Wave-structure Interaction Research Articles

A double-layer non-hydrostatic model for simulating wave-structure and wave-jet interactions

Waves are pivotal factors in coastal areas, and effective simulation of wave-related phenomena is crucial. This paper presents the extension of the non-hydrostatic model from single-layer σ transformation to double-layer σ transformation in order to stabilize submerged structures and jet orifices under wave environment. The Lagrangian-Eulerian method is adopted for tracking the free surface in this model. This updated model is validated through comparisons against a series of test cases, including wave structure interaction and horizontal jet under waves. A good agreement between the model results and experimental data is achieved, demonstrating the capability of the developed model to fix the submerged object to resolve wave-structure and wave-jet interactions. Thus, the proposed double-layer σ model can be seen as a useful tool to simulate problems in coastal dynamics.

Spatial variations in numerical wave tanks with active wave generating–absorbing system

Wave–structure interaction can be investigated in detail by numerical experiments, such as Navier–Stokes solvers with Volume Of Fluid models to capture the free surface. The quality of the wave field in such Numerical Wave Tanks largely depends on the boundary conditions to generate or/and absorb the waves. In case of regular waves, instead of obtaining a uniform wave field throughout the wave tank, spatial variations in crest height and trough depth are found with beat lengths smaller than the wave length. In this paper, three different wave absorbing boundary conditions are investigated for their effects on the wave field uniformity: the Original Sommerfeld Boundary Condition, a Generalized Sommerfeld Boundary Condition, and a method including Relaxation Zones. An extensive analysis, involving the decomposition of the waves into incident and reflected waves at first order and higher order harmonics is required to explain the phenomenon of spatial variations. It is concluded that Relaxation Zones provide the most spatially uniform wave fields, at the cost of larger computational domains. The spatial variations in the Original and Generalized Sommerfeld Boundary Conditions are found to also be contributed from the superposition of the second order incident bound waves and the second order reflected free waves. This effect is found to be more significant for steeper waves. A graded mesh method at the absorbing side of the tanks is proposed to minimize the spatial variations.

Faster than real-time, phase-resolving, data-driven model of wave propagation and wave–structure interaction

A machine learning time-series prediction approach is proposed for wave propagation and wave load prediction. Under unidirectional wave conditions and variable bathymetry, given a wave gauge upstream, a model is shown to reproduce wave elevation or wave forces downstream under irregular steep and either non-breaking or breaking conditions. Attempts to perform the opposite calculation, predicting upstream conditions from downstream measurements, results in higher error, likely due to information loss under breaking conditions. For choice of machine learning approach, comparisons show that the Time-series Dense Encoder (TiDE) approach results in a good balance between model complexity, stability, computational time, and error. Over a flat bottom, time-series of wave elevation can be predicted up to 10 wavelengths away, though with a degraded accuracy compared to shorter distances. Similar results are shown for time-series of forces on a vertical cylinder, showing better results than a simple Morison approach, as used in engineering tools such as OpenFAST, but with a similarly fast computational time. Generalizations show that training on irregular wave data permit extrapolations to periodic wave cases. Finally, the same method also is also demonstrated at field-scale, comparing results between two offshore buoys.

Experimental analysis of wave–structure interaction for very large modular floating structures

Very large floating structures represent a relatively new frontier in offshore engineering, offering diverse opportunities for ocean utilization and management. These structures, characterized by their sizable dimensions and relatively low bending stiffness, are often constructed modularly and connected flexibly. Consequently, studying very large modular floating structure (MFS) requires considering both multibody hydrodynamics and connector dynamics. This study experimentally investigates the hydrodynamic behavior of MFS in waves, examining configurations ranging from a single module to three modules, with the measurements of their motions and deformations. Various wavelengths are considered, and the wave-induced loads on the hinge connections between floating modules are also recorded. Results show that attaching additional modules to an existing module decreased surge responses, while heave and pitch responses remained relatively unaffected. Examination of wave-induced deformations reveals that maximum deformations occur when the wavelength approximated the module length, consistent with hogging and sagging phenomena. Notably, the middle module experienced the most pronounced deformations due to constraints from both front and rear modules. Furthermore, the analysis of forces exerted on hinge joints reveals strong nonlinear characteristics. Forces at different harmonic components varied with wavelength, with the contribution from higher harmonics posing a risk of fatigue damage to the connectors. Serving as an experimental benchmark, these results contribute to the development and validation of numerical methods and offer guidance for the structural design of hinged connectors in floating bodies.

Time-domain simulation of nonlinear motions of moored floating body in irregular waves using rankine source method

This study introduces a three-dimensional time-domain Indirect Boundary Integral Equation Method (IBIEM) for simulating the motion of the floating body in both regular and irregular waves. The method systematically addresses second-order wave loads, focusing on low-frequency motions induced by low-frequency wave loads, crucial for the stability of offshore structures. Unlike traditional methods, the time-domain IBIEM simplifies the analysis by simultaneously considering all wave components of irregular waves, making the calculation of nonlinear wave loads more straightforward and intuitive. An approximate second-order equation of motion is proposed, simplifying the computational process by eliminating the need for solving boundary value problems for second-order radiation forces. The IBIEM is coupled with a quasi-static mooring model based on the elastic catenary equation, accurately capturing the influence of mooring systems on the response of the floating body. Validation against model tests and established numerical methods demonstrates the accuracy of the developed code in predicting the dynamic behavior of offshore structures. Applied to various scenarios, including a truncated cylinder, the barge, H2FPSO, and K-Semi, the results show strong agreement with experimental data, confirming the reliability and effectiveness of the method in simulating complex wave-structure interactions, making it a valuable tool for offshore structure design and analysis.

Experimental decomposition of nonlinear hydrodynamic loads and hydroelastic responses in wave–structure interactions of monopile wind turbines

This study explores the nonlinear effects of hydrodynamic loads and hydroelastic responses in monopile-supported offshore wind turbines, with a focus on their harmonic structures. High-quality experimental data were collected in a shallow water basin across various irregular waves. Their harmonic components up to the fourth order were successfully isolated using a novel four-phase decomposition technique, which effectively extracts harmonics from random time series. The results highlight significant contributions of higher-order harmonics across various sea states. Specifically, two physical models were employed: a flexible monopile to capture structural hydroelastic deformations during large wave events and a rigid monopile to accurately estimate hydrodynamic loads without hydroelastic effects. Additionally, numerical results from fully nonlinear potential-flow calculations were compared, revealing that while the potential-flow solver underestimates total wave loading, especially for higher harmonics. In terms of the free-surface elevations and hydrodynamic forces, this study confirms that their higher-order harmonics align well with the scaling of their corresponding linear components in both amplitude and phase. This enables the prediction of higher-order profiles based solely on their linear components. However, this efficient model is inadequate for accurately estimating the higher-order harmonics of monopile's hydroelastic responses during these extreme wave events, highlighting the need for further refinement.

A Cartesian grid-based model for simulating wave-structure interaction problems

A Cartesian grid-based model for simulating wave-structure interaction problems

Air effects on solitary waves impinging and overtopping an impermeable seawall

Considering the presence or absence of air, the solitary waves impinging on an impermeable structure were numerically investigated to discuss solitary wave characteristics such as surface elevation, pressure, vorticity, eddy viscosity, and force on structures under different initial conditions. The volume of fluid (VOF) model (Wu, 2004) was employed to simulate solitary waves impinging an impermeable structure. Besides, the LES turbulent module was utilized to capture the turbulent phenomenon generated by wave-structure interactions, particularly after wave breaking. The present model was verified by comparing the simulation results with the experimental data (Hsiao and Lin, 2010). The findings demonstrated that the model more accurately represents tsunami wave behavior compared to simulations that did not account for air, especially in cases where wave breaking occurs prior to overtopping, entraining more air into the water. Detailed comparisons between simulations with and without air presence reveal that simulations excluding air exhibited delayed wave breaking, a more distant breaking point, and the absence of an air pocket behind the seawall. Despite these differences, the simulations showed excellent agreement with the laboratory results. Moreover, it was shown that the presence of air dissipated part of wave energy. Earlier the stage of waves broke, the more air was entrained, making the effects of air on the waves more noticeable. The highest fluid velocity was observed at the breaking point in front of the structure, while the strongest forces were experienced by the structure at the breaking location behind it.

Numerical and Experimental Power Output Estimation for a Small-Scale Hinged Wave Energy Converter

Wave energy converters (WECs) integrated into breakwaters present a promising solution for combining coastal protection with renewable energy generation, addressing both energy demands and environmental concerns. Additionally, this integration offers cost-sharing opportunities, making the overall investment more economically viable. This study explores the potential of a hinged point-absorber WEC, specifically designed as a floating hinged half-sphere, by assessing the device’s power output and comparing two different breakwater configurations. To evaluate the device’s performance, a comprehensive numerical and experimental approach was adopted. Numerical simulations were carried out using a radiation-diffraction model, a time domain tool for analyzing wave–structure interactions. These simulations predicted average power outputs of 25 kW for sloped breakwaters and 18 kW for vertical breakwaters located at two strategic sites: the Port of Leixões and the mouth of the Douro River in Portugal. To validate these predictions, a 1:14 scale model of the WEC was constructed and subjected to testing in a wave–current flume, replicating different sea-state conditions. The experimental results closely aligned with the numerical simulations, demonstrating a good match in terms of relative error and relative amplitude operator (RAO). This alignment confirms the reliability of the predictive model. These findings support the potential of integrating WECs into breakwaters, contributing to port energy self-sufficiency and decarbonization.

Multi-dimensional modeling of solitary wave–structure interaction problems by using a [formula omitted]-LES-SPH model

The interaction mechanisms between waves and marine structures are a popular research topic. This paper applies the weakly compressible smoothed particle hydrodynamics (WCSPH) method to study the dynamics of green water overtopping. To enhance the accuracy of the simulations, the SPH method coupled with the large eddy simulation (LES) model is employed for numerical investigations. Initially, we validate the effectiveness of the model by simulating the generation of solitary waves and irregular waves, as well as numerically reproducing the water surface morphology during the interaction between solitary waves and the deck. Subsequently, the validated model is used to study the dynamic characteristics of different types of waves overtopping, revealing significant variations in their motion. Furthermore, we investigate the effect of deck roughness during the entire green water overtopping process in terms of both protrusions extent and distribution, confirming that a reasonable setting of the protrusions can greatly reduce the wave impact loads on the deck, thereby protecting the structure. Additionally, a three-dimensional model is developed to study the green water problem, and we find that the turbulence phenomenon is more pronounced in the three-dimensional scenario.

The past, present and future of multi-scale modelling applied to wave-structure interaction in ocean engineering.

Concepts and evolution of multi-scale modelling from the perspective of wave-structure interaction have been discussed. In this regard, both domain and functional decomposition approaches have come into being. In domain decomposition, the computational domain is spatially segregated to handle the far-field using potential flow models and the near field using Navier-Stokes equations. In functional decomposition, the velocity field is separated into irrotational and rotational parts to facilitate identification of the free surface. These two approaches have been implemented alongside partitioned or monolithic schemes for modelling the structure. The applicability of multi-scale modelling approaches has been established using both mesh-based and meshless schemes. Owing to said diversity in numerical techniques, massively collaborative research has emerged, wherein comparative numerical studies are being carried out to identify shortcomings of developed codes and establish best-practices in numerical modelling. Machine learning is also being applied to handle large-scale ocean engineering problems. This paper reports on the past, present and future research consolidating the contributions made over the past 20 years. Some of these past as well as future research contributions have and shall be actualized through funding from the Newton International Fellowship as the next generation of researchers inherits the present-day expertise in multi-scale modelling. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

Multi-Fidelity Learned Emulator for Waves and Porous Coastal Structures Interaction Modelling

A thorough understanding and treatment of wave-structure interaction (WSI) mechanics is essential for the rigorous engineering design of coastal protections. Conventional numerical analysis methods are accurate and generalize well, but are heavily dependent on the adopted mesh resolution and frequently incur substantial computational costs. To bypass these limitations, a meshless multi-fidelity residual neural network (MRNN) emulator is introduced in this study to infer the spatio-temporal responses arising from WSI. MRNN first employs a ‘low-fidelity’ simulator to learn basic WSI relationships by training on simulations obtained using a coarse numerical mesh. Subsequently, a ‘high-fidelity’ (HF) simulator is then employed to learn the mapping between numerical simulations performed using the coarse mesh and additional detailed fine meshes. The results indicate that MRNN is a highly robust emulator which requires significantly less HF data through its hierarchical framework compared to conventional single-fidelity data-driven strategies. By way of example, the MRNN emulator is applied to the cases of a porous dam break and breakwater. A broad spectrum of WSI responses, such as water through the porous dam medium, can be accurately captured using the MRNN emulator which is benchmarked against a conventional numerical modelling with a fine mesh. The computational efficiency of the MRNN is shown to be independent of the mesh resolution and complexity of the studied partial differential equations. It provides a generic and utilitarian emulator for any engineering problem of interest.

The influence of wave modelling on the motions of floating bodies

In recent years OpenFOAM studies have focused on pure wave modelling and wave-structure interaction. Considering that there is a lack of transparency concerning effects of different motion modelling settings in OpenFOAM, this paper presents the influence of different numerical setups on the accurate modelling of wave-induced motions. This is achieved by applying the interFoam solver included in OpenFOAM-v2206 with the waves2Foam toolbox. The optimal numerical setup is studied with a two-dimensional box-like ship idealisation heaving in varying wave lengths while the wave steepness remains constant. Different numerical setups are considered for accurate wave modelling, the modelling of wave excitation forces for the case of a static structure, and heave motion modelling. Finally, the optimal setup that is found is applied for a 3D ship case in head waves with heave and pitch coupling. As far as practically possible, the results are validated against experimental data. It is shown that strict requirements for mesh density and time step for accurate wave modelling result in accurate excitation force and motion results. Reflections from the relaxation zones and different mesh density layers cause inaccuracies. It is concluded that simple numerical cases are suitable for studying optimal numerical setups for more complex simulation cases.

Estimating metocean environments associated with extreme structural response to demonstrate the dangers of environmental contour methods

Extreme value analysis (EVA) uses data to estimate long-term extreme environmental conditions for variables such as significant wave height and period, for the design of marine structures. Together with models for the short-term evolution of the ocean environment and for wave–structure interaction, EVA provides a basis for full probabilistic design analysis. Alternatively, environmental contours provide an approximate approach to estimating structural integrity, without requiring structural knowledge. These contour methods also exploit statistical models, including EVA, but avoid the need for structural modelling by making what are believed to be conservative assumptions about the shape of the structural failure boundary in the environment space. These assumptions, however, may not always be appropriate, or may lead to unnecessary wasted resources from over design. We demonstrate a methodology for efficient fully probabilistic analysis of structural failure. From this, we estimate the joint conditional probability density of the environment (CDE), given the occurrence of an extreme structural response. We use CDE as a diagnostic to highlight the deficiencies of environmental contour methods for design; none of the IFORM environmental contours considered characterise CDE well for three example structures.

Prototype-scale laboratory observations of wave force reduction by an idealized mangrove forest of moderate cross-shore width

A prototype-scale physical model was used to study wave height attenuation through an idealized mangrove forest and the resulting reduction of wave forces and pressures on a vertical wall. An 18 m transect of a Rhizophora forest was constructed using artificial trees, considering a baseline and two mangrove stem density configurations. Wave heights seaward, throughout, and shoreward of the forest and pressures on a vertical wall landward of the forest were measured. Mangroves reduced wave-induced forces by 4%–43% for random waves and 2%–38% for regular waves. For nonbreaking wave cases, the shape of the pressure distribution was consistent, implying that the presence of the forest did not change wave-structure interaction processes. Analytical methods for determining nonbreaking wave-induced loads provided good estimations of measured values when attenuated wave heights were used in equations. The ratio of negative to positive force ranged between 0.14 and 1.04 for regular waves and 0.31 to 1.19 for random waves, indicating that seaward forces can be significant and may contribute to destabilization of seawalls during large storms. These results improve the understanding of wave-vegetation-structure interaction and inform future engineering guidelines for calculating expected design load reductions on structures sheltered by emergent vegetation.

Acceleration of a wave-structure interaction solver by the Parareal method

Potential flow theory-based solvers are commonly used in ocean engineering to investigate the interactions between ocean waves and floating bodies. Depending on assumptions, several methods have been proposed. Among them, the Weak-Scatterer method is an interesting trade-off in the sense that this approach is not limited in theory by the small wave amplitudes and small body motions assumptions of linear methods. Moreover, this approach is in practice more stable than the fully non-linear methods. An implementation of the Weak-Scatterer method is the WS-CN code (Letournel, 2015; Chauvigné, 2016; Wuillaume, 2019).The computational time of the WS-CN code which is considered in the present study is relatively long for engineering purposes. In order to reduce it, the present paper presents an implementation of the Parareal method in the WS-CN code. The Parareal method is an algorithm for parallelizing a simulation in time that can accelerate the complete simulation (Lions, 2001) . This is a key difference in comparison to other acceleration techniques which have been studied in the literature (e.g. the Fast Multipole Method (FMM), the precorrected Fast Fourier Transform (pFFT) method, … ). To the authors’ knowledge, the present study is the first to couple the Parareal method to a potential flow theory-based wave-structure interaction solver. It is shown that the method can significantly reduce the computational time for small wave steepness, but that the performance decreases rapidly with increasing steepness.

Semi-analytical approach to study wave interaction with a pair of obliquely submerged heterogeneous flexible structures

ABSTRACT Analyzing inclined flexible plates of varying thickness is crucial for optimising and attaining precise control over wave reflection and transmission. This is particularly significant in the context of breakwater construction. In contrast to horizontal breakwaters, inclined barriers can penetrate multiple layers of fluid with varying particle velocities, facilitating interactions and causing wave breaking, which results in the dissipation of wave energy. Moreover, compared to vertical structures, inclined ones demonstrate more effective wave attenuation. In the context of the present study, we investigate the interaction of water waves with a pair of obliquely submerged flexible thin plates characterised by non-uniform thickness. In order to model this complex physical scenario, we employ the principles of linear water wave theory in conjunction with Kirchhoff's thin plate theory. By employing repeated integration and Green's integral theorem, we reduce the boundary value problem to a system of coupled integral equations. Through appropriate approximations, we solve this system and obtain numerical values for various hydrodynamic quantities. This model provides comprehensive results for both horizontal and vertical plates, making it highly versatile. We examine the impact of varying thickness and the inclination of the two flexible plates to understand their roles in the wave scattering process and the associated physical parameters. The results obtained from this study shed light on the intricate dynamics involved in wave-structure interactions and can inform the design and optimisation of breakwater systems.

Wave–structure interaction by a two–way coupling between a fully nonlinear potential flow model and a Navier–Stokes solver

A two-way domain decomposition coupling procedure between a fully nonlinear potential flow model and a Navier–Stokes solver capturing the free surface with a Volume of Fluid method is used to study wave–structure interaction applied to offshore wind turbines. Away from the structure, the large-scale inviscid wave field is modeled by the potential code. Wave generation and absorption in this 3D hybrid model take place in the outer potential domain. The codes exchange data in the region around their common boundaries. Through the two-way coupling, waves propagate in and out of the viscous subdomain, making the hybrid algorithm suitable to study wave diffraction on marine structures, while keeping the viscous subdomain small. Each code uses its own mesh and time step. Subdomains are overlapping, therefore continuity conditions on velocity and free surface have to be verified on two distinct coupling surfaces at any time. Parallel implementation with communications between the models relying on the Message Passing Interface library allows calculations on large spatial and temporal scales. The coupling algorithm is first tested for regular nonlinear waves and then applied to simulate wave loads exerted on a vertical monopile in 3D. Attention is paid to the high-order components of the horizontal force.

Evaluation of the Hydrodynamic Properties and Performance Efficiency of a Three-Row Permeable Vertical Breakwater

Coastal protection structures reduce risks and economic losses by eliminating coastal erosion, wave damage, and flooding. Fixed breakwaters are used along the coast but are often inappropriate due to their negative environmental impact. Permeable breakwaters resemble a row of breakwaters with continuous walls and are proposed as a more environmentally friendly alternative. The wave-structure interaction and flow behavior of this type of breakwater are more complex but must be analyzed before designing it. This study develops a mathematical model of wave interaction with a permeable three-row vertical breakwater based on the least squares method. Comparison with experimental measurements of the reflection, transmission, and dissipation coefficients shows that the mathematical model adequately reproduces most of the important features of the results. This study provides a deeper understanding of the hydrodynamic performance of a permeable three-row vertical continuous wall breakwater.

Floating wind turbine response in uni- and multi-directional nonlinear waves by numerical and experimental investigations

Natural sea waves are typically multi-directional. However, the existing studies on the interaction of waves and structures mostly concentrate on uni-directional waves. In this study, using a higher-order boundary element method based on the nonlinear potential flow theory and the perturbation expansion technique, a numerical model is developed to investigate the hydrodynamic performance of a semi-submersible wind turbine foundation in uni- and multi-directional waves. Comprehensive validations with the wave-tank experiment are conducted. It is found that the significant platform response increases with the peak wave period in uni-directional irregular waves, while the high-frequency “energy” ratio changes little. The significant wave height hardly influences motion responses from either the time- or the frequency-domain perspective. In multi-directional irregular waves, the translational motions exhibit monotonicity with wave directionality. The energy concentration around the primary direction leads to a dominant wave-frequency motion and an increase in the high-frequency “energy” ratio. Although the individual modal motion responses are variable functions of wave nonlinearity, their averaged translational and rotational motions are nearly constant, indicating an energy transition or a trade-off relationship among the modal motions. In addition, unlike the uni-directional wave case, the low- and high-frequency “energy” ratios increase quadratically and decrease linearly with the significant wave height in multi-directional waves, respectively. All these findings demonstrate that wave directionality can change the wave–structure interaction properties and therefore needs to be adequately considered in engineering applications.