Wave Surface Elevation Research Articles

Three-dimensional numerical simulation of a cylindrical oscillating water column (OWC) device placed in a wave flume

A three-dimensional computational fluid dynamic (CFD) model is developed for simulating a cylindrical Oscillating Water Column (OWC) device for harvesting wave energy. The single-phase CFD model solves the Reynolds-Averaged Navier-Stokes (RANS) equations using the finite element method for simulating the wave motion and uses an aerodynamic model to simulate the flow through the air turbine. The model is implemented to simulate wave energy harvesting of a cylindrical OWC device. Through harmonic decomposition, it is found that the first harmonic wave surface elevation oscillates like a piston in the OWC chamber. However, both the amplitude and phase of the second harmonic wave surface elevation vary significantly along the wave direction in the OWC chamber, demonstrating a sloshing mode of the second harmonic. This study further proved the reduction of the capture width ratio caused by the transverse sloshing mode when the wavelength is the same as the wave flume width. The effect of the width of the wave flume on the peak CWR is found to be negligibly small when the wave flume width is three times the OWC diameter.

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.

Hydrodynamics of focused waves acting on netting that extends above the mean sea level

Extreme ocean waves are typically strongly nonlinear, with extreme wave energy concentrated above the static water surface, which has a complex impact on the hydrodynamics of structures extending above the mean sea level. In this study, we designed netting with three different heights above the water surface and two different solidities, and tested the hydrodynamics of these netting under a series of focused waves through physical model tests. The three heights (h) were designed to account for possible nearshore tidal and wave variations. The results indicate that the wave forces of the netting having sharper and steeper crest than those of the wave surface in the time domain, while it is opposite in frequency domain. Moreover, the wave forces changed significantly with increasing height of the netting above the water surface. Wave forces on netting above water were up to 0.8 and 2.0 times greater than those below water for h = 7.25 cm and h = 14.5 cm, respectively. Regardless of solidity, the rate of increase in netting wave forces gradually decreased with growing wave amplitude when h = 0 cm or h = 7.25 cm, but gradually increased when h = 14.5 cm. The force ratios of the two netting solidities were relatively stable and did not change with wave amplitude. The force ratios were always greater than the solidity ratio, mainly because of the drag coefficient in Morison's equation. Furthermore, steep waves acting on netting wound cause obvious vibration of the wave force because of water jet phenomenon, while the jet have little effect on wave surface elevation in 0.5 m behind the netting. Therefore, for aquaculture facilities such as fixed marine aquaculture cages, the netting design is not only limited by the solidity, but should also consider the hydrodynamic influence of the height that the netting extends above the water.

Scale effect on wave planing performance of amphibious aircraft at constant speed

Scaled model testing is commonly recognized as a valuable approach for predicting aircraft performance in the aeronautical applications. However, challenges arise in the case of wave planing events for amphibious aircraft due to difficulties in satisfying the scaling laws of Reynolds number and Froude number simultaneously in a water tank. Therefore, it is important to evaluate the scale effect of regular wave planing process for amphibious aircraft. In this study, by fixing the Froude number, five geosim cases with different scale factors (1/1, 1/2, 1/4, 1/8 and 1/16) are carried out based on the Reynolds-Averaged Navier–Stokes equations (RANS) framework. The hydrodynamic and aerodynamic characteristics at different scales are respectively examined in detail through several physical results, including acceleration, pressure, shear force, velocity and free surface elevation. Comparative analyses among all scaled models reveal that the aerodynamic and hydrodynamic performance both monotonously change with the scale factor, yet the proportion of aerodynamic and hydrodynamic loads remains within a reasonably small range. Furthermore, the results indicate that the scale effect primarily stems from the lack of similarity in Reynolds number, thus resulting in the discrepancies of boundary layer, wave surface elevation and flow separation between the scale model and prototype.

Stereo vision based systems for sea-state measurement and floating structures monitoring

Using computer vision techniques such as stereo vision systems for sea state measurement or for offshore structures monitoring can improve the measurement fidelity and accuracy with no significant additional cost. In this paper, two experiments (in-lab/open-sea) are conducted to study the performance of stereo vision system to measure the water wave surface elevation and rigid body heaving motion. For the in-lab experiment, regular water waves are generated in a wave tank for different frequencies and wave heights, where the water surface is scanned by the stereo vision camera installed on the top of the tank. Surface elevation inferred by the stereo vision is verified by an installed stationary side camera that records the water surface through the tank transparent side window, water surface elevation measured by the side camera recordings is extracted using edge detection algorithm. During the in-lab experiment a heaving buoy is installed to test the performance of Visual Simultaneous Localization and Mapping (VSLAM) algorithm to monitor the buoy heave motion. The VSLAM algorithm fuses a buoy onboard stereo vision recordings with an embedded Inertial Measurement Unit (IMU) to estimate the 6-DOF of a rigid body. The Buoy motion VSLAM measurements are verified by a KLT tracking algorithm implemented on the video recordings of the stationary side camera. The open-sea experiment is implemented in Lake Somerville, Texas. The stereo vision system is installed to measure the water surface elevation and directional spectrum of the wind generated irregular waves. The open-sea wave measurements by the stereo vision are verified by a Sofar commercial wave buoys deployed in the testing location.

Incident component extraction from disturbed waves around large fixed cylindrical structures

The parameters of incident waves are critical for real-time wave load estimation of structures in service. Nonetheless, it is challenging to characterize incident waves accurately using the measured wave surface elevation around large fixed cylindrical structures due to the interaction with the structure in the wave field. To provide a better understanding of incident waves, which are usually buried in directly measured waves, a new time-domain method for the extraction of first-order and second-order incident waves around large fixed cylindrical structures is proposed. In contrast to most existing separation methods that are suitable for structures with equal reflection coefficients, the amplitude and phase changes of near-field waves around cylindrical structures can be determined by considering the significant diffraction effect, and then the time-frequency characteristic of the wavelet transform is employed, which enables the extraction of incident waves in the time domain. The accuracy of the proposed method is studied using several examples with known incident waves which are generated with the OpenFOAM. The numerical results show that the deviations between the exact and extracted incident waves change from 6.16% to 16.77% for different wave conditions. To further investigate the performance of the proposed method, an experimental study on waves around a mono-pile offshore wind turbine (OWT) is conducted in the laboratory of the Ocean University of China. The predicted results basically agree well with the target waves in terms of amplitude and phase. The deviations between predicted waves using the proposed method and target waves are 110% smaller than those between directly experimental measured waves and target waves for all tested conditions. Finally, 48 h of measured wave data were obtained during calm and typhoon periods around a mono-pile OWT located near Rudong County, Jiangsu Province, in the Yellow Sea of China. There are almost 150% and 30% differences between the extraction results and measured data in the time series and statistical wave heights, respectively, which means that employing disturbed wave data as the input for calculating real-time wave loads leads to deviations that cannot be ignored.

Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data

Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave surfaces from sparse measurements like radar. Existing reconstruction methods either rely on computationally intensive optimization procedures or simplistic modelling assumptions that compromise the real-time capability or accuracy of the subsequent prediction process. We therefore address these issues by proposing a novel approach for phase-resolved wave surface reconstruction using neural networks based on the U-Net and Fourier neural operator (FNO) architectures. Our approach utilizes synthetic yet highly realistic training data on uniform one-dimensional grids, that is generated by the high-order spectral method for wave simulation and a geometric radar modelling approach. The investigation reveals that both models deliver accurate wave reconstruction results and show good generalization for different sea states when trained with spatio-temporal radar data containing multiple historic radar snapshots in each input. Notably, the FNO demonstrates superior performance in handling the data structure imposed by wave physics due to its global approach to learn the mapping between input and output in Fourier space.

Adjoint-based high-order spectral method of wave simulation for coastal bathymetry reconstruction

Bathymetry is an important factor affecting wave propagation in coastal environments but is often challenging to measure in practice. We propose a method for inferring coastal bathymetry from spatial variations in surface waves by combining a high-order spectral method for wave simulation and an adjoint-based variational data assimilation method. Recursion-formed adjoint equations are derived to obtain the sensitivity of the wave surface elevation to the underlying bottom topography to any desired order of nonlinear perturbation. We also develop a multiscale optimisation method to eliminate spurious high-wavenumber fluctuations in the reconstructed bathymetry data caused by sensitivity variations over the different length scales of surface waves. The proposed bottom detection method is validated with a realistic coastal wave environment involving complex two-dimensional bathymetry features, non-periodic incident waves and nonlinear broadband multidirectional waves. In numerical experiments at both laboratory and field scales, the bathymetry reconstructed from our method agrees well with the ground truth. We also show that our method is robust against imperfect surface wave data in the presence of limited sampling frequency and noise.

Numerical study of the effect of central platform motion on the wave energy converter array

Placing multiple wave energy converters (WECs) on a central floating platform has become a popular approach of ocean energy conversion in recent years. The strong interaction between the WECs and the platform brings a number of technical challenges for the design of such devices. The present study investigates the effect of the platform motion on the WEC array of a typical ocean energy harvesting device, consisting of a central support platform and eight point-absorber WECs arranged in a circular array. The numerical studies are performed in four stages based on the potential flow solver ANSYS-AQWA. The power absorption of each WEC in isolation and of eight WECs operating simultaneously is evaluated and compared in the first and second stages respectively, revealing the interaction among the WECs. The effect of a fixed and a floating platform on the power absorption of the WEC array is investigated in the next two stages. The systematic studies demonstrates that the heave motion of the platform improves the power absorption of the WEC array for most wave frequencies tested, due to the increase in the wave-surface elevations around the WECs and the phase differences of the heave motion between the WECs and the platform. The opposite is true for the pitch motion of the platform. Furthermore, the WEC dimension, the platform dimension, and the distance between the WECs and the platform should be optimized based on the actual operating sea conditions to increase the wave-surface elevations and the phase differences. Otherwise, the motion of the platform should be restricted as much as possible.

Forward prediction of surface wave elevations and motions of offshore floating structures using a data-driven model

Accurate predictions of surface waves and subsequent wave-induced vessel motion have the potential to improve safety and efficiency for a wide range of offshore operations, such as active control of wave energy converters and floating wind turbines. In this paper, an Auto-Regressive model is proposed to predict surface waves and vessel motions based on the measured time sequences at a particular location. Based on numerically synthesized wave data, it is shown that band-pass filtering with a single cut-off frequency can improve the accuracy of predictions. These prediction results suggest that the narrower the spectral bandwidth, the more accurate predictions. However, digital filters cannot be implemented in the context of real-time prediction due to non-causality. For practical forecast, prediction of offshore floating structures could be treated in much the same as a physical filter as it only responds significantly over a limited range of frequencies. Analysis of wave basin test data confirms this hypothesis, making the forecasting of floating body motions promising.

INVESTIGATION ON THE DISCRETIZATION OF THE REALISTIC IRREGULAR WAVE GENERATION REGION THROUGH THE WAVEMIMO METHODOLOGY

Aiming to contribute to the research related to the sea wave energy conversion, the present paper approaches an investigation of the discretization used in the region of imposition of the prescribed velocity boundary condition, which is necessary for the WaveMIMO methodology. This methodology is employed for the numeric generation of irregular waves based on realistic sea state data. These data (obtained from TOMAWAC software in the present study) are treated to obtain orbital profiles of wave propagation velocity, which are imposed as boundary conditions on the wave channel. In this study, the realistic data considered refers to a point close to the Molhes da Barra, located on the coast of the municipality of Rio Grande, Rio Grande do Sul, Brazil. The numerical simulations were performed in Fluent, a computational fluid dynamics (CFD) software based on the finite volume method (FVM). The volume of fluid (VOF) multiphase model was used on the treatment of the water-air interface. Free surface elevation data obtained when the region of imposition of the prescribed velocity boundary condition was subdivided into 8, 11 and 14 segments were compared. The results found show that the 14 segments discretization represents more precisely the free surface elevation of irregular waves.

Numerical validation of an effective slender fault source solution for past tsunami scenarios

To estimate tsunami hazards, it is first necessary to have reliable data relating to the rupture characteristics, such as epicenter, fault geometry, uplift speed, and duration. We made use of a mathematical model that combines analytical and machine learning technique capable of retrieving rupture characteristics from acoustic data. The model was applied with short computational times to data recorded by the comprehensive nuclear-test-Ban Treaty organization hydrophones during four tectonic events that were reported to trigger tsunami waves. The presented inverse problem model for acoustic waves with adequate tsunami propagation tools can be used as a complementary technique alongside tsunami warning systems due to the high propagating speeds of the sound in the ocean. In this paper, the validity of the solutions provided by the inverse problem model is tested by using the calculated earthquake parameters as input to the Cornell multi-grid coupled tsunami numerical model, which, in turn, output surface wave elevations (tsunami) to be compared against deep-ocean assessment and reporting of tsunamis buoy data.

Empirical formulas for near-bed wave orbital velocity parameters involved in maximum wave load in random wave trains

This paper presents empirical methods utilizing recently developed formulas (Kawamata and Kobayashi., 2022; Kawamata et al., 2018) to predict the maximum wave forces on near-bed structures and wave-induced movement ratios of isolated rocks in random wave trains. The methods assume that the maximum wave load occurs when the velocity semi-amplitude defined as half the difference between successive negative and positive peaks of the near-bed wave orbital velocity is maximized. The empirical formulas for the velocity-waveform parameters at the maximum velocity semi-amplitude in a random wave train were derived from the near-bed velocities and surface elevations measured in laboratory wave flumes. The laboratory formula for the maximum velocity semi-amplitude was reviewed and improved with near-bed wave orbital velocities and surface elevations estimated from pressure measurements under a wider range of wave conditions in the field. The newly developed formulas for the velocity-waveform parameters at velocity semi-amplitude maxima, combined with the previously developed formulas, showed reasonable agreement with the maximum wave forces measured on the artificial reef models under random waves in a laboratory wave flume as well as with the movement ratio of quarry rocks (median mass = 0.40 t) observed in a field test.

Experimental Study on the Aerodynamic Performance and Wave Energy Capture Efficiency of Square and Curved OWC Wave Energy Conversion Devices

To develop novel wave energy conversion devices (WECDs) with excellent performance, the relative wave height and pressure in the chambers of square and curved oscillating water column (OWC) WECDs were compared through physical model tests, and the effects of regular incident wave factors, the opening length, the opening width, and the chamber volume on the aerodynamic performance and wave energy capture efficiency (WECE) of the WECDs were investigated. The results indicated good chamber performance for both the square and curved OWC WECDs. As the incident wave height increased, the wave surface elevation, WECE, and pressure in the chamber all increased, while the relative wave height in the chamber decreased. When the opening length, width, and area of the WECD increased, both the relative wave height and chamber pressure increased. The relative wave height in the chamber increased with decreasing chamber volume; however, the chamber pressure and intrachamber WECE decreased with increasing chamber volume. It is recommended that, in actual engineering applications, the overall efficiency of the device be improved by increasing the opening length, width, area and volume of the air chamber.

On wave–current interaction in deep and finite water depths

Interaction of linear and nonlinear, long-crested waves with currents in deep and finite water depths is studied by use of the computational fluid dynamics approach. Various wave conditions are considered by systematically changing the wave height and the wavelength. Several current profiles are studied as polynomial functions of water depth following the profiles and magnitudes of the available ocean current data. Both following and opposing currents are considered, and in total, 26 wave–current configurations are investigated. The two-dimensional study is carried out computationally by solving the Navier–Stokes equations for a laminar flow. The governing equations are solved by use of the finite volume approach in an open-source computational fluid dynamics package, namely OpenFOAM. Modifications are made to an existing wave-making toolbox, waves2Foam, to generate combined nonlinear waves and currents in deep and finite waters. Results of the numerical wave–current tank are compared with the existing laboratory measurements and overall very good agreement is observed. Discussion is provided on the effect of these currents on the change of the wave field, including quantitative change of the surface elevation, wave profile, pressure distribution, and fluid particle velocity of waves. Overall, it is observed that opposing current has a remarkable impact on the wave field, and the particle velocity and wave height are affected the most from the presence of the current.

Improved analysis method on extreme upwell of irregular waves for the airgap of floating platforms based on OTG-13

Analysis on air gap is an essential job for the design of the semi-submersible platforms. According to OTG-13 by DET NORSKE VERITAS (DNV) in 2019, the extreme up well in severe irregular waves is the most dominant negative gain of the air gap and should be paid close attention to. Accordingly, in the present study, firstly the frequency-domain analysis method was introduced to predict the extremum of waves up well under a relatively severe sea state among the survival conditions. And the calculation results were found to be much larger than the experimental data of the model test (relative error can be 30%–75%). This leads to the extremely conservativeness of air gap evaluation according to OTG-13. Consequently, further studies were done to explore the deeper reason for such conservativeness. By analyzing the whole process of calculation, the misestimate of the two "details": the viscous effect of water and the wave asymmetry factors, are found to be the causes of the conservativeness of the OTG-13. Then, an improved analysis method of extreme upwell based on the computational fluid dynamics (CFD) solution of wave surface elevation was presented and found to be more practical. In fact, the relative error can be less than 10% in the case that those two "details" are evaluated more precisely. Next, the influence of those two "details" on the extreme upwell were further quantitatively discussed respectively by variable-controlling approach, and it is noticed that the accurate estimation of the wave asymmetry is dominated (relative error can thus reduce to 10%–23%). Finally, a more reasonable preliminary design method was proposed, which is by introducing the actual wave asymmetry factor to the calculation of the extreme up well and air gap based on the CFD solution.

Hydrodynamic responses of a reversed L type floating breakwater integrated with a wave energy converter impacted by extreme waves

This research studies the hydrodynamic responses of a reversed L type floating breakwater integrated with a wave energy converter moored by a vertical pile in extreme sea states and intermediate water depth in a numerical wave tank based Navier-Stokes equations. Three wave-type representations (solitary, regular, and focus waves) of the same wave state are considered. The surface wave elevation, heave motion, wave force, impulse, wave moment on the mooring pile, moment of impulse, pressure distribution and flow field are investigated and compared. The comparison shows that different waves yield to diverse peak hydrodynamic responses. Largest wave force and moment are found in the regular wave condition, while largest heave motion, impulse and moment of impulse are obtained for the solitary wave. The pressure distribution on the bottom of the floater under the solitary wave shows a distinct character from the two others. The effect of the PTO damping parameter with the focus on the maximum wave force and moment is discussed and it is revealed that there exists an optimal PTO damping force for which the minimum wave force on the floater is obtained. This study therefore gains an insight into the hydrodynamic responses under different extreme waves.

Control-oriented wave surface elevation forecasting strategies: Experimental validation and comparison*

Optimal control strategies are a key development step towards commercialization of wave energy converters (WECs). Most of these rely on optimization routines to find a suitable control action to maximize WEC power production. Nevertheless, most of these solutions make use of device dynamical models, with the free-surface elevation as the external (uncontrollable) input, effectively representing the incoming wave field. Consequently, predictive strategies, such as model predictive control, strongly depend on the availability of future wave information, and hence suitable forecasters are commonly used to ‘restore’ the causality of the optimization problem. Motivated by the intrinsic requirement of suitable forecasting strategies within optimal WEC control, this study provides a validation and comparison of different algorithms, including adaptive and non-adaptive techniques, based on experimental data. The paper focuses on the adaptability of each algorithm, which must be capable to fit properly each wave surface elevation signal, thus not affecting the optimality condition by providing poor prediction results.

Effects of heave motion of an elastically supported floating oscillating water column device on wave energy harvesting efficiency

The main aim of this paper is to analyze the effects of the heave motion of an elastically supported floating oscillating water column device (OWC) on wave energy harvesting efficiency through two-dimensional computational fluid dynamics simulations. After the numerical model is validated using experimental data, it is used to analyze the effect of the natural frequency ratio on the hydrodynamic efficiency of the OWC. The natural frequency ratio is the ratio of the natural frequency to the wave frequency. The numerical results prove that the natural frequency ratio must be greater than 3 for achieving the best hydrodynamic efficiency. The best hydrodynamic efficiency decreases with the decrease in the natural frequency ratio when the latter is 3. If the natural frequency ratio is smaller than 3, both the amplitudes of wave surface elevation and the displacement of the OWC chamber increase but the harvested energy reduces because the relative motion of the wave surface and the OWC device is small. The energy dissipation due to vortices does not have a strong contribution to the reduction of energy at small natural frequencies.

IRREGULAR WAVEMAKER (PISTON TYPE) IN A NUMERICAL AND PHYSICAL WAVE TANK

This paper describes the design and execution of a wavemaker system (piston type) in the Dokuz Eylül University Hydraulic Laboratory flume to perform hydraulic model tests using regular and irregular waves. In this study, we will focus on generating the irregular waves from the target JONSWAP spectrum using an adjusted random phase method; also, the control software of the wavemaker is described. An identical numerical channel wave to the physical flume was modeled to compare and observe the irregular wave profile using Flow 3D, one of the advanced computational fluid dynamics (CFD) software. The paddle movement was validated by comparing the experimental converted irregular wave surface elevations to the wave spectrum to the numerical models of several waves.