT computational efficiency. This made it possible to generate finely resolved 3D focused overturning waves and analyze their geometry and kinematics. In this paper, we first summarize the NWT equations and numerical methods. We then introduce a typical simulation of an overturning rogue wave, and analyze the sensitivity of its geometry and kinematics to water depth and maximum angle of directional energy focusing. We find that an overturning rogue wave can have different properties depending on whether it is in the focusing or defocusing phase at breaking onset. The maximum focusing angle and the water depth largely control this situation, and therefore the main features of the rogue wave crest, such as its 3D shape and kinematics.

A wavelet-based algorithm to estimate ocean wave group parameters from radar images

In recent years, new remote sensing techniques have been developed to measure two-dimensional (2-D) sea surface elevation fields. The availability of these data has led to the necessity to extend the classical analysis methods for one-dimensional (1-D) buoy time series to two dimensions. This paper is concerned with the derivation of group parameters from 2-D sea surface elevation fields using a wavelet-based technique. Wave grouping is known to be an important factor in ship and offshore safety, as it plays a role in dangerous resonance phenomenons and the generation of extreme waves. Synthetic aperture radar (SAR) data are used for the analysis. The wavelet technique is introduced using synthetic ocean surfaces and simulated SAR data. It is shown that the group structure of the ocean wave field can be recovered from the SAR image if the nonlinear imaging effects are moderate. The method is applied to a global dataset of European Remote Sensing satellite (ERS-2) wave mode data. Different group parameters including the area covered by the largest group and the number of groups in a given area are calculated for over 33 000 SAR images. Global maps of the parameters are presented. For comparison, classical 1-D grouping parameters are calculated from colocated wave model data showing good overall agreement with the wavelet-derived parameters. ERS-2 image mode data are used to study wave fields in coastal areas. Waves approaching the island of Sylt in the North Sea are investigated, showing the potential of the wavelet technique to analyze the spatial wave dynamics associated with the bottom topography. Observations concerning changes of wavelength and group parameters are compared to linear wave theory.