Wave-induced Forces Research Articles

Fluid–structure interaction analysis of a piezoelectric wave energy converter positioned at the wave surface

The hydroelastic effects of an elastic plate and its piezoelectric characteristics under wave forces are examined in this study. The hydroelastic analysis models fluid motion and hydrodynamic pressure using viscous flow theory, solved through a combination of the Reynolds–averaged Navier–Stokes equations, the continuity equation, and the shear stress transport turbulence model. The finite element method is employed both to solve the hydroelastic motion of the plate and to calculate the static electric field. Unlike previous studies where the piezoelectric plate was fully submerged in water, this work places the plate on the wave surface. This approach serves two purposes: to increase the static pressure difference between the upper surface and lower surface of the plate and to amplify the wave-induced forces. A detailed analysis of strain energy, plate deformation, and electric voltage distribution is also presented.

Kinematics of nonlinear waves over variable bathymetry. Part I: Numerical modelling, verification and validation

Fluid particle kinematics due to wave motion (i.e. orbital velocities and accelerations) at and beneath the free surface is involved in many coastal and ocean engineering applications, e.g. estimation of wave-induced forces on structures, sediment transport, etc. This work presents the formulations of these kinematics fields within a fully nonlinear potential flow (FNPF) approach. In this model, the velocity potential is approximated with a high-order polynomial expansion over the water column using an orthogonal basis of Chebyshev polynomials of the first kind. Using the same basis, original analytical expressions of the components of velocity and acceleration are derived in this work. The estimation of particle accelerations in the course of the simulation involves the time derivatives of the decomposition coefficients, which are computed with a high-order backward finite-difference scheme in time. The capability of the numerical model in computing the particle kinematics is first validated for regular nonlinear waves propagating over a flat bottom. The model is shown to be able to predict both the velocity and acceleration of highly nonlinear and nearly breaking waves with negligible error compared to the corresponding stream function wave solution. Then, for regular waves propagating over an uneven bottom (bar-type bottom profile), the simulated results are confronted with existing experimental data, and very good agreement is achieved up to the sixth-order harmonics for free surface elevation, velocity and acceleration.

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.

Numerical Study of Hydrodynamic Characteristics of a Three-Dimensional Oscillating Water Column Wave-Power Device

The impact of wave-induced forces on the integrity of stationary oscillating water column (OWC) devices is essential for ensuring their structural safety. In our study, we built a three-dimensional numerical model of an OWC device using the computational fluid dynamics (CFDs) software OpenFOAM-v1912. Subsequently, the hydrodynamic performance of the numerical model is comprehensively validated. Finally, the hydrodynamic performance data are analyzed in detail to obtain meaningful conclusions. Results indicate that the horizontal wave force applied to the OWC device is approximately 6.6 to 7.9 times greater than the vertical wave force, whereas the lateral wave force is relatively small. Both the horizontal and vertical wave forces decrease as the relative water depth increases under a constant wave period and height. In addition, the highest dynamic water pressure is observed at the interface between the water surface and device, both within and outside the front wall of the gas chamber. The dynamic water pressure at different locations on the front chamber increases and subsequently decreases as the wave frequency increases.

Analysis of floating platform-mooring system-pile-soil interactions under wave loadings: A case study of the triangle-shaped semi-submersible platform

The floating platform-mooring system-pile-soil interactions under wave loadings represent a complex yet understudied aspect of floating offshore wind turbines (FOWTs). This paper presents the development and application of an Incompressible Material Point Method-Finite Element Method-Material Point Method (IMPM-FEM-MPM) model to simulate these interactions for a triangle-shaped semi-submersible platform (Tri-SSP), which serves as the foundation of China's first deep-sea FOWT, named ‘Fuyao.’ The proposed model is validated by studying the hydrodynamic responses of the OC4-DeepCwind platform. Under regular waves, increasing wave heights lead to heightened motion amplitudes, with the Tri-SSP exhibiting distinct phase differences between surge, pitch, and heave motions. Anchor Group 1 experiences significant peak tensions, ranging from 2.26 MN to 4.47 MN, which influence soil displacement, shear forces and bending moments along the pile shaft, emphasizing the impact of wave loading on pile-soil interactions. Under 1-h irregular waves, tension in Anchor Group 1 reaches extreme levels, with tensions up to 8 MN observed, underscoring the critical role of mooring systems in mitigating wave-induced forces. The calculated maximum stress within the pile indicates the structural integrity of the DH36 steel pile under these conditions. Comparisons of hydrodynamic responses, both with and without pile-soil interactions, show minimal discrepancies in motion amplitudes, indicating a minor influence on the dynamics of the platform and mooring system. These findings contribute to the understanding of complex interactions in deep-sea FOWTs, informing design and operational strategies for enhanced stability and performance.

A physical model study on the hydraulic performances of vertical breakwaters with retreated wave walls

This paper describes a 2D physical model study on the hydraulic performances of composite vertical breakwaters with retreated wave walls. The research is an expansion of a previous experimental study by the same Authors: a very large number of experiments, in the order of 2,000, have been carried out by exploring and varying a wide range of wave and geometrical parameters of the structure, to investigate their effect and importance. In order to make feasible the execution of this large number of tests, a small-scale wave flume was used and regular wave conditions were reproduced. The influence of the wave wall retreat has been investigated in terms of wave-induced forces, reflection coefficients and wave overtopping discharges, comparing the hydraulic performances of structures with retreated walls with those of a flushed wall configuration under the same wave conditions. The large number of experiments allowed to formulate a detailed description of the complex phenomena at hand, providing statistical indicators that can be used as guidelines for preliminary design purposes of such structures, quantifying the relevant sources of uncertainty. The analysis confirmed and extended the previous findings and indicates that, on average, the hydraulic performances of structures with retreated crown wall vary significantly from those of flushed wall configurations. Specifically: (I) the forces acting on the wave wall increase of a factor up to 1.5, due to the occurrence of impulsive loads; (II) the forces acting on the caisson trunk decrease of a factor up to 0.91; (III) the global forces can decrease reaching a minimum reduction factor of 0.87, although some dangerous exceptions, in which equal or larger loads, than those occurring for standard flushed wall configuration, have been registered; (IV) the reflection coefficients decrease of a factor up to 0.83; (V) the wave overtopping discharges increase up to 2.55 times those with flushed walls.

Non-Hermitian non-equipartition theory for trapped particles

The equipartition theorem is an elegant cornerstone theory of thermal and statistical physics. However, it fails to address some contemporary problems, such as those associated with optical and acoustic trapping, due to the non-Hermitian nature of the external wave-induced force. We use stochastic calculus to solve the Langevin equation and thereby analytically generalize the equipartition theorem to a theory that we denote the non-Hermitian non-equipartition theory. We use the non-Hermitian non-equipartition theory to calculate the relevant statistics, which reveal that the averaged kinetic and potential energies are no longer equal to kBT/2 and are not equipartitioned. As examples, we apply non-Hermitian non-equipartition theory to derive the connection between the non-Hermitian trapping force and particle statistics, whereby measurement of the latter can determine the former. Furthermore, we apply a non-Hermitian force to convert a saddle potential into a stable potential, leading to a different type of stable state.

Analysis of Wave-Induced Forces on a Floating Rectangular Box with Analytical and Numerical Approaches

A three-dimensional mathematical hydrodynamic model associated with surface wave radiation by a floating rectangular box-type structure due to heave, sway, and roll motions in finite water depth is investigated based on small amplitude water wave theory and linear structural response. The analytical expressions for the radiation potentials, wave forces, and hydrodynamic coefficients are presented based on matched eigenfunction expansion method (MEFEM). The correctness of the analytical results of wave forces is compared with the construction of a numerical model using the open-source boundary element method code NEMOH. In addition, the present result is compared with the existing published experimental results available in the literature. The effects of the different design parameters on the floating box-type rectangular structure are studied by analyzing the vertical wave force, horizontal wave force, torque, added mass, and damping coefficients due to the heave, sway, and roll motions, and the comparison analysis between the forces is also analyzed in detail. Further, the effect of reflection and transmission coefficients by varying the structural width and drafts are analyzed.

Hydrodynamic coefficients of mussel dropper lines derived from large-scale experiments and structural dynamics

The expansion of marine aquaculture production is driven by a high market demand for marine proteins and a stagnation of wild catch of fish. Bivalve farming, i.e., the cultivation of oysters, mussels and scallops, is an important part of the ongoing market dynamics and production expansion. As marine spatial planning is considering various use purposes, available space for near-shore aquaculture is already becoming scarce; this has fueled research and development initiatives to enable production installations further offshore. The highly energetic conditions at more exposed offshore marine sites lead to increased loads on aquaculture systems and their components and it is still not sufficiently understood how the load transfer from oceanic environmental conditions onto shellfish-encrusted surfaces attached to elastic ropes may be appropriately quantified. This study data gathered large-scale data sets in a wave tank facility, which are used to validate a novel, numerical model, building on the dynamics of rope structures which allows for the determination of the hydrodynamic loads transferred to the dropper lines. The forces and hydrodynamic parameters are measured and numerically analyzed. Based on the results, drag and inertia coefficients are determined. A drag coefficient of CD=1.1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_\ extrm{D} = 1.1$$\\end{document} and an inertia coefficient of CM=1.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_\ extrm{M} = 1.7$$\\end{document} are recommended to model shellfish-encrusted dropper lines exposed to oscillatory flows with KC =\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$=$$\\end{document} 40–90. The numerical model for the determination of wave-induced forces on mussel dropper lines is developed and validated using the experimental data. It employs a modified Morison equation, which takes into account the displacement of the mussel dropper line. The influence of varying aquaculture-related parameters is discussed by applying the numerical model. Based on the gathered insights, recommendations can be given from an engineering point of view concerning the optimal placement of mussel aquaculture within the water column.

Wave forces and moments on concave and vertical front caissons supported on piles

ABSTRACT The present paper details the total wave-induced forces and moments on the circular cum parabola shape (CPS-PSB) and vertical front pile-supported breakwaters (VF-PSB) through a comprehensive experimental investigation under intermediate to deep water conditions. The model was subjected to the action of random waves with peak wave periods ranging from 1s to 2.6s. The total wave forces and moments were measured using a six-component force balance. VF-PSB experiences maximum wave force at lower submergence and the vertical force decreases exponentially as relative depth increases. In the case of CPS-PSB, the variation of vertical force with relative depth is similar to the energy loss. The horizontal wave forces on both PSB models decrease with their relative submergence as the wave exposure frontal area. The induced moments are higher for longer waves and higher submergence. CPS-PSB experiences lesser force and moment than VF-PSB.

Wave interaction with a rigid porous structure under the combined effect of refraction–diffraction

Water wave scattering, trapping, and generation by a thin porous structure placed on an uneven bottom are studied approximately. The classical eigenfunction expansion method is employed for the uniform bottom, whereas the Galerkin-Eigenfunction expansion method is employed for the uneven bottom. The solution is derived in the form of a system of algebraic equations through matching procedure. Wave reflection, transmission, and wave-induced forces on the porous structure and backwall are investigated under the combined refraction–diffraction effect. In the scattering problem with periodic bottom, Bragg resonance is minimized at the Bragg frequency, whereas the porous structure at other frequencies maximizes wave reflection. Consequently, wave transmission is very low for all wave frequencies in this situation. In the wave trapping problem, forces on the porous structure and the backwall are reduced substantially when the water depth ratio decreases. Feasible locations of the porous structure are shown at which wave reflection and forces on it and backwall are optimized. In the wave generation problem, the comparison of results for flat and uneven bottoms reveals that waves have a smaller amplitude at infinity as uniform bottom levels become farther for relatively small values of the reciprocal of the wave-effect parameter (C).

Predictive capabilities of data-driven machine learning techniques on wave-bridge interactions

To explore coastal bridge safety subjected to extreme waves during coastal natural hazards, numerical simulations that combine finite element methods and experimental data have been recognized as effective in computing wave-induced loads on coastal bridges. However, the structural design and performance assessment for bridge networks require laborious efforts and massive computational resources to account for uncertain scenarios. To provide reliable wave force estimation tools and facilitate the associated risk assessment, this study performs a hydrodynamic experiment on the wave-bridge interactions and develops data-driven Long-Short-Term-Memory (LSTM) Machine Learning (ML) models for time series forecasting of wave forces. Specifically, a 1:30 scale bridge superstructure specimen is used for the wave test in the wave channel. Different solitary wave and regular wave conditions are tested. Time histories of wave profiles, wave-induced forces, and pressures are measured and served as a dataset basis for the training of LSTM models. High-performance LSTM prediction models are developed through the tuning of different hyperparameters. The well-trained models have high accuracy and could predict the wave force time series based on the excitation wave profiles in seconds. It is envisioned that LSTM models could provide more reliable estimations with the development based on more data sources, providing a fast path for structural design, analysis, and maintenance.

Short-term analysis of extreme wave-induced forces on the connections of a floating breakwater

In the design of floating breakwaters, assessment of the extreme wave-induced loads on the connections, their weakest element, is required to ensure structure survival. This case study provides guidelines for estimating the extreme wave-induced forces on the connections of a floating breakwater. A Boundary Element Method (BEM) solver was applied to obtain the time-domain response of an array of five pontoons anchored to the sea bottom with elastic mooring lines. The hydrodynamic behaviour of the structure was assessed for short-duration sea states with different wave peak periods and oblique wave directions. Two peak selection criteria were applied to obtain force distributions, and several different probability density functions (PDF) were fitted to the resulting data. The extreme wave-induced forces on every connection and sea state were estimated for two different exceedance levels during a typical 3-h sea state. Based on the results, combination of the Peaks Over Threshold (POT) method and generalized Pareto distribution results is proposed for estimating the wave-induced design forces on the connections of floating pontoon breakwaters.

Interactions between Surface Waves, Tides, and Storm-Induced Currents over Shelf Waters of the Northwest Atlantic

A coupled wave–tide–circulation model is used to investigate wave–current interactions (WCIs) over the shelf waters of the Northwest Atlantic (NWA) during Hurricane Earl (2010). WCIs have substantial impacts on hydrodynamics in the upper ocean. The significant wave heights are modulated by WCIs, particularly over regions with strong current gradients, with a reduction up to ~2.1 m (20%) during the storm. Noticeable decreases in surface elevations and tidal currents occur in regions with strong tides such as the Gulf of Maine, mainly due to the wave-enhanced bottom stress. Over regions with weak tidal currents, wave effects on currents are dominated by two competitive processes between wave-induced forces and wave-enhanced mixing. The former strengthens surface currents (up to ~0.55 m/s) and increases the peak storm surge (up to ~0.48 m). The latter is responsible for the reduction in storm-induced surface currents (up to ~0.94 m/s) and anticyclonic modulation of current directions. Vertically, WCIs extend the strong vertical current shear and shift it downward during the storm, which enhances the local mixing and changes the structures of near-inertial oscillations (NIOs). Moreover, tidal currents also change the magnitudes of the NIOs and subtidal currents and affect the intensity of WCIs.

Numerical and experimental modeling of wave-induced forces on submarine pipeline buried in the soil of different engineering properties

In the present paper, the wave-induced forces on the submarine pipeline buried in porous soil having different properties are studied. The mathematical problem is solved using the higher-order boundary element method, and the numerical results are validated with experimental results obtained through rigorous model tests. Four different types of Kuwaiti marine soil: Al-Khiran, Al-Koot, Sabiya, and Shuaiba are considered in the present study. The effect of burial depth of the submarine pipeline in the soil seabed, incident wave period and wave height, and hydraulic conductivity of the soils on the wave forces acting on the submarine pipeline is analyzed in a detailed manner. The study reveals that for moderate burial depth of the pipeline in the soil bed, the wave force acting on the submarine pipeline can be reduced up to 50% for soil having less hydraulic conductivity. The measured wave forces and numerical predictions are matching well for a wide range of wave, soil and structural parameters.

Assessment of Hydrodynamic Loads on an Offshore Monopile Structure Considering Hydroelasticity Effects

Regular and irregular waves were numerically generated in a wave canal to investigate hydrodynamic loads acting on a wind turbine monopile and to predict its structural response. The monopile was implemented in the canal and modeled as a flexible structure, with the turbine blades and rotors considered as a point mass situated at the top of the monopile. Fluid–structure interaction (FSI) simulations were performed by coupling a structure solver based on a finite element method (FEM) with an unsteady Reynolds-averaged Navier–Stokes (URANS) equations solver of the finite volume method (FVM). The FSI simulations considered the two-way interaction between the deformable structure and the fluid flow. The URANS equations solver was coupled with the volume of fluid (VoF) method to account for the two-phase flow. In regular waves, numerically predicted total load coefficients occurring at the monopile’s first eigenfrequency compared favorably to experimental measurements. A deviation between calculations and measurements was observed for the total loads in irregular waves. This deviation occurred due to the smaller wave energy density of the numerically predicted irregular wave. Hydroelasticity effects increased wave-induced forces by about 6% and wave induced bending moments by about 16% in regular waves. A relatively strong whipping event was observed, which characterized the hydroelasticity response bending moment of the monopile in irregular long-crested waves. This whipping event also had a significant influence on the loads on the monopile. These investigations demonstrated the favorable use of FSI simulations to predict hydroelasticity effects on a monopile.

Wave interaction with an elliptic disc submerged in a two-layer fluid

Wave interaction with a horizontal elliptic disc submerged in a two-layer fluid is studied here assuming linear theory. An elliptic coordinate system is used to solve the three-dimensional problem analytically. The fluid region is divided into a number of subregions and by means of separation of variables, velocity potential in each region is expressed in terms of series of Mathieu and modified Mathieu functions of real argument. Matching conditions along with the orthogonal properties of eigenfunctions provide solutions for the fluid velocity potentials. Numerical results are presented for the wave-induced forces and moments. The effect of variations in the depth of submergence of the disc, angle of incidence of the incoming wave, density ratio of the fluid and aspect ratio of the disc on these physical quantities have been analyzed. In particular, sudden amplification of forces and moments have been observed at certain frequencies when the disc is situated at close proximity to the interface. Various other behaviors of the solution are investigated in some detail.

A novel ensemble model using artificial neural network for predicting wave-induced forces on coastal bridge decks

A novel ensemble model using artificial neural network for predicting wave-induced forces on coastal bridge decks

Hydrodynamic analysis of floating tunnel with submerged rubble mound breakwater

The wave interaction with a Submerged Floating Tunnel (SFT) of two different shapes (rectangular and circular) in the presence of a submerged rubble mound breakwater (SRMB) is analyzed using Multi-Domain Boundary Element Method (MDBEM). Furthermore, three typical SFT cross-sections (rectangular, trapezoidal, and circular) of equal area and structural height in the presence of SRMB under similar operating conditions are investigated as comparative study to analyse the influence of SFT shape on hydrodynamic performance. The performance of the tunnel configurations is analyzed as a (a) measurement in terms of hydrodynamic efficiency and (b) criterion for tunnel structure safety. In both shallow and intermediate water depth regions, the critical wave number and the critical angle of incidence followed by resonant wave reflection are identified, and suitable structural parameters of SRMB such as structural porosity in the armour layer, relative crest width, relative gap width between the SFT and the SRMB, structural width and position (relative draft of tunnel structure measured from the free water surface) of SFT are investigated. The present parametric investigation of SFT with SRMB reveals an improved wave transformation properties for a specific range of water depth. The coupling of SRMB has resulted not only in a reduction of wave-induced force acting on SFTs, but also in improved performance in wave transformation characteristics as a coastal protection structure, which is substantially determined by SRMB structural properties. Due to the presence of SRMB, the SFT's safety is improved, which may also add stability to the SFT. A comparative study of different distinct cross-sections of SFTs indicates that, due to its shape, the circular SFT has a reduced reflection capability and lower wave-induced force with nearly the same wave transmission as the rectangular and trapezoidal SFT. The study performed on the coupled SFT and rubble mound breakwater may be useful in determining the suitability of breakwaters not only for maintaining shore dynamics but also for protecting important floating structures for underwater transit.

Semi-analytical study of the first order horizontal force induced by oblique waves on the array of circular columns of offshore wind turbines equipped with permeable cylinders

This paper studied the incident of linear oblique waves to circular columns of offshore wind turbines in conjunction with concentric and non-concentric thin permeable cylinders. The unique research objective of this work is to assess the possibility of using permeable vertical cylinders to reduce wave forces on the column of offshore wind turbines. The developed semi-analytical method benefits from the mathematical relation between Bessel functions to express the BEM-related integrals in the Fourier modes of the Hankel function and to calculate singular integrals indirectly. Moreover, Graf's addition theorem for Bessel functions was used for shifting between different coordinate systems to avoid calculating related integrals numerically. The basic geometries parameters such as permeability parameter, cylinders arrangement and the radius of the permeable cylinders, and the wavenumber on the horizontal wave-induced force were studied. The results are presented in graphs. The results indicate that covering the columns of DeepCwind and OC3 wind turbines with the permeable cylinders or using the permeable cylinders upstream helps reduce the horizontal wave-induced force at a particular permeability parameter. The results of this research are beneficial in the design of columns of offshore wind turbines and other structures with vertical piles, such as semi-submersibles.