Focused Wave Groups Research Articles

Impact of rogue waves on semi-submersible platforms: An experimental investigation of wave run-up and air-gap responses

The wave run-up and air-gap responses of semi-submersible platforms under extreme sea conditions are crucial design considerations for ensuring the structural integrity and safety of marine engineering operations. This study investigated the impact of rogue waves on the wave run-up and air-gap responses of semi-submersible platforms using a transient focusing wave group to accurately simulate irregular seas. Comparative model tests were conducted on a semi-submersible platform under both rogue and non-rogue-wave conditions. The platform motions and air-gap responses were analysed using spectral analysis, extreme-value statistics, and wavelet methods. Rogue waves were found to significantly affect the air-gap response spectrum, increasing the nonlinearity of both the wave run-up and air-gap responses. Different locations on the platform exhibited varying statistical and spectral response characteristics. Rogue waves modified the instantaneous properties of wave elevation, thereby increasing the energy levels in the system. This study confirmed that rogue waves significantly influence the air-gap responses and wave run-up of semi-submersible platforms, suggesting that they should be considered when designing and planning the operations of these platforms. This study offers a comprehensive understanding of the complex interactions between rogue waves and large maritime structures and provides insights for improving safety and performance under extreme sea conditions.

Experimental and numerical study on focused wave generation using different energy modes

This paper reports an experimental and numerical study on the generation of freak waves related to the spatiotemporal focusing mechanism, where multiple water waves converge at a specific point in space and time to produce a large transient wave. A new energy distribution mode of constant-difference wave number (CDK) within the wave group is proposed and applied to both a physical and a numerical flume to generate focused waves, with primary attention given to the water surface elevation, underlying kinematics, and internal spectrum structure during the focused wave generation process. The classical experiment by Baldock et al. [“A laboratory study of nonlinear surface waves on water,” Philos. Trans. R. Soc., Ser. A 354, 649–676 (1996)], which used a constant-difference wave period within the wave group, is chosen for comparison. Spectral analysis shows that the CDK energy distribution mode can easily stimulate multiwave resonance in the focused wave group, where significant energy transfer from the main frequencies to higher harmonics is observed. Compared with the data from Baldock et al. [“A laboratory study of nonlinear surface waves on water,” Philos. Trans. R. Soc., Ser. A 354, 649–676 (1996)], the CDK wave group produces larger focused wave crests with higher propagation speeds and larger velocity gradients near the water surface due to strong multiwave resonance. The effects of the input spectrum, incident amplitude and initial water depth under different energy modes on focused-wave generation are analyzed. All the results indicate that the CDK energy distribution mode can produce larger focused waves compared to other energy distribution modes, which offers a novel approach for generating freak waves in the laboratory.

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.

Dispersive Wave Focusing on a Shear Current: Part 2—Nonlinear Effects

Continuing our recent work [Ellingsen et al., Water Waves (2024)] we investigate the influence of vertically sheared currents on the surface elevation as well as the kinematics of dispersively focusing wave groups up to second order in steepness. The groups are assumed long crested in deep water which may travel at oblique angles with the current, which has a depth-dependent profile in both magnitude and direction. A strong but realistic shear current affects the wave surface elevation only slightly but the wave-induced horizontal velocity beneath the point of focus is very significantly affected, and new phenomena occur at second order. Firstly, a shear current causes wave-induced superharmonic velocity to be nonzero, contributing significantly for moderate wave steepness. At linear order, following (opposing) shear causes horizontal velocities to be amplified (reduced); for crest-focused wave groups, the superharmonic contribution reduces the influence of shear, whereas for trough-focused waves the velocity change from linear and second-order waves add, causing a substantially larger shear-induced effect. Secondly, the sub-harmonic mean flow is not strictly a return flow, but can follow the direction of wave propagation at the depths nearest the surface. Thirdly, unlike the case without shear where the subharmonic mean flow vanishes in the limit of zero bandwidth, it can now tend to a finite value in the narrowband limit. The criterion for this to happen is that the shear current has nonzero curvature.

Impact of focused wave groups on pier structures: a case study of severe breaking waves at Pont del Petroli during storm Gloria

In January 2020, the footbridge connecting the seaward platform of the Pont del Petroli pier to Badalona beach collapsed due to the severe sea storm named Gloria. Approximately 15 m of the footbridge fell into the sea as a result of prolonged wave action and strong impacts. To understand the complex interaction between waves and structures that led to the pier’s collapse during the storm, a composite modelling approach was developed. The loads on each pier element were initially evaluated using the meshless DualSPHysics code, which employs the Smoothed Particle Hydrodynamics (SPH) method. This evaluation was conducted under severe wave conditions analogous to those experienced during the storm. Numerical models informed the design of an experimental campaign carried out at the Maritime Engineering Laboratory of Universitat Politècnica de Catalunya—BarcelonaTech, using the CIEM large-scale wave flume facility in Barcelona, Spain. Post-storm bathymetric surveys revealed significant alterations in the seabed profile near the affected infrastructure, including sediment deposition and a reduction in water depth from 10 m to 8 m. Consequently, it was anticipated that wave transformation and breaking in the vicinity of the structure would be substantially affected. To explore this phenomenon, various extreme wave impacts were experimentally simulated using focused wave groups. The physical model findings unveiled the forces that the pier endured during the storm Gloria. The results indicate that wave phases influence individual waves, with waves that are biased and asymmetric experiencing higher peaks than those focused on the crest. This insight helps to explain the structural failure of the footbridge during the storm and underscores the importance of considering wave phase impacts in the design and assessment of coastal infrastructure. The combined numerical and experimental approach provides a comprehensive understanding of the forces at play, contributing valuable knowledge to the field of coastal engineering and infrastructure resilience.

Overtopping Flow Velocity Characterisation Of Focused Waves On Promenades Using The Bubble Image Velocimetry Technique

This study characterises the flow velocity of individual extreme waves that overtop promenades using the bubble image velocimetry (BIV) technique (Ryu et al., 2005). Experimental tests were carried out in the small-scale wave flume CIEMito, at the Marine Engineering Laboratory (LIM) of the Universitat Politècnica de Catalunya – BarcelonaTech (UPC), and the obtained images were post-processed to calculate the flow velocities. The ultimate objective of the experimental campaign is to develop more precise models for forecasting wave overtopping of structures with an emergent toe, commonly found on sandy beaches and frequently utilized as promenades or waterfronts in most urbanized coastal environments. The NewWave theory (Tromans et al., 1991) was used to simulate the extreme individual wave overtopping in a real random sea state. The NewWave theory establishes a correlation between the expected form of a large wave in a linear sea state and the bulk characteristics of the sea state. Using focused wave groups instead of long-duration irregular wave time series offers several benefits. It improves the ability to repeat experiments and enhances measurement capabilities by providing greater temporal resolution in models used to investigate significant wave interactions (Hofland et al., 2014). Additionally, due to the compactness of focused wave groups, wave absorption becomes unnecessary. The research identifies two distinct case studies with varying wave forcing, tidal regimes and coastal layouts. This work presents a case study of a typical Mediterranean Sea configuration, which is a micro-tidal environment with steep and relatively short foreshores and pocket beaches. The study aims to characterize the overtopping flow velocity on the selected structure, and the feasibility of non-intrusive measurements such as a BIV technique has been investigated. The work includes preliminary results.

A machine learning architecture for including wave breaking in envelope-type wave models

Wave breaking is a complex physical process about which open questions remain. For some applications, it is critical to include breaking effects in phase-resolved envelope-based wave models such as the non-linear Schrödinger. A promising approach is to use machine learning to capture breaking effects. In the present paper we develop the machine learning architecture to model breaking developed by Eeltink et al. (2022) further, potentially enabling more detailed breaking physics to be captured. We show that this model can be trained on focused wave groups but can also capture breaking in random waves and modulated plane waves. Analysis of the model suggests that the machine learning has broken the problem into two—one part which detects whether the wave is breaking and another which captures the subsequent behaviour, consistent with the way human scientists routinely understand the breaking problem.

Transient gap resonance between two closely-spaced boxes triggered by nonlinear focused wave groups

A two-dimensional (2D) viscous numerical wave flume is developed based on OpenFOAM® to investigate the transient gap resonance problem triggered by nonlinear focused wave groups. The narrow gap is formed by two closely-spaced boxes, where the weather-side box is allowed to heave freely under wave actions, but the rear one is firmly fixed. The overset mesh method is introduced in the numerical model to capture the weather-side box's large-amplitude motion accurately. This work mainly focuses on the coupled effects of free-surface nonlinearity and heave-freedom of the weather-side box on the fluid oscillations in the gap and heave motions of the weather-side box. The heave-freedom of the weather-side box is demonstrated to play an important effect on the period in which the maximum value of non-dimensional amplitude of fluid oscillation in the gap occurs. It is revealed that the free-surface nonlinearity significantly affects the nonlinear fluid oscillations in the gap but has a limited effect on the heave motions of the weather-side box. The four-phase combination method is further employed to conduct the higher harmonic component analysis to clarify the effects of higher harmonic components on the nonlinear response of fluid and box.

Numerical study on performance of submerged permeable breakwater under impacts of multi-directional focused wave groups

Multi-directional waves focusing is considered a crucial method for generating extreme waves, posing a significant threat to coastal infrastructure and personal property. In recent years, there has been widespread construction of permeable submerged breakwaters as a preventive measure against extreme wave damage. Therefore, this study aims to assess the attenuation of multi-directional focused waves by both permeable and impermeable submerged breakwaters based on nonhydrostatic numerical wave model (NHWAVE). Effects of several key parameters are carefully examined. According to research findings, permeable submerged breakwaters offer significant benefits in reducing the wave amplitude, flow velocity, water elevation, and energy flux of multi-directional focused wave groups, while also effectively inhibiting the transfer of wave energy to higher frequencies. Additionally, we observe alternating positive and negative vortices occur at the boundary of the permeable submerged breakwater. The findings of this study are expected to advance the investigation into the hydrodynamic characteristics of submerged permeable breakwaters subjected to focused waves.

Laboratory and non-hydrostatic modelling of focused wave group evolution over fringing reef

This paper presents physical experiments and numerical simulations to study the propagation of focused waves group across hypothetical fringing reef profiles. A wave flume is 69 m long and 1.0 m deep, and the reef cross section is made up of a reef face, a reef flat and a vertical wall. A reef crest of 0.085 m is optionally constructed on the outside to replicate the reef crown. By focusing wave trains of the JONSWAP or constant wave amplitude spectrum, the transient wave group is generated on the reef slope. Free surface elevations and flow velocity are measured over time along the flume's centreline. The focused wave process and the development of higher harmonics as a result of the nonlinear interaction over the reef face are clearly visible in the wavelet and FFT analyses of the observed free surface elevation. Low frequency wave is increasing on the reef flat while these short-period wave motions are primarily absorbed by rapid breaking on reef edge and crest. On the flat, it is discovered that reef crest has the effect of reducing short-period wave motion and increasing long-period wave motion. A numerical multi-layer non-hydrostatic wave model is employed and its ability to describe the propagation of focused wave groups over fringing reef profiles is assessed.

Dispersive Wave Focusing on a Shear Current: Part 1—Linear Approximations

We consider the evolution and kinematics during dispersive focussing, for a group of waves propagating atop currents varying with depth. Our analysis assumes long-crested linear waves propagating at arbitrary angles relative to the current. Although low steepness is assumed, the linear model is often a reasonable approximation for understanding rogue waves. A number of analytical approximate relations are derived assuming different sub-surface current profiles, including linearly varying current, exponentially varying current, and currents of arbitrary depth profile which are weakly sheared following the approximation of Stewart and Joy (Deep Sea Res. Abs. 21, 1974). The orbital velocities are likewise studied. While shear currents have modest influence on the motion of the envelope of the wave group, they significantly change wave kinematics. Horizontal orbital velocities are either amplified or suppressed depending on whether the shear is opposing or following, respectively. To illustrate these phenomena we consider a real-world example using velocity profiles and wave spectra measured in the Columbia River estuary. Near the surface at the point where focusing occurs, horizontal orbital velocities are, respectively, increased and decreased by factors of 1.4 and 0.7 for focusing groups propagating on following and opposing shear (respectively, upstream and downstream in the earth-fixed reference system). The implications for the forces a focusing wave group can exert on vessels and installations are profound, emphasising the importance of considering current profiles in maritime operations.

Dynamic response analysis of the TetraSpar floater in waves: Experiment and numerical reproduction

The initial proof of concept model scale test campaign for the TetraSpar floating wind turbine substructure is presented here along with a detailed response analysis and numerical reproduction. The tests were conducted at scale 1:60 in wind and waves with the pitch-regulated DTU 10 MW wind turbine. The floater was tested in two configurations: semi-submersible and spar. The experimental setup and program is described in detail followed by system identification for natural frequencies and damping. The responses of the floater in the two configurations to hydrodynamic loading are analysed and compared. The analysis includes irregular sea states and focused wave groups at both 0° and 30° heading. The hydrodynamic damping of the floaters was quantified in decay tests, showing a clear linear and second-order component. It was observed that the semi-submersible configuration had significantly larger motion response than the spar configuration in ultimate limit state wave conditions. Emphasis is placed on the mooring loads and the tensions in the support lines for the ballasted keel. The increased ballast of the spar keel led to larger loads in these support lines. Further, second- and higher-order wave forcing were observed in responses of both configurations. A numerical model based on first-order radiation-diffraction theory, second-order Newman loads and additional Morison viscous forcing is set up. The model damping is calibrated against the measurements at each sea state. It is demonstrated that after this calibration, the model is able to reproduce the floater response and tower top accelerations with good accuracy, both in the linear range and at the natural floater frequencies, with heave in the storm sea state as the exception. The dynamic tensions in the keel lines are found to depend strongly on the lines projection to the inline wave direction. Also this behaviour is reproduced accurately by the model, although with some under-prediction in one of the lines in the rated wind sea state, which is linked to differences in the experimental pre-tension for the six lines.

Focused wave group propagation over fringing reef and its impact on the vertical wall mounted on a reef flat: Experiment and RANS modeling

This paper presents flume experiments and numerical simulations of focused wave group propagation over an idealized fringing reef profile and its impact on the vertical wall mounted on reef flat. The large transient wave group is produced over the steep fore-reef slope by focusing JONSWAP wave trains. The numerical simulations are performed using the compressible two-phase OpenFOAM model. Wavelet and FFT analysis of the surface elevation time histories clearly show wave focusing process and the generation of higher harmonics due to the nonlinear wave-wave interactions. For the high peak frequency cases, the low frequency wave motion increases gradually after wave breaking, but the peak frequency motion still dominates energy spectrum partially due to wave defocusing and reformation of broken waves. However, the magnitude of low frequency wave motion is higher than those around peak frequency and high harmonics for the lower peak frequency cases. It is found that the contribution of low frequency wave motion to the total force exerted on the wall is comparable to or higher than peak frequency wave motion. The effect of geometry characters of fringing reef and focusing position on the maximum horizontal force on the vertical wall is investigated utilizing the validated OpenFOAM model.

Modeling Green Water Load on a Deck Mounted Circular Cylinder

Abstract This article uses scaled physical and numerical modeling to investigate an idealized but complicated problem in which green water impacts a circular cylindrical structure located on top of a fixed box representative of a vessel. A focused wave group was used to overtop the box and generate the green water event, which resembled a plunging wave with air entrainment. The plunger collapsed and ran across the deck before impacting and then scattering from the cylinder. To test the adequacy of the physical modeling, nominally identical experiments were conducted in two different laboratories, in different countries. The numerical modeling comprised computational fluid dynamics (CFD) simulations performed using openfoam. The flow features, the force on the cylinder, and the surface elevation on top of the box are compared in detail across the two physical models and the CFD. Consistent load measurements were obtained from the two physical model tests, with force impulse results differing by less than 10%, underscoring the validity of the results, even accounting for the complexity of flow–structure interactions. A comparison with numerical model results reveals some sensitivity to experimental precision in the flow measurements on top of the box and the green water load. Nonetheless, the overall force impulse discrepancy between experiments and numerical models is within 15%, highlighting that the robustness of the methods was used despite these sensitivities. The sensitivity to CFD mesh and iterating the incident wave to match CFD and experiment are also explored. The agreement between experiment and CFD serves as an example of the utility of CFD for modeling green water loads.

The influence of spectral bandwidth and shape on deep-water wave breaking onset

Deep-water surface wave breaking affects the transfer of mass, momentum, energy and heat between the air and sea. Understanding when and how the onset of wave breaking will occur remains a challenge. The mechanisms that form unforced steep waves, i.e. nonlinearity or dispersion, are thought to have a strong influence on the onset of wave breaking. In two dimensions and in deep water, spectral bandwidth is the main factor that affects the roles these mechanism play. Existing studies, in which the relationship between spectral bandwidth and wave breaking onset is investigated, present varied and sometimes conflicting results. We perform potential-flow simulations of two-dimensional focused wave groups on deep water to better understand this relationship, with the aim of reconciling existing studies. We show that the way in which steepness is defined may be the main source of confusion in the literature. Locally defined steepness at breaking onset reduces as a function of bandwidth, and globally defined (spectral) steepness increases. The relationship between global breaking onset steepness and spectral shape (using the parameters bandwidth and spectral skewness) is too complex to parameterise in a general way. However, we find that the local surface slope of maximally steep non-breaking waves, of all spectral bandwidths and shapes that we simulate, approaches a limit of$1/\tan ({\rm \pi} /3)\approx 0.5774$. This slope-based threshold is simple to measure and may be used as an alternative to existing kinematic breaking onset thresholds. There is a potential link between slope-based and kinematic breaking onset thresholds, which future work should seek to better understand.

EXPERIMENTAL AND NUMERICAL STUDY ON OBLIQUE WAVE-IN-DECK LOADS

Most studies on wave-in-deck loads focus on head-on wave impingement whereas wave-in-deck loads due to waves incident from oblique directions are rarely reported. Numerical simulations for oblique wave-in-deck loads were presented in Iwanowski et al. (2002), Brodtkorb (2008) and Chen et al. (2018). However, in these studies, only numerical validations were performed against either two-dimensional experiments or empirical formulations due to a lack of experimental results. In light of this, we present the experimental results for wave impacts on a solid deck model due to a transient focused wave group incident from oblique direction in this study. The oblique experimental data is compared with the head-on counterpart by Santo et al, (2020) to investigate the incident wave angle effect on wave-in-deck loads. Numerical simulations are carried out to reproduce both the head-on and oblique wave-in-deck experiments using a three-dimensional (3D) numerical wave tank (NWT), and flow field information is interrogated to derive physical insights into complex wave-deck interactions. The solid deck model is a representative of a typical 2nd generation North Sea topside structures commonly exposed to severe winter weather. The configuration is also applicable to coastal structures such as bridges, piers, jetties or docks.

Influences of Floater Motion on Gap Resonance Triggered by Focused Wave Groups

Influences of Floater Motion on Gap Resonance Triggered by Focused Wave Groups

Nonlinear computation for focused wave groups on abrupt depth transitions

Focused wave groups in intermediate water depth propagating over varying abrupt depth transitions are studied numerically and experimentally. The experiments well validate the fully nonlinear model by a conformal mapping method. The generation of second-order and third-order harmonics is observed near the top of the submerged step, as well as the decrease of the main (first-order) components propagating along with the step. In addition, an enhancement of kurtosis occurs just after the step with a high-trailed profile, revealing a considerable asymmetry of the surface elevations. In addition, a wave group passing two or three steps is also investigated numerically. More submerged obstacles effectively strengthen the reflection capability in terms of the reflection coefficients computed with the amplitude of wave envelopes. Although the harmonics manifest a higher risk of extreme waves on abrupt depth transitions, the increase of water depth changes might not further enhance the maximum skewness and kurtosis over the varying bottom.

Physical and numerical modelling of extreme wave conditions

This paper presents the results of an experimental and numerical investigation into the generation of realistic model scale extreme waves for survivability testing of offshore structures. The objective of this investigation was to develop a numerical method to accurately model the maximum wave height (Hmax) and wave spectrum of a realistic focused wave group that was embedded into an irregular sea state. The sea state selected for this investigation was based on extreme conditions recorded during a Tropical Cyclone. The sea state was experimentally modelled using NewWave theory and was subsequently replicated in a computational fluid dynamics (CFD) numerical wave tank. The wave component amplitudes and phase angles were derived from the experimental data, which were then used to generate a polychromatic wave in CFD. The NewWave formula was then modified by applying an exponential function which intended to explicitly amplify the largest waves in the wavefield while applying minimal amplification to the remainder of the waves. This technique reduced the difference between the experimental and numerical Hmax while maintaining a level of spectral similarity. The methodologies presented in this paper are appropriate for modelling realistic extreme sea states for model scale survivability testing of offshore structures.

A two-layer viscous Boussinesq-type model for surface waves: Derivation, analysis, numerical implementation, and verification

A two-layer viscous Boussinesq-type model is developed to simulate the wave energy dissipation during wave propagation in deep water. The viscous terms are incorporated into both the dynamic and kinematic boundary conditions at the free surface, and the corresponding analytical solution of the second-order amplitude has been derived for the first time. The linear and nonlinear properties of the model are analyzed with different viscosity coefficients. When the viscosity coefficient is 1 × 10−4 m2/s, the linear phase velocity, decay rate, second-order amplitude, and velocity profiles of the viscous model are accurate for up to h/L0 (h is water depth, L0 is characteristic wavelength) ≈ 8.66, 5.86, 3.60, 3.60, and 7.51 within 1% error, respectively. The finite difference method is adopted for the numerical implementation of the model. To verify the linear and nonlinear properties of the model, computed results for linear waves and focused wave group in deep water are compared with linear analytical solutions and experimental data, respectively.