Regular Wave Field Research Articles

Wave-Current Interaction Effects on the OC4 DeepCwind Semi-Submersible Floating Offshore Wind Turbine

In order to investigate the hydrodynamic performances of semi-submersible type floating offshore wind turbines (FOWTs), particularly the effect of body-wave-current interaction, the OC4 FOWT is considered in the presence of co-existing regular wave and uniform current fields. The wind loads are not considered at this stage. The problem is treated in the framework of potential-flow theory in the frequency domain, assuming waves of small steepness, and the solution is obtained by using a perturbation expansion method for the diffraction potential with respect to the normalized current speed. Analytical and numerical formulations have been used to treat the inhomogeneous free-surface boundary condition involved in the hydrodynamic problem formulation for the derivation of the associated perturbation potential. The hydrodynamic loads were obtained after evaluating the pressure field around the multi-body configuration using three different computer codes. The results from the three computer codes compare very well with each other and with the numerical predictions of other investigators. Finally, the mean second-order drift forces are calculated by superposing their zero-current values with the corresponding current-dependent first-order corrections, with the latter being evaluated using a ‘heuristic’ approach.

Stochastic CFD numerical model, algorithm, and simulation on regular wave fields

This paper invites higher-order derivative numerical technology to research the stochastic characteristics in regular wave fields. The randomness of the parameters vector was incorporated during the stochastic space establishment, by which, the stochastic CFD numerical model and algorithm were developed in the study. Meantime, Taylor expansion coupled with the perturbation was also utilized to realize the investigation on the random behaviours of the regular wave fields where the perturbative values of the parameters vector included 1%, 2%, and 3%. The results indicated the merit of the stochastic CFD numerical model and algorithm in wave field research.

Investigation on cylinder water entry in regular wave field using large eddy simulation

Objects entering water into a wave instead of calm water involve complex multiphase flow phenomena. Large eddy simulation (LES) is used to numerically investigate the water entry of a small-scale cylinder in a regular wave field. A free-motion model of the cylinder is established using the sliding grid technique. The velocity boundary wave-generation method is employed, where a second-order Stokes wave analytical solution is applied at the inlet, and wave-absorbing sources are added in regions far from the water entry region. By comparison with the experimental results, the numerical scheme in this study can capture the cavity evolution, movement of the entering body, and even the closure of splashes. The influence of the four wave phases on the vertical entry and various water entry angles are investigated. The cavities are primarily influenced by the velocity field direction and wave slope in different wave phases. Based on this, a theoretical correction approach has been proposed, showing good agreement with the numerical results. The different characteristics of the deep seal for the against-wave entry and following-wave entry cases are discovered. The multiphase flow field caused by vertical entry is more complex than inclined entry because of the splash difference. The cylinder drag is primarily derived from the contact between the cylinder and asymmetrical cavity.

Surface gravity wave-induced drift of floating objects in the diffraction regime

Floating objects will drift due to the action of surface gravity waves. This drift will depart from that of a perfect Lagrangian tracer due to both viscous effects (non-potential flow) and wave–body interaction (potential flow). We examine the drift of freely floating objects in regular (non-breaking) deep-water wave fields for object sizes that are large enough to cause significant diffraction. Systematic numerical simulations are performed using a hybrid numerical solver, qaleFOAM, which deals with both viscosity and wave–body interaction. For very small objects, the model predicts a wave-induced drift equal to the Stokes drift. For larger objects, the drift is generally greater and increases with object size (we examine object sizes up to$10\,\%$of the wavelength). The effects of different shapes, sizes and submergence depths and steepnesses are examined. Furthermore, we derive a ‘diffraction-modified Stokes drift’ akin to Stokes (Trans. Camb. Phil. Soc., vol. 8, 1847, pp. 411–455), but based on the combination of incident, diffracted and radiated wave fields, which are based on potential-flow theory and obtained using the boundary element method. This diffraction-modified Stokes drift explains both qualitatively and quantitatively the increase in drift. Generally, round objects do not diffract the wave field significantly and do not experience a significant drift enhancement as a result. For box-shape objects, drift enhancement is greater for larger objects with greater submergence depths (we report an increase of$92\,\%$for simulations without viscosity and$113\,\%$with viscosity for a round-cornered box whose size is$10\,\%$of the wavelength). We identify the specific standing wave pattern that arises near the object because of diffraction as the main cause of the enhanced drift. Viscosity plays a small positive role in the enhanced drift behaviour of large objects, increasing the drift further by approximately$20\,\%$.

Numerical investigation of wave-cylinder interaction based on a momentum source wave generation method

A momentum source function is constructed for wave generation based on linear wave theory. Based on Navier-Stokes equation and volume of fluid (VOF) method, a three-dimensional numerical wave tank (NWT) is established. Regular and irregular waves can be simulated by applying the momentum source function to NWT, and the expected wave characteristic parameters and wave spectrum are obtained. Furthermore, the load characteristics of two types of cylinders, fully piercing cylinder (FPC) and truncated cylinder (TC), are studied under regular wave field combined with boundary data immersed method (BDIM). Results show that the transverse force exerted on cylinders is dominated by inertial force. And because of the effects of the cylinder on wave profile and drag force, the maximum transverse force occurs soon after the wave node passes through the centerline of the cylinder. Compared with the FPC, the drag force has a greater influence on TC.

Numerical study for nonlinear hydrodynamic coefficients of an asymmetric wave energy converter

In this study, the nonlinear dynamic behavior of an asymmetric Wave Energy Converter (WEC) was studied on a 1/11-scale model based on a numerical and experimental method in a regular wave field. The numerical analysis involved both frequency-domain and time-domain solutions. The frequency-domain solution was based on linear potential flow theory using the WAMIT® model whereas the time-domain solution was based on the Reynolds-Averaged Navier-Stokes (RANS) equation using the OpenFOAM® model. The pitch response amplitude operators obtained from the numerical results were compared with experimental data. Additionally, the nonlinear dynamic behavior of the asymmetric WEC due to various wave heights and periods obtained through the experiments were compared with the OpenFOAM results. Wave excitation moments and hydrodynamic coefficients based on the linear solution approach were separately obtained for the fixed asymmetric WEC induced by waves and the forced oscillating motion with OpenFOAM. Moreover, frequency-domain solutions based on linear potential flow theory were obtained in order to ascertain the nonlinear effects observed in the OpenFOAM results. It was found that a higher motion amplitude could be attributed to nonlinear hydrodynamic coefficients on the asymmetric WEC calculated by the forced oscillation motion of the RANS-based solution.

Wave action on a vertical wall with a submerged horizontal plate: Analysis of phase variation of forces and probability of exceedance

In this study, experiments on the wave forces and moments acting on a Vertical Wall (VW) and a VW attached to a horizontal plate (VWHP) subjected to regular and random wave fields were conducted. In the experiments, the phase lag between the horizontal and vertical wave forces was analyzed for the regular waves and the probability density was analyzed for the random waves. The experimental results showed that attaching a horizontal plate with a length equal to the water depth to a VW at a position corresponding to 28.5% of the water depth reduced the 95% non-exceedance value of the normalized horizontal wave force from 1.05 to 0.8 for a relative water depth of d/Lp = 0.1, where d is the water depth and Lp is the wavelength of the peak period. For d/Lp = 0.5, the corresponding reduction was from 0.6 to 0.17. The results of this study can be used to optimize the design of VW- and VWHP-type marine structures.

Experimental Study on the Correlation Between Wave Overtopping and Reflection Over an Absorbing Revetment: Non-Breaking Wave Conditions

Lee, W.D.; Choi, S.; Hwang, T.; Park, J.R., and Hur, D.S., 2021. Experimental study on the correlation between wave overtopping and reflection over an absorbing revetment: Non-breaking wave Conditions. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 584–588. Coconut Creek (Florida), ISSN 0749-0208. This study performed a hydraulic model experiment to analyze the correlation between wave overtopping and reflection over an absorbing revetment in regular wave fields without wave breaking. Regular waves that last 1.2–2 s and 1.0–2.6 cm high were generated in a two-dimensional wave tank with a depth of 50 cm. With respect to the experimental conditions, an absorbing revetment with two layers of Tetrapods (TTPs) installed on a foundation mound of sand stone was considered. To calculate the reflection coefficient, the time waveform measured using the wave gauges was substituted into a two-point method to separate the incident and reflected waves, while the overtopping rate was directly measured in a separate overtopping tank. According to the experimental results, the water surface waveform in front of the revetment differed depending on the presence of wave overtopping. Under the overtopping condition, the water level in front of the revetment increased and then gradually decreased. Under the non-overtopping condition, the water level continuously increased and then quickly decreased. With respect to wave reflection, under the non-overtopping condition, the reflection coefficient increased as the surf similarity parameter increased. Under the overtopping condition, the distribution of the reflection coefficient was below a certain level and exhibited no clear trend. As the surf similarity parameter increased, the water level at the time of wave overtopping increased. In addition, the longer the duration of wave overtopping, the greater the overtopping rate was. According to the analysis of the correlation between wave overtopping and wave reflection within the same period, the reflection coefficient generally decreased as the overtopping rate increased. However, this phenomenon was not observed in any of the experimental results.

A Physical Model of Wave Attenuation in Pancake Ice

A physical model is discussed that mimics the interaction between ocean waves and a multitude of loose pancake ice floes, which form the outer edge of the Arctic and Antarctic marginal ice zones during winter sea ice formation. The pancakes were modeled by using ice cubes with different concentrations, while waves were generated mechanically. The ice cubes had a dimension of a few centimeters, which was two orders of magnitude smaller than the dominant wavelength. Experiments consisted of tracking the propagation of regular and irregular wave fields along the flume as they crossed the ice cover to measure the rate of ice-induced wave attenuation. Results indicate that wave attenuation increases with ice concentration with only 30% of energy allowed to pass through high-density covers. Wave energy is attenuated across the entire spectral domain and is strongest at high frequencies. This results in a downshift of the spectral peak.

Numerical modeling of nonlinear sloshing of liquid in a container coupled with barge subjected to regular excitation

The sloshing phenomenon of liquid in a partially filled tank mounted rigidly within a barge exposed to regular wave field has been considered for numerical investigation. This paper details the numerical scheme developed in time domain to study the interaction of wave induced barge motion with sloshing oscillations in a partially filled container. The sloshing time history results obtained from the numerical scheme adopted are validated with experimental measurements of Nasar et al. (2008) The harmonics present in the sloshing oscillation for the liquid fill levels (25%, 50% and 75%) have been analyzed.

Wake effect assessment of a flap type wave energy converter farm under realistic environmental conditions by using a numerical coupling methodology

Ocean Energy Europe has estimated that 100 GW of ocean energy capacity (wave and tidal) could be deployed in Europe by 2050. Along with the European targets it is expected that large farms of Wave Energy Converters (WECs) will be installed in the sea and, as part of the consenting process for their installation, it will be necessary to quantify their impact on the local environment. The objective of this study is to improve the assessment of WEC farms impact on the surrounding wave field (wake effect) through the use of a numerical coupling methodology. The methodology consists of a Boundary Element Method (BEM) solver to obtain the wave perturbation generated by the WEC farm for the near-field accounting for the wave-body interactions within the farm whilst a Wave Propagation Model (WPM) based on the mild-slope equations determines the wave transformation in the far-field. The near-field solution obtained from the BEM solver is described as an internal boundary condition in the WPM and then it is propagated throughout the WPM numerical domain. The internal boundary is described by imposing the solution of the surface elevation and velocity potential at the free-surface at each instant of time along a line surrounding the WEC farm.As a case study the methodology was applied to flap type WECs that are deployed in shallow water conditions. The validation of the technique was done first for a single flap and then for a farm of 5 flaps. Once validated, a realistic scenario was assessed by quantifying the impact of irregular sea states composed of long crested waves on a large WEC farm composed of 18 flaps and located on a real bathymetry. The irregular waves were obtained by superposing the regular wave field solutions for all wave frequencies represented in the considered sea state based on the linear water wave theory. Within the limits of this theory these simulations demonstrate the versatility of the methodology to accurately represent the impact of a WEC farm on the surrounding wave climate. The influence of the peak period and the spacing between flaps on the WEC farm wake effect was assessed as well.

Evolution of the correlation wavefield extracted from seismic event coda

The seismic correlation wavefield constructed from stacked cross-correlograms of event signals displays a wide range of features as a function of inter-station distance. The character of such correlation arrivals changes markedly with the segment of the wavefield employed. All such correlation arrivals arise from the interaction of seismic phases that have a common slowness at the pair of stations being correlated. It takes some time before a clear correlation field is established, but after 1 h from event initiation a weak version of the regular wavefield emerges accompanied by many phases that have no counterpart in the direct source excitation. Such arrivals are produced by the interaction of seismic phases with common propagation legs, and have time-distance behaviour controlled by the differences in accumulated phase. The regular phases fade with time and then distinct arrivals in the correlation field arise when there are many ways in which combinations of seismic phases have the same difference in propagation legs. There are many more such possibilities for steeply travelling waves in the late coda, so that a relatively stable correlation field develops. The properties of the correlation field as a function of time can be well described by using a representation in terms of generalized rays supplemented by the contribution from the fundamental mode Rayleigh wave.

The nature of Earth's correlation wavefield: late coda of large earthquakes

The seismic correlation wavefield constructed from the stacked cross-correlograms of the late coda of earthquake signals at stations across the globe provides a wealth of observed pulses as a function of inter-station distance. The interval from 3 to 10 h after the onset of major earthquakes is employed for the period range from 15 to 50 s. The observations can be well matched by synthetic seismograms for a radially stratified Earth. Many of the correlation phases have similar time behaviour to those in the regular wavefield, but others have no correspondence. All such correlation phases can be explained by the interaction of arrivals with a common slowness at the each of the stations being correlated. Using a generalized ray description of the seismic wavefield, the time-distance behaviour of these correlation phases arises from differences in accumulated phase on different propagation paths through the Earth. Distinct arrivals emerge from the correlation field when there are many ways in which combinations of seismic phases can arise with the same difference in propagation legs. The constituents of the late coda are dominated by steeply travelling waves, and in consequence features associated with multiple passages through the whole Earth emerge distinctly, such as high-order multiples of PKIKP .

Vortex kinematics around a submerged plate under water waves. Part II: Numerical computations

This paper presents numerical computations of the flow generated by a horizontal plate immersed in a regular wave field, and associated loads acting on the plate. This numerical work is the continuation of the Poupardin et al. (2012) experimental study. This numerical study is original in the way that the vortical aspects of the flow are not neglected. Therefore, a 2D Lagrangian Vortex method is used as a numerical scheme. These methods are particularly well suited for the computation of unsteady and highly rotational flows in an open domain. The velocity field is decomposed into rotational and potential components, using the Helmholtz decomposition. The rotational part of the velocity is calculated by the Biot–Savart equation using vortex particles. The plate is modelled by a distribution of normal dipoles and the wave field is taken into account by means of a Stokes formulation, which completes the potential part of the velocity.Firstly, the numerical code is validated by means of comparison with the experimental results of Poupardin et al. (2012). In particular, the complex vortical activity and the mean flow velocity field are well reproduced and physically analysed. Secondly, forces acting on the plate are analysed on a wide range of parameters by varying the plate immersions and lengths. In the end, a new scaling is found for the lift forces acting on the plate based on the modified Stokes velocity (i.e. the bottom Stokes velocity for a water depth equals to the plate immersion) and the square of the plate length.

Regular Waves-induced Seabed Dynamic Responses around Submerged Breakwater

In case of the seabed around and under gravity structures such as submerged breakwater is exposed to a large wave action long period, the excess pore pressure will be generated significantly due to pore volume change associated with rearrangement soil grains. This effect will lead a seabed liquefaction around and under structures as a result from decrease in the effective stress. Under the seabed liquefaction occurred and developed, the possibility of structure failure will be increased eventually. In this study, to evaluate the liquefaction potential on the seabed quantitatively, numerical analysis was conducted using the expanded 2-dimensional numerical wave tank model and the finite element elasto-plastic model. Under the condition of the regular wave field, the time and spatial series of the deformation of submerged breakwater, the pore water pressure (oscillatory and residual components) and pore water pressure ratio in the seabed were estimated.

Mid-depth oil concentration due to vertical oil dispersion in a regular wave field

An experimental program is organized to investigate the vertical oil dispersion of surface oil spills in a regular wave field. Various waves characteristics and different volumes of oil spills are tested to assess the oil concentration variations at two sampling stations. It is found that the oil concentration due to vertical oil dispersion follows an ascending diagram to reach a maximum and then decreases while oil slick passes the location. The maximum mid-depth oil concentration (Cmax) at the farther sampling station is 30–50 % less than the concentration at the closer sampling station to the spill location. A 50 % increase in oil spill volume causes 30–60 % growth in oil concentrations. The relations between oil concentration and important parameters such as wave characteristics, amount of spilled oil and the distance of sampling stations from the spill location are indicated and also oil concentration variations are quantified. Two equations are derived through statistical analysis of the obtained experimental data, which estimate the magnitude and time of maximum oil concentration.

Power Generation Using Mechanical Wave Energy Converter

Ocean wave energy plays a significant role in meeting the growing demand of electric power. Economic, environmental, and technical advantages of wave energy set it apart from other renewable energy resources. Present study describes a newly proposed Mechanical Wave Energy Converter (MEWC) that is employed to harness heave motion of floating buoy to generate power. Focus is on the conceptual development of the device, illustrating details of component level analysis. Employed methodology has many advantages such as i) simple and easy fabrication; ii) easy to control the operations during rough weather; and iii) low failure rate during normal sea conditions. Experimental investigations carried out on the scaled model of MWEC show better performance and its capability to generate power at higher efficiency in regular wave fields. Design Failure Mode and Effect Analysis (FMEA) shows rare failure rates for all components except the floating buoy.

Prediction of Wave Loads on Tidal Turbine Blades

Wave loads are one of the main contributors to fatigue loads of tidal turbine blades. Because of this, they are a determinant parameter for calculation of turbine blade life time. To avoid cost associated with oversizing blades or replacing a damaged blade, it is essential to evaluate the loads acting on the turbine, and especially wave loads on the blades, with the best possible accuracy.Experience from wind industry is valuable for horizontal axis tidal turbine design and loads acting on the blade can be estimated using the same methods, even if the loads are different. This article presents the main features of a code written with Matlab, able to predict thrust force and torque on each blade while the turbine is operating in a regular wave field. The quasi-static Blade Element Momentum theory is combined here with an added mass force modeling. The linear wave theory is employed to describe the water particle velocity due to waves. This velocity is, as a first approximation, simply added to a uniform stream velocity to account for wave-current interaction.The analytical results are validated by comparing them with experimental data obtained by testing a 1.475m-diameter rotor towed in a 260m-long wave tank, for different combinations of current speeds and wave characteristics. This emphasizes the importance of wave effects and dynamics in the design of tidal turbine blades.

Mean and Turbulence Properties of a Neutrally Buoyant Round Jet in a Wave Environment

An experimental study of a turbulent round jet discharged into a regular wave field is presented. The particle image velocimetry (PIV) technique was employed to measure instantaneous velocity fields of the flow. Quantitative mean and turbulence properties were obtained using ensemble- and phase-averaged methods. Both the jet potential core region and self-similar region were measured. Three different wave heights were used to examine the effect of wave steepness on the jet properties. Measurements were also taken at three different phases to examine the wave phase effect. Experimental results demonstrate that the mean jet width, turbulence intensity, and Reynolds stress increased significantly when the jet was acted on by the waves. In addition, the jet mean kinetic energy decreased whereas the turbulent kinetic energy increased when the jet was under the waves, indicating an increase in turbulence. The wave phase has an insignificant effect on the both the mean and turbulence properties. The turbulent kinetic energy budget in the self-similar region at different wave conditions was also examined. It was found that the turbulent production, advection, and dissipation terms all increase with the increase of the wave height.

Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods

We determine adjoint equations and Fréchet kernels for global seismic wave propagation based upon a Lagrange multiplier method. We start from the equations of motion for a rotating, self-gravitating earth model initially in hydrostatic equilibrium, and derive the corresponding adjoint equations that involve motions on an earth model that rotates in the opposite direction. Variations in the misfit function χ then may be expressed as , where δ ln m = δm/m denotes relative model perturbations in the volume V, δ ln d denotes relative topographic variations on solid–solid or fluid–solid boundaries Σ, and ∇Σδ ln d denotes surface gradients in relative topographic variations on fluid–solid boundaries ΣFS. The 3-D Fréchet kernel Km determines the sensitivity to model perturbations δ ln m, and the 2-D kernels Kd and Kd determine the sensitivity to topographic variations δ ln d. We demonstrate also how anelasticity may be incorporated within the framework of adjoint methods. Finite-frequency sensitivity kernels are calculated by simultaneously computing the adjoint wavefield forward in time and reconstructing the regular wavefield backward in time. Both the forward and adjoint simulations are based upon a spectral-element method. We apply the adjoint technique to generate finite-frequency traveltime kernels for global seismic phases (P, Pdiff, PKP, S, SKS, depth phases, surface-reflected phases, surface waves, etc.) in both 1-D and 3-D earth models. For 1-D models these adjoint-generated kernels generally agree well with results obtained from ray-based methods. However, adjoint methods do not have the same theoretical limitations as ray-based methods, and can produce sensitivity kernels for any given phase in any 3-D earth model. The Fréchet kernels presented in this paper illustrate the sensitivity of seismic observations to structural parameters and topography on internal discontinuities. These kernels form the basis of future 3-D tomographic inversions.