Irregular Wave Train Research Articles

Effect of shoaling length on rogue wave occurrence

The impact of shoaling on linear water waves is well known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least qualitatively, this effect has been partially attributed to the ‘rapid’ nature of the shoaling process, i.e. shoaling occurs over a distance far shorter than that required for waves to modulate themselves and adapt to the reduced water depth. Through a theoretical model and highly accurate nonlinear simulations, we disentangle the respective effects of the length and angle of a shoal's slope. We investigate the effects of the shoaling process rapidness on the evolution of key statistical and spectral sea-state parameters. We let the wave field evolve over a slope with constant angle in all cases while we vary the slope length. Our results indicate that the non-equilibrium dynamics is not affected by the slope length, because further extending the slope length does not influence the magnitude of the statistical and spectral measures as long as the non-equilibrium dynamics dominates the wave evolution. Thus, the shoaling effect on rogue waves is deduced to be mainly driven by the slope magnitude rather than the slope length.

Characterization of Overtopping Volumes from Focused Wave Groups over Smooth Dikes with an Emerged Toe: Insights from Physical Model Tests

This research examines the overtopping volumes associated with focused wave groups on smooth dikes with an emerged toe. Focused wave groups are employed to represent the highest waves of random sea states in a compact form, obviating the need to model the entire irregular wave train. This study investigates how overtopping volumes are affected by focus location and phase. A total of 418 experimental tests were gathered and analyzed. Data with overtopping volumes below 600 L per meter (prototype conditions) were excluded in order to focus on extreme overtopping events, resulting in 324 relevant test cases. The experiments used first-order wave generation theory to analyze structural response. Subsequent studies will address the errors induced by this approximation and compare it with second-order wave generation. The experiments simulated extreme wave impacts on an idealized coastal layout, comprising a 1:6.3 foreshore slope and three different dike slopes, including vertical structures, with the initial still water level set below the dike toe. This study employed the NewWave theory to generate focused wave groups, with the objective of extending recent research on wave overtopping under varied conditions. The results, analyzed in both dimensional and non-dimensional forms, indicate that overtopping volumes are significantly influenced by the focus phase. Critical focus locations were identified at a distance of one-third of the deep-water wavelength from the toe.

Study of Velocity Changes Induced by Posidonia oceanica Surrogate and Sediment Transport Implications

An analysis of the interactions between wave-induced velocities and seagrass meadows has been conducted based on the large-scale CIEM wave flume data. Incident irregular wave trains act on an initial 1:15 sand beach profile with measurement stations from the offshore of a surrogate meadow until the outer breaking zone, after crossing the seagrass meadow. The analysis considers variability and peaks of velocities, together with their skewness and asymmetry, to determine the effects of the seagrass meadow on the near bed sediment transport. Velocity variability was characterized by the standard deviation, and the greatest changes were found in the area right behind the meadow. In this zone, the negative peak velocities decreased by up to 20.3%, and the positive peak velocities increased by up to 11.7%. For more onshore positions, the negative and positive peak velocities similarly decreased and increased in most of the studied stations. A progressive increase in skewness as the waves passed through the meadow, together with a slight decrease in asymmetry, was observed and associated with the meadow effect. Moving shoreward along the profile, the values of skewness and asymmetry increased progressively relative to the position of the main sandbar. The megaripple-like bedforms appeared earlier when the meadow was present due to the higher skewness, showing a belated development in the layout without the meadow, when skewness increased further offshore due to the proximity of the breaker sandbar. To assess the sediment transport capacity of a submerged meadow, the SANTOSS formula was applied, showing that in front of the meadow, there was a higher sediment transport capacity, whereas behind the meadow, that capacity could be reduced by up to 41.3%. In addition, this formula was able to produce a suitable estimate of sediment transport across the profile, although it could not properly estimate the sediment volumes associated with the bedforms generated in the profile.

Statistical distributions of free surface elevation and wave height for out-of-equilibrium sea-states provoked by strong depth variations

As unidirectional irregular wave trains propagate over a steep shoal, the sea-state becomes out-of-equilibrium and is continuously affected by the non-equilibrium dynamics (NED) over dozens of characteristic wavelengths. Using the set of accurate numerical simulations of Zhang et al. (2022), the NED effects on the probability distributions of free surface elevation and wave height, the statistical moments and maximum wave statistics are investigated, in both near-field and far-field regions after the water depth transition. The primary contribution of this work is to assess the applicability and limitations of several popular statistical distribution models in describing non-equilibrium statistics. In addition, a new distribution of the free surface elevation in a lognormal shape is proposed, which predicts the non-equilibrium free surface statistics with satisfactory performance and characterizes well the skewness–kurtosis relationship in the short scale. It is shown that the statistics in the far-field region are significantly influenced by the near-field wave-wave interaction, and beyond the capability of all statistical models considered here. Despite this complexity, the sea-state in the far-field region exhibits lower freak wave probability than a Gaussian sea-state. Implications of these findings for engineering practices are discussed.

Groupiness effect on irregular wave train propagation and impact on cylinder

A wave flume based on solving the Reynolds-averaged Navier-Stokes equation is modelled to simulate the irregular wave group interacting with a cylinder. The irregular wave groups are generated based on the wave envelope spectrum and the improved JONSWAP spectrum. The wave-making boundary and the momentum source term for wave-making and wave dissipation are developed based on the irregular wave theory. To suppress excessive growth of turbulent viscosity, a modified formula for turbulent viscosity is implemented in the shear stress transport turbulence model. Several sets of irregular waves with different groupiness factors are simulated. The effects of groupiness on the wave parameters, wave run-up height and wave force on the cylinder are investigated. The results show that the wave parameters increase as the groupiness increase. The group height factor has a larger influence on the significant wave height than the group length factor. The group length factor mainly influences the average wave period and average wavelength. When the average wavelength is larger than the diameter of the cylinder, the increase in wave group length results in a decrease in wave run-up height and wave force on the cylinder.

Real-time model for wave attenuation using active plate breakwater based on deep reinforcement learning

This paper presents a numerical study of the interaction between irregular waves and actively controlled plate breakwater based on deep reinforcement learning (DRL), in which wave attenuation performance is mainly discussed. A numerical wave flume (NWF) is built and an in-house solver is developed to integrate CFD and DRL. Validations on wave generation and interaction between incident waves and the plate are carried out. An NWF-DRL coupled model is proposed to simulate the actively controlled plate moving to attenuate waves, where the motion of the plate is controlled by DRL. It is shown that under the regular wave and trichromatic wave group, both the trained agents can obviously reduce the wave height compared to that under fixed plate. Moreover, the further trained agents can reduce the transmitted wave heights to a significantly low level in the three more complex and unknown irregular wave cases. Meanwhile, the model does a great job of preventing the development of focused wave height in an irregular wave train. This research first examines the wave attenuation of a DRL-controlled breakwater in irregular wave environments, which may offer fresh perspectives on wave attenuation and even the design of intelligent marine equipment.

Floating hydroelastic circular plate in regular and irregular waves

An understanding of the hydroelastic response of a flexible circular plate to water waves is relevant to many problems in ocean engineering ranging from offshore wave energy converters and solar wind devices to very large floating structures such as floating airports and ice sheets. This paper describes results from physical model tests undertaken in the COAST laboratory at the University of Plymouth. Response amplitude operators (RAOs) of a floating flexible circular disk are determined for incident monochromatic and irregular wave trains, the latter defined by JONSWAP spectra. Free-surface displacements are measured using wave gauges, and the plate motion recorded using a QUALISYS® motion tracking system. Different basin depths and plate thicknesses are considered in order to quantify the effects of water depth and flexural plate rigidity on the overall dynamic behaviour of the circular disk. We present synchronous and subharmonic nonlinear responses for monochromatic waves, and displacement spectra for irregular waves. The measured wave hydrodynamics and disk hydroelastic responses match theoretical predictions based on linear potential flow theory.

Numerical simulation of waves overtopping over impermeable sloped seadikes

In this study, a numerical model of white water overtopping of regular waves over an impermeable seadike is developed using the Volume of Fluid (VOF) method based on Reynolds-Averaged Navier-Stokes (RANS). The numerical model is favored due to the challenges in experimentally quantifying the hydrodynamic features of overtopping flow, particularly at the beginning of the crest, as well as the uncertainty in various design formulae estimating wave overtopping rates. Such uncertainties are caused by insufficient wave height statistics in irregular wave trains, which may be addressed by taking into account overtopping rates of regular wave tests as well as robust statistical distributions of wave heights and periods. For this purpose, first, by ensuring the numerical model's validity, effective hydraulic and structural parameters on regular waves overtopping are investigated and their dimensionless forms are determined using the dimensional analysis method. Based upon the developed model and in-depth estimation of dimensionless parameters' effect on overtopped layer thickness, the overtopping velocity at the beginning of the crest, and the average overtopping rate, the wave breaker type is determined to be highly effective at reducing overtopping parameters. By analyzing the numerical model run results, formulae are proposed to predict the layer thickness, the wave overtopping velocity at the beginning of the crest, and the average wave overtopping rate independent of the flow characteristics on the slope seaward. Comparing the results of the proposed formulae with other researchers highlights the appositeness and reliability of the numerical simulation and the proposed formulae. Using the obtained formulae of layer thickness and overtopping velocity, along with consideration of sliding, toppling, and floating criteria, appropriate criteria are proposed to control the overtopping safety for pedestrians and vehicles. Moreover, compared to the average overtopping rate, the overtopping velocity and layer thickness parameters are found to be more appropriate in investigating the overtopping risk for pedestrians and vehicles.

Response of Wave Dissipating Blocks Composing a Detached Breakwater to Waves with Various Periods

We discuss the response of the wave dissipating blocks composing a detached breakwater to the waves with various periods, based on both the experimental and numerical results. First, in the hydraulic experiments, the number of the blocks fallen by the irregular waves was the largest when the still water level is moderate, namely the HWL. When the large and long wave is incident, the overflow that lasted for a long time fell many blocks at the back of the breakwater. When the irregular waves, long wave, and irregular waves are continuously incident in this order, the first irregular wave train shifted several blocks, and the subsequent long wave dropped these shifted blocks, displacing the blocks around them, whereafter the second irregular wave train dropped many of the displaced blocks. Second, in the vertically two-dimensional calculations, when the long wave struck the breakwater, a large-scale vortex was created near the seabed in front of the breakwater and remained during the pushing wave. The overflow due to the long wave generated negative wave pressure at the top behind the breakwater. Based on both the numerical and experimental results behind the breakwater, when a large positive wave pressure is generated after a negative wave pressure that is not large in absolute value, the number of fallen blocks will reduce. When large and short waves cause overtopping, and negative wave pressure frequently appears behind a breakwater, the blocks at the back of the breakwater can gradually shift, loosening their engagement.

Sensitivity analysis of extreme loads acting on a point-absorbing wave energy converter

There are many uncertainties associated with the estimation of extreme loads acting on a wave energy converter (WEC). In this study we perform a sensitivity analysis of extreme loads acting on the Uppsala University (UU) WEC concept. The UU WEC consists of a bottom-mounted linear generator that is connected to a surface buoy with a taut mooring line. The maximum stroke length of the linear generator is enforced by end-stop springs. Initially, a Variation Mode and Effect Analysis (VMEA) was carried out in order to identify the largest input uncertainties. The system was then modelled in the time-domain solver WEC-SIM coupled to the dynamic mooring solver Moody. A sensitivity analysis was made by generating a surrogate model based on polynomial chaos expansions, which rapidly evaluates the maximum loads on the mooring line and the end-stops. The sensitivities are ranked using the Sobol index method. We investigated two sea states using equivalent regular waves (ERW) and irregular wave (IRW) trains. We found that the ERW approach significantly underestimate the maximum loads. Interestingly, the ERW predicted wave height and period as the most important parameters for the maximum mooring tension, whereas the tension in IRW was most sensitive to the drag coefficient of the surface buoy. The end-stop loads were most sensitive to the PTO damping coefficient.

Numerical study of coastal wave profiles at the sandy beaches of Nowshahr (Southern Caspian Sea)

This study aimed to investigate the capability of the one-dimensional (1D) mode of the Simulating WAves till SHore (SWASH), as a non-hydrostatic wave-flow model with six vertical layers, to reproduce the cross-shore wave evolution. For this purpose, the given model was initially calibrated for wave energy and the outputs were then verified with the field data measured at the Southern Caspian Sea. The calibration coefficients obtained for wave breaking are significantly less than the ones which have been mostly reported in previous studies for the two-dimensional (2D) mode of the SWASH. Although the reproduced wave height parameters are generally in good accordance with the field observations, the period parameters and the number of waves are overestimated and underestimated by the model, respectively. Moreover, the inaccuracies at the shallow stations are worse than at the transitional depths. The overestimation in both the reproduced energy of infragravity waves (IG) and their wavelength along with the underestimation in the wind-wave energy content are also among the factors responsible for the model deficiencies. The findings have revealed that the overestimation of the reproduced IG waves is the main reason for the underestimation of the breaking dissipation rate for irregular wave trains in the 1D mode. Therefore, more intensive breaking dissipation via selecting lower coefficient values is necessary to exhaust a certain energy content from longer waves in the 1D mode. This approach ultimately induces an over-dissipation of short wind-waves.

Application of Arbitrary Lagrangian–Eulerian strips with fully nonlinear wave kinematics for force estimation

The initial design of offshore constructions generally uses a combination of model tests and second-order wave theory to reconstruct the wave kinematics to determine wave forces using the Morison equation. This routine becomes difficult to apply to steep waves without model test data where the second-order theory is not valid. In this article, a novel approach combining a fully nonlinear numerical wave tank (NWT) using the σ-grid with strip theory and the Morison equation in an Arbitrary Lagrangian–Eulerian (ALE) framework is presented. This provides improved wave kinematics from the nonlinear numerical wave tank, an improved representation of the instantaneous velocity field associated with the instantaneous location of the free surface, making an accurate estimation of the wave hydrodynamics of highly nonlinear and breaking waves possible at a reasonable computational cost.The method is verified by comparing the calculated wave kinematics for a fifth-order Stokes wave with the analytical solution. The procedure for the estimation of the hydrodynamic loads on a cylinder is validated using comparisons with model test data for wave forces on a cylinder due to regular, irregular and focussed waves. A good agreement is seen for the estimated wave forces, including for the breaking waves in the irregular wave train. Some overestimation of the wave forces due to irregular waves is seen due to the frequency-independent force coefficient used in the Morison equation. The results demonstrate the potential of the ALE method combined with a nonlinear NWT to evaluate a three-hour irregular sea state simulation and generate wave loading statistics for the initial stochastic design of offshore structures without model test data.

A novel method in generating freak wave and modulating wave profile

More and more attentions have been paid on freak wave since it leads to serious damages on marine structures. The conventional method is to conduct linear superposition in frequency domain to obtain freak waves. In this study, the expected freak wave is firstly embedded in an irregular wave train and then transformed into frequency domain by Fast Fourier Transform (FFT). Because of the visualization and maneuverability in time domain, the profile of freak wave can be modulated conveniently. Therefore, special freak wave cases such as Three Sisters Wave (TSW), can also be obtained by this method. The correction on wave spectrum for freak wave train is firstly presented. It was then validated in experiments. The results show that the method is efficient to generate freak waves and TSW, and has good agreements in both time domain and frequency domain. The advantage of the proposed method is that the other waves can be maintained very well when modulating the profile of freak wave. The novel method is helpful to investigate the mechanism of freak wave-structures interaction in deep.

Emergence of Solitons from Irregular Waves in Deep Water

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.

Towards a Computational Fluid Dynamics implementation of the critical wave groups method

The prediction of extreme ship responses continues to be an important and longstanding topic in ship hydrodynamics with a significant focus on developing probabilistic methods based on simple descriptions of the hydrodynamics that mainly provide qualitative observations. While simple nonlinear hydrodynamic formulations provide insight into extreme events, their underlying assumptions can prevent accurate quantitative representations of the mechanisms that are ultimately responsible for the extreme responses.Thus, research must strive to utilize increasingly more accurate hydrodynamic formulations to provide quantitative evaluations of extreme events. The present work aims to integrate extreme event probabilistic research based on the critical wave groups (CWG) method and fully nonlinear Computational Fluid Dynamics (CFD) to achieve a high fidelity representation of extreme events. This aim is achieved by embedding deterministic wave groups into irregular wave trains with known responses to produce different states at the moment of wave group encounter. The new framework is demonstrated by predicting the probability of exceedence of roll with a 2-D midship section of the Office of Naval Research Tumblehome hull in Sea State 7. The framework showcases how CFD and CWG can together reduce the computational burden of predicting extreme ship responses.

Wave–bottom interaction and extreme wave statistics due to shoaling and de-shoaling of irregular long-crested wave trains over steep seabed changes

Abstract

Statistics of long-crested extreme waves in single and mixed sea states

Most of the studies on extreme waves are focused on the systems with single-peak wave spectra. However, according to the statistics of occurrence, the bimodal spectral system is also frequent in real sea conditions. In order to summarize the statistics of extreme waves, irregular wave trains under single-peak and bimodal spectra for long durations are simulated in this paper, based on a two-dimensional High Order Spectral (HOS) numerical wave tank. A large number of configurations have been tested under unimodal and bimodal spectra. The investigation on the wave trains under single-peak spectrum indicates that although in conditions often referred as deep water (kph > π), the relative water depth has a significant influence on the probabilities of occurrence of extreme waves. A detailed analysis of the combined effect of Benjamin-Feir Index (BFI) and relative water depth is provided. However, the situation is more complex in real sea conditions, which may exhibit multimodal spectra. We focus in this study on long-crested bimodal spectra characterized by the same significant wave height Hs and mean zero-crossing period Tz of the sea states as the single-peak spectrum. The wave conditions under bimodal spectrum present milder extreme wave statistics than those under single-peak spectrum. In addition, mixed ocean systems with equivalent energy distribution (i.e., Sea-Swell Energy Ratio (SSER) is close to 1.0) and larger separation between partitions (i.e., Intermodal Distance (ID) > 0.10) are the less prominent to extreme waves appearance. The comparison of the mixed sea states and the corresponding single independent systems demonstrates that the complexity of the underlying physics of a given sea state (for instance the presence of modulational instability or other nonlinear process) cannot be deduced by an analysis limited to the statistical content of the combined sea state. The wave energy being distributed among frequencies plays a major role. Additionally, Gram-Charlier distribution can accurately predict the probability of large waves (1.5 < H/Hs < 2.0) compared to the MER distribution, but it underestimates the statistics of the wave height distribution when H/Hs is larger than 2.0 for both single-peak and bimodal states.

Properties of breaking irregular waves over slopes

The present study numerically investigates the breaking and spectral characteristics and geometric properties of breaking irregular waves over slopes for different incident waves. The growth of wave non-linearity and wave energy redistribution during shoaling and breaking process are observed to be major factors in determining the free surface elevation skewness and spectral bandwidth. In general, the variation of the breaker indices with the surf similarity parameter is found to be mainly governed by the type of wave breakers. The wave breaker type further depends on the seabed slope, incident wave parameters and water depth at the location of wave breaking. The study further explores the geometric properties for both spilling and plunging irregular wave breakers. The wave deformation due to wave-seabed interaction plays a major role in affecting the breaker shapes. Every individual breaking wave in the irregular wave train possesses different wave profiles and breaker characteristics. In order to study these parameters in a probabilistic way, the statistics of the breaker characteristics and the breaker shape parameters are investigated. The lognormal distribution is noticed to be the most suitable fit for the wave crest steepness and asymmetry factors. This study is performed using the open-source computational fluid dynamics (CFD) based numerical model. The numerical model is validated for a submerged bar under breaking irregular waves and the numerical results are compared with experimental data. The transformations of the free surface elevation due to wave shoaling, wave breaking and wave decomposition are explored.

Experimental study of breaker index of normal and oblique incident unidirectional and multidirectional irregular waves on slope

Most studies of wave breaking on slopes to date have investigated regular waves or normal incident unidirectional waves. In this study, wave breakings of normal and oblique incident irregular waves and multidirectional irregular waves on a 1:15 slope were investigated. The breaking criteria of irregular waves based on significant wave height and individual wave height were determined. Firstly, breaker indexes calculated using significant wave heights at incipient breaking were analyzed; they were substantially lower than the breaker indexes of regular waves. The breaker index formulae of irregular waves are presented based on the referred formula of regular waves. Furthermore, the breaker indexes of oblique incident waves were larger than the breaker indexes of normal incident waves. However, wave directionality had little effect on breaker indexes under the present experimental conditions. Secondly, the breaker index (the ratio of significant wave height to water depth) in surf zone was analyzed. It increased with a decrease in relative water depth. Thirdly, information of individual waves in irregular wave trains was tracked by the wave-by-wave method. The breaker indexes derived by individual wave heights were larger than the incipient breaker indexes derived from significant wave heights. Based on previous empirical formulae, some relatively simple expressions are proposed to calculate individual breaking wave heights for unidirectional irregular waves.

On Efficient Surrogate Model Development for the Prediction of the Long-Term Extreme Response of a Moored Floating Structure

Abstract This study focuses on the development of efficient surrogate models by polynomial chaos expansion (PCE) for the prediction of the long-term extreme surge motion of a moored floating offshore structure. The structure is subjected to first-order and second-order (difference-frequency) wave loading. Uncertainty in the long-term response arises from contrasting sea state conditions, characterized by significant wave height, Hs, and spectral peak period, Tp, and their relative likelihood of occurrence; these two variables are explicitly included in the PCE-based uncertainty quantification (UQ). In a given sea state, however, response simulations must be run for the associated Hs and Tp; in such simulations, typically, a set of random amplitudes and phases define an irregular wave train consistent with that sea state. These random amplitudes and phases for all the frequency components in the wave train introduce additional uncertainty in the simulated waves and in the response. The UQ framework treats these two sources of uncertainty—from Hs and Tp on the one hand, and the amplitude and phase vectors on the other—in a manner that efficiently yields long-term surge motion extreme predictions consistent with more expensive Monte Carlo simulations (MCS) that serve as the “truth” system. To reduce uncertainty in response extremes that result from sea states with a low likelihood of occurrence, importance sampling is employed with both MCS- and PCE-based extreme response predictions. Satisfactory performance with such efficient surrogate models can help in assessing the long-term response of various offshore structures.