Wave Elevation Research Articles

Gaussian process metamodels for floating offshore wind turbine platforms

The dynamics of floating offshore wind turbines (FOWT) are quite complex as it involves interactions in multiple domains. The dynamic response of FOWT is numerically evaluated using coupled aero-hydro-servo-elastic analysis. In the design stages, the dynamic analysis of FOWT is carried out for different environmental conditions. These analyses can be time-consuming and computationally expensive. This paper proposes the use of metamodels based on the Gaussian process for representing the hydrodynamics and structural dynamics of the floating platform. The input to Gaussian process metamodels is taken as wave elevation, forces and moments at the interface of the tower and platform. The output of the metamodels is the displacements (surge, sway and heave) and the rotations (roll, pitch and yaw) of the platform. Three different Gaussian process metamodels are considered in this paper — Standard Gaussian Process, Variational Heteroscedastic Gaussian Process and Sparse Spectrum Gaussian Process. The construction of the metamodels is demonstrated for an NREL 5MW turbine supported on an ITI barge platform. The performance of the Gaussian metamodels is compared in terms of evaluation indices, convergence, residuals and computational efficiency. The sensitivity analysis of the metamodels is carried out to verify that the interdependence between the variables is captured accurately. All three Gaussian process metamodels are found to be effective in emulating the response of the platform. These models can be effectively used in situations where simple and computationally inexpensive models are required.

Spectral wave explicit weak-scattering approach for higher harmonic wave loads and ringing response of flexible monopile

This paper presents an accurate potential decomposition strategy for wave–structure interactions, known as the spectral wave explicit weak-scattering approach, where the entire original problem is divided into incident and scattered components. The incident component is evaluated using spectral models in advance; hence, only the scattered component is to be solved via a higher-order boundary element approach. The proposed coupled model is validated using published experimental and computational fluid dynamics results for wave interactions with a vertical cylinder. The results obtained are consistent with wave elevations and wave loads for regular waves and focused wave groups. A finite-element numerical model is applied to measure the severity of structural responses. Fluid–structure interactions are simulated by converting the obtained pressures into equivalent nodal forces, and new nodal velocities are converted into boundary conditions. The ringing response of a bottom-fixed monopile due to moderately steep focused wave groups is discussed based on various focal positions relative to the monopile, incident wave conditions, and damping ratios. The time–frequency characteristics of the ringing phenomenon are successfully revealed via wavelet analyses.

Experimental uncertainty of a physical model of a tanker moored to a terminal in a port

This paper presents the uncertainty modelling of experimental results for a physical model of a tanker moored to a terminal inside a port. The physical model was built for an oil terminal at the port of Leixões in Portugal. The model incorporates the new modified port layout, as well as a future 300 m extension of the port outer north breakwater to enhance operational conditions. The physical model tests were performed on a scale of 1:80 in the Portuguese Civil Engineering Laboratory (LNEC). A generic mooring system of four mooring lines and two fenders is simulated using a nonlinear spring system. Decay tests are carried out to evaluate the natural periods of the moored model. Then, tests are carried out for the moored model in waves. The major aim of the experimental study is to obtain novel results for the wave elevation and direction at various locations inside the port, the ship motions at six degrees of freedom, and loads on mooring lines and fenders including the modified port layout. As the physical model measurements are subjected to different types of uncertainties, a systematic uncertainty analysis is carried out here, following ITTC guidelines and recommendations, to quantify all possible sources of uncertainties. The results are discussed, and several conclusions are reached. Based on the experimental results, the presented physical model study may replicate the results for waves and motions with uncertainties less than 9% of the significant amplitudes. The assessment of the applied nonlinear spring model reveals load predictions on the moorings, with uncertainties less than 4% of the maximum mooring loads.

Comparison of full-scale measurements and seakeeping calculations for two research vessels in the Adriatic Sea

The paper describes two experimental campaigns of seakeeping measurements for two research vessels in the Adriatic Sea and comparison of the experimental results with the seakeeping calculations. The waves and vessel motions are simultaneously measured at seas. Sea surface elevation of wind waves is measured using a wave buoy, freely floating near the vessel. Measurements of vessel motions are performed using motion sensors mounted on the bridge deck. Measurements are performed for different heading angles between the prevailing wave direction and the vessel. Time signals of the measured waves and resulting heave and pitch motions are treated statistically and subjected to spectral analysis. Wave-induced vessel responses are also calculated by the spectral analysis, employing the 3D panel method for transfer functions. Measured wave spectra are approximated by the standard JONSWAP spectra for that purpose. Statistical properties of the measured and calculated wave-induced motions are then compared. The results of the seakeeping calculations are in fair agreement with the measurements, except for mean zero-crossing period of the responses in following seas, where considerable discrepancies are found.

Modeling ocean waves and investigation of oceanic wave spectra for wave-to-wire system

The oceanic wave energy is a profuse and sustainable source of clean energy but its enourmous potential is under-exploited. Even though the idea of energy harnessing from oceanic waves is not new, the developments in wave energy conversion technologies are still in an embryonic stage. In most of the studies associated to wave-to-wire systems, oceanic waves are taken as regular waves with a fixed amplitude and a fixed frequency. The main area of focus of the previous studies includes the different conversion stages of the wave-to-wire system, particularly the mechanical, and the electrical conversion stage of the energy and the modeling of oceanic waves for such studies remained neglected in such studies. However, the actual oceanic waves can be presented with the sum of various frequencies to show a specific sea-states with significant wave height and the peak period as the main characterizing parameters. In this study, detailed mathematical modeling of oceanic waves is offered and various wave spectra are investigated for their application in wave-to-wire-based system studies. The best-suited wave spectra are identified parametrically and thereafter it is used for the generation of wave elevation time series in the proposed method presented in this study. The generated time series are appliesd in wave-to-wire systems for the investigation of wave energy conversion devices to mimic the real sea environment. Based on inverse fast Fourier transforms, oceanic wave elevation time series are determined which will be acting as input data for any of the wave energy converters deployed for the capturing of useable energy.

Properties of complex damping Helmholtz–Duffing oscillator arising in fluid mechanics

The current paper presents the first treatment to obtain the solution of a complex Helmholtz–Duffing oscillator. This model has described the elevation of the surface waves in fluid mechanics. The non-perturbative approach is used to convert the nonlinear oscillator to a linear oscillator to derive the solution of the complex nonlinear oscillator. This paper has opened the path for a new way to study more complex nonlinear elevation of surface waves.

Abstract 13312: Can the Extent of Late Gadolinium Enhancement on Cardiac Magnetic Resonance Be Predicted by the 12-Lead Electrocardiogram?

Background: In hypertrophic cardiomyopathy (HCM), late gadolinium enhancement (LGE) on cardiac magnetic resonance imaging (CMR) is an in vivo marker of replacement fibrosis with a continuous relationship between amount of LGE and both risk for sudden death and development of endstage disease. Cost and accessibility can limit routine utilization of CMR. In contrast, electrocardiogram (ECG) is an inexpensive readily available test and identifies patients with myocardial scarring in ischemic heart disease. Its ability to identify presence and extent of LGE in HCM is unknown. Methods: 1983 consecutive HCM patients were included; 62% male, average wall thickness 18 ± 3mm, and 36% with resting LV outflow tract obstruction ≥ 30mmHg. ECGs were analyzed for LV hypertrophy, T wave abnormalities, ST-segment depression or elevations, abnormal Q waves, conduction disease, atrial enlargement and QTc prolongation. Extent of LGE was quantified and expressed as a proportion of total LV myocardium. Results: 822 (41%) had no LGE, while 1161 (59%) had LGE, including 687 (35%) with <5%, 299 (15%) with 5-9%, 92 (5%) with 10-14%, and 83 (4%) with ≥ 15%. Compared to no LGE, Patients with LGE were more likely to have pathologic T wave inversions (55% vs. 36%, p<0.01), positive T waves in aVR (34% vs. 20%, p<0.01), and ST-depressions (29% vs. 21%, p<0.01), with no difference in LV hypertrophy, bundle branch block, pathologic Q waves, first degree AV block, QTc prolongation ≥ 480ms, or ST-elevations (p>0.05). Notably, as extent of LGE increased there was a corresponding progressive increase in the prevalence of both positive T waves in aVR (20% in no LGE to 42% in ≥ 15% LGE, p<0.01) and pathologic T wave inversions (36% in no LGE to 61% in ≥ 15% LGE, p<0.01) but with no incremental differences in ST depressions (p>0.05). In contrast, 43% of patients with LGE did not have either positive T waves in aVR or pathologic T wave inversions, including 34% with ≥ 15% LGE. Conclusion: Most ECG findings including pathologic Q waves have no relation to presence or extent of LGE. While positive T waves in aVR and pathologic T wave inversions are associated with LGE, they have limited sensitivity. These finding support that routinely evaluated ECG abnormalities do not predict presence or extent of scarring in HCM.

Abstract 12835: Predictors of Utilization of Multi-Vessel Percutaneous Coronary Revascularization vs. Bypass Surgery in Patients Hospitalized With Non-ST Wave Elevation Myocardial Infarction and Comorbid End-Stage Renal Disease: A Nationwide Analysis

Introduction: The appropriate strategy for revascularization in patients with coronary artery disease (CAD) and concomitant end-stage renal disease (ESRD) is unknown. The aim of this study was to determine the hospital and patient levels predictors of the type of revascularization strategy pursued in patients hospitalized with non-ST wave elevation myocardial infarction (NSTEMI) and ESRD. Methods: Study cohorts were derived from the Nationwide Inpatient Sample (NIS) 2016-19. Study variables were identified using ICD-10-CM-codes. Patients presenting with cardiogenic shock were excluded. The primary outcomes were the predictors of the type of revascularization strategy pursued. Multivariable logistic regression was used to adjust for potential confounders. Results: There were a total of 87,800 hospitalizations for NSTEMI with comorbid ESRD, out of which 8060 (53%) underwent multi-vessel PCI and 6909 (46%) underwent CABG. Patients undergoing CABG were younger, had a lower proportion of females, and higher burden of comorbidities (including arrhythmias, coagulopathy, valvular heart disease, morbid obesity, and active drug abuse disorder) than those undergoing MvPCI. Multivariate patient-level and hospital-level predictors are demonstrated in Figure 1. As expected, CABG was associated with significantly higher odds of in-hospital mortality (OR:2.01 (1.3-3.1), p<0.01), length of stay (8.9 days longer, p<0.01), and total hospitalization charges (152,527$ higher, p<0.01) as compared to MvPCI. There was no difference in the odds of stroke between both cohorts. Conclusion: Patient-level factors (including female gender, age, comorbidities (arrhythmias, peripheral vascular disease, diabetes, coagulopathy, history of CABG or PCI, prior stroke/TIA), and hospital levels factors (bed size, hospital procedural volume) independently predicted the type of revascularization strategy pursued in patients hospitalized for NSTEMI with ESRD.

Thermo‐Compositional Structure of the South American Platform Lithosphere: Evidence of Stability, Modification, and Erosion

AbstractConstraints on the structure of cratonic lithosphere are essential to improve our understanding of craton formation, evolution and long‐term stability. Here, we perform a joint inversion for the thermal and compositional structure of the mantle lithosphere below the South America Platform, using Rayleigh wave group velocities, elevation, and geoid height. Thick thermal lithosphere (200–300 km) is found below the southern Amazonian and São Francisco Cratons and adjoining Parecis and eastern Paraná Basins. The southern Rio de la Plata Craton also retains a 200–250 km thick keel. Compositionally, Amazonian, São Francisco, and Rio de la Plata lithosphere has a metasomatic and possibly eclogite signature similar to that of North American Proterozoic collision belts. Parecis and eastern Paraná lithosphere has likely been altered by Mesozoic plume activity throughout most of its depth, while the rest of the Paraná Basin and the Chaco and Pantanal Basins appear to have lost the lithospheric root below ∼100 km depth that was there during intracratonic basin formation. The low elevation and high geoid of the western Paraná Basin requires a dense (eclogite) layer within the crust/shallow lithosphere, possibly associated with the NeoProterozoic Western Paraná Suture Zone and/or Mesozoic plume activity, while topography and geoid of the basins further west and of the western Rio de la Plata craton seem affected by dynamic (subduction‐related) topography. Thus, the variable geophysical structure of the platform lithosphere reflects a history that involves besides some stable keels, significant modification and thinning.

A Model Sensitivity Study of Ocean Surface Wave Modulation Induced by Internal Waves

AbstractNonlinear internal waves are an upper ocean phenomenon that drives horizontal surface current gradients, which in turn modulate ocean surface waves. Under certain conditions, this wave‐current interaction creates ocean surface roughness heterogeneity, in the form of alternating rough/smooth bands. In this study, we investigate the sensitivity of the modulation effect to internal wave properties and develop sea states using simulations of individual internal wave solitons. We utilize a phased‐resolved two‐layer fluid model to capture the evolution of surface waves deterministically. We conduct extensive simulations with a wide range of parameters, including fluid layer density ratio, internal wave amplitude, and parametric wind speed. We use the ratio of the mean surface slope between the rough and smooth bands, which are identified in the simulated surface wave field, to systematically investigate their response to the internal wave forcing across all our simulation cases. Our results show that, among the internal wave parameters, the upper‐lower layer density ratio causes the strongest surface heterogeneity. Spectral analysis of the surface wave elevation and slope variance reveals that the wavenumbers above the peak are most impacted. We demonstrate that accounting for the internal wave‐induced modulation requires including wave steepness statistics, for example, when modeling air‐sea exchange using a surface roughness, z0, parameter. Currently, these statistics are not included in typically coupled modeling schemes, and these systems cannot account for the impact of internal waves, even if the solitary wave phenomena are resolved.

Experimental investigations on the hydrodynamics of a multi-body floating aquaculture platform exposed to sloping seabed environment

The coastal area near islands has become a key area for aquaculture because of the long offshore distance and suitable wave conditions. There is a topographic change near the islands, and the reflected waves generated by the topography modify the wave field in the aquaculture area, which may cause structural damage to the offshore net cage. Most studies on the hydrodynamic characteristics of aquaculture structures do not consider the effects of topography. Therefore, we investigated the hydrodynamic characteristics and wave field of a multi-body floating aquaculture platform under the influence of sloping seabed by leveraging a physical model approach. The results show that the low-frequency component of the surge motion of the cage on the weather side increases significantly under the influence of sloping seabed. However, the heave and pitch motions change slightly. Considering the presence of the sloping seabed, the wave elevations inside cages have been changed too., The wave breaking inside the cage on the weather side becomes more evident when the incident wavelength is equal to the width of the cage. And its wave response gradually shifts from wave frequency to high frequency. Regarding the cage on the lee side, the wave response inside it is positively correlated with the incident wavelength. The results of this study provide a reference for the design and optimization of aquaculture structures anchored near islands.

Higher-order gap resonance and heave response of two side-by-side barges under Stokes and cnoidal waves

Coupled piston-mode fluid response and the heave motion of two identical barges in side-by-side configuration is studied under finite-depth and shallow-water waves using a two-dimensional fully nonlinear numerical wave tank. To understand possible critical responses of the gap flow and the floating barge, regular-wave conditions which are able to excite up to 5th-order nonlinear gap resonance and also the resonant heave motion of the barge are considered. In shallow-water waves, high-frequency oscillations, featured by secondary peaks in the time histories, are observed for both wave elevation in the gap and the heave motion of the barge. The shallow-water wave-induced 4th- or 5th-order gap resonance can be equally crucial as the 1st- and 2nd-order resonances due to finite-depth waves. At higher-order gap resonance, the higher-harmonic heave motion of the barge is negligibly small, in contrast to the gap-flow response. Compared with fixed barges, the free-heave motion of an upstream barge tends to increase the wave elevation in the gap in most of the resonant conditions, except at 1st-order gap resonance where the gap response is greatly reduced. When the resonant heave motion of a floating barge, either located upstream or downstream, is excited, significant barge motion is observed. However, the relative motion between the gap flow and the floating barge is seen to be very small, ascribed by small phase difference between the two. The present study suggests that the effects of heave motion and water-depth should be carefully considered in the design of side-by-side marine operations, and hiding the small bunkering ships behind the large receiving ships is regarded as a preferred arrangement during the bunkering operations in offshore and coastal environments.

Analytical and numerical investigation of edge waves near a vertical breakwater over a convex bottom

Vertical breakwaters are commonly built on the shore, and their existence must influence the character of nearshore dynamics. Analytical solutions based on linear-shallow water equation are derived for edge waves on a convex exponential profile which may be used to idealize the actual bottom profile with a vertical breakwater at the shoreline. The free surface elevation of the edge waves is described using the first kind of the Bessel functions of order ν. The amplitude profiles are similar to those of edge waves on a sloping beach but confined to a narrower offshore domain near the vertical breakwater. The dispersion relationship is derived from the no-flux boundary condition at the vertical breakwater. The wave number is not only related to the frequency but also the water depth at the vertical breakwater and the profile parameter. The group velocity increases rapidly to the maximum value with the increase of frequency, then decreases slowly and finally approaches the classic shallow water wave celerity of the depth at the vertical breakwater. The possible reason for this distinct behavior may be because dynamic characteristics of edge waves are highly dependent on the profile. Moreover, an extensively validated Boussinesq wave model is used to conduct numerical experiments for edge waves induced by surface bumps. The numerical results are consistent with the proposed solutions, confirming the validity of the new analytical solutions.

Computational fluid dynamics predictions of critical hydrodynamics thresholds in the erodibility of inland waterway bank by ship-induced waves

A three-dimensional numerical simulation method based on the resolution of Navier–Stokes equations is used to determine the causal relationship between the ship-induced waves and the erosion phenomenon of the inland waterway banks, and also to provide the critical conditions for waterway bank protection. The erosion process of the bank is defined here as the criterion in which the movements of the discrete medium blocks and particles that form the banks by the action of ship waves undergo a significant jump beyond the critical value of Froude number (Frc). By investigating the wave elevation drawdowns nearby the waterway banks, it is shown that the normal impact force and tangential shear stress caused by ship-induced waves are the main culprits of bank erodibility. The numerical results show that by approaching the Frc, the increasing rate of drawdown reaches its maximum causing a jump in the force of total pressure, which in turn gives a rise to a peak in the shear stress on the waterway bank.

On analytical solutions for transient water waves radiated by cylinders

Analytical solutions for transient water waves radiated by a circular cylinder in deep water are studied in this paper. Within the framework of the potential flow and linear water wave theory, time-domain solutions are analytically derived based on decomposition of the velocity potential consisting of an instantaneous term and a memory term. These two terms are solved by satisfying the governing equations and initial boundary conditions. Transient concentric water waves are further studied and evaluated for a pulsating circular cylinder which expands and contracts radially. Results are compared with those from other numerical models with a good agreement in terms of wave elevation on the free surface. Analytical solutions obtained in this work can be considered as a benchmark in time-domain analysis for linear hydrodynamic problems, and are of help to the theory and application of wavemakers and transient water waves.

Validation of the Satellite Method for Measuring Spectra of Spatially Inhomogeneous Sea Waves

A method for retrieving 2D spatial spectra of sea wave elevations and slopes from high resolution (about 1 m) satellite imagery has been developed that also allows for assessing sea wave angular distributions. A validation of the suggested method was carried out based on the results from a comprehensive experiment that included both satellite imaging of the Black Sea water area and sea truth under controlled conditions. The retrieval of spatial wave spectra from fragments of a satellite image and comparison with the results of measuring the frequency spectra from sea truth data obtained using an array of string wave recorders were carried out. Wave spectra from remote and in situ data are consistent in the frequency range of 0.2–1.1 Hz, corresponding to wavelengths from 1.3 to 39 m.

Empirical estimation of the breaker index using a stereo camera system

To understand the wave-breaking phenomenon that affects coastal structures and sediment transport, various experiments have been conducted using an experimental wave flume equipped with point observation instruments including wave gauges. However, it has been still challenging to precisely measure the wave propagation in the breaking region. In this study, the water surface elevation is observed using stereo cameras, and a modified index for the breaking wave height is proposed. Water surface fields are retrieved spatially and temporally from synchronized stereo images using the wave acquisition stereo system (WASS), and then the breaking wave height, location, and wave front slope angle (WFSA) are analyzed. For the verification of the camera system, a three-dimensional reconstructed map is compared with the wave elevation measured by the wave gauge. The critical WFSA is empirically formulated and used to modify the breaker index. We verify the proposed breaker index formula by applying the index to the spilling breakers with a wide range of relative water depths. The prediction of the breaker index that rapidly decreases under high relative water depth conditions is considerably improved. Using the proposed critical WFSA formula and modified breaker index, the breaking wave heights in coastal areas can be accurately estimated.

Large eddy simulation of focused breaking waves with different wave steepness

The profile of fluid field and wave geometry, kinematic and dynamic characteristics of focused breaking waves in finite water depth with different wave steepness are studied with a constant wave steepness wave focusing method in this paper. The flow field is solved by the two-phase flow model in REEF3D based on the incompressible Navier–Stokes equation and the Large Eddy Simulation (LES) model to simulate the complex breaking process. The numerical model is validated by comparing wave elevation of both focused non-breaking and breaking case with the experimental results and satisfactory agreements are achieved. A series of simulation cases with different global steepness are carried out to analyze the focused waves of different breaking types. The difference between the preset focused condition and the real ones and the area of air cavity rolled by the wave jets are both indicates that the process of wave focusing and breaking show a strong nonlinear profile. The maximum values of the horizontal velocity occur after the impingement moment and can reach 2.5 Cp for extreme steep waves. Three typical wave breaking criteria in finite water depth are calculated and discussed successively. For the geometric criterion analysis, the global wave steepness and local steepness have a good performance both for predicting wave breaking and presenting the breaking intensity. The kinematic breaking criterion ratio shows that the previous threshold 1 at the breaking incipient scenario is not sufficient to predict the wave breaking. Besides, it is found that the time interval when the kinematic breaking criterion ratio big than 1 may related to the wave breaking type. The energy changing rate for both the focusing and dissipation processes increase linearly with the global wave steepness and show a good ability as a dynamic breaking criterion and also prove the asymmetric profile of breaking waves.

Phase-resolved wave prediction for short crest wave fields using deep learning

The phase-resolved wave prediction of short crest waves is important to marine structures for both predicting deterministic motion and assisting decision-making. The present short crest wave phase-resolved prediction methods utilize Fast Fourier Transform (FFT) to process wave elevation fields in a large area, and these methods have shortcomings in calculation efficiency, calculation accuracy, and convenience. This paper proposes a long short-term memory wave prediction model (LSTM-WP model) based on deep learning to achieve a phase-resolved wave prediction of short crest waves. A tank experiment is conducted to verify and analyze the LSTM-WP model. From the results, it can be found that the LSTM-WP model provides high-precision predictions for the short crest wave surface under sea states of levels 4–7. Furthermore, the effects of the direction spectrum, predicted distance, and lead steps are discussed. It can be found that as the direction of the short crest wave becomes more concentrated, the prediction error rises more rapidly with increasing sea states. As the predicted distance increases, the prediction error of the LSTM-WP model increases linearly. As the number of lead steps increases, the prediction error of the LSTM-WP model shows a trend of first decreasing and then increasing.

An efficient frequency-domain method for computing transient responses of floating structures to irregular waves

Traditionally, computing dynamic responses of floating structures to waves can be conducted efficiently in the frequency domain, but only steady-state responses are computed. For computing transient responses of floating structures to irregular waves, this paper, assuming that the frequency response functions (FRFs) have been obtained from running a hydrodynamic software, develops an efficient frequency-domain method using pole-residue operations. In contrast to the pole-residue method using “true” poles in the Laplace domain, the proposed frequency-domain approach assigns “artificial” poles associated with the wave-structure system directly from the given FRFs. The proposed method is easy to implement and efficient in computational time, especially when the FFT algorithm is utilized; its accuracy is verified by using a time-domain method through numerical examples of an FPSO system to regular and irregular wave elevations.