Wave Surface Elevation Research Articles

Numerical Simulation of Solitary Wave Forces on A Vertical Cylinder on A Slope Beach

Wave forces acting on a vertical cylinder at different locations on a slope beach in the near-shore region are investigated considering solitary waves as incoming waves. Based on the Reynolds-averaged Navier-Stokes equations and the k-ε turbulence model, wave forces due to the interaction between the solitary wave and cylinder are simulated and analyzed with different incident wave heights and cylinder locations. The numerical results are first compared with previous theoretical and experimental results to validate the model accuracy. Then, the wave forces and characteristics around the cylinder are studied, including the velocity field, wave surface elevation and pressure. The effects of relative wave height, Keulegan-Carpenter (KC) number and cylinder locations on the wave forces are also discussed. The results show that the wave forces exerted on a cylinder exponentially increase with the increasing incident wave height and KC number. Before the wave force peaks, the growth rate of the wave force shows an increasing trend as the cylinder moves onshore. The cylinder location has a notable effect on the wave force on the cylinder in the near-shore region. As the cylinder moves onshore, the wave force on the cylinder initially increases and then decreases. For the cases considered here, the maximum wave force appears when the cylinder is located one cylinder diameter below the still-water shoreline. Furthermore, the fluid velocity peaks when the maximum wave force appears at the same location.

Freak wave in high-order weakly nonlinear wave evolution with bottom topography change

In deep-water, quasi-resonant four-wave interaction gives rise to the occurrence probability of extreme wave height, which leads to freak wave as a natural disaster. As water wave enters shallow water, four-wave interaction becomes weak and wave shoaling makes this effect become complicated. This study conducts a Monte Carlo simulation in modified Nonlinear Schrödinger equation considering bottom topography change, and gives spatial evolution of high-order nonlinearity in wave train from statistical moment. The result indicates, slope angle plays an important role in a shallow water depth, and steep slope brings about a significant enhancement of extreme event in distribution of maximum wave height and surface elevation.

Wave Propagation Studies in Numerical Wave Tanks with Weakly Compressible Smoothed Particle Hydrodynamics

Generation and propagation of waves in a numerical wave tank constructed using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) are considered here. Numerical wave tank simulations have been carried out with implementations of different Wendland kernels in conjunction with different numerical dissipation schemes. The simulations were accelerated by using General Process Graphics Processing Unit (GPGPU) computing to utilize the massively parallel nature of the simulations and thus improve process efficiency. Numerical experiments with short domains have been carried out to validate the dissipation schemes used. The wave tank experiments consist of piston-type wavemakers and appropriate passive absorption arrangements to facilitate comparisons with theoretical predictions. The comparative performance of the different numerical wave tank experiments was carried out on the basis of the hydrostatic pressure and wave surface elevations. The effect of numerical dissipation with the different kernel functions was also studied on the basis of energy analysis. Finally, the observations and results were used to arrive at the best possible numerical set up for simulation of waves at medium and long distances of propagation, which can play a significant role in the study of extreme waves and energy localizations observed in oceans through such numerical wave tank simulations.

Effect of Double-Side Curved Baffle on Reducing Sloshing in Tanks under Surge and Pitch Excitations

Sloshing is associated with the structural safety of liquid storage vessel. Installing the baffles inside the containers would be beneficial for the mitigating the damage due to the severe sloshing. In this study, an innovative type of double-side curved baffle was proposed to evaluate its effect on reducing sloshing in a rectangular tank under surge and pitch excitation. For comparison with conventional baffles, effects of the vertical baffle and the T-type baffle on mitigating sloshing were also studied experimentally and numerically by analyzing the free surface wave elevation as well as the hydrodynamic pressure on the tank wall. The effective stress at the double-side curved baffle along the height direction of the baffle is much smaller than that at the T-type baffle although they have the same mitigation effect on sloshing wave heights. The sloshing-induced effective stress on the double-side curved baffles was analyzed by varying their radian. Findings show that the effective stress on the baffle tends to decrease with the increase in the radian. The velocity field was presented to observe effect of the baffles on sloshing with the aid of ADINA and laboratory experiments conducted on a hexapod motion platform.

Breaking-Wave Induced Transient Pore Pressure in a Sandy Seabed: Flume Modeling and Observations

Previous studies on wave-induced pore pressure in a porous seabed mainly focused on non-breaking regular waves, e.g., Airy linear waves or Stokes non-linear waves. In this study, breaking-wave induced pore pressure response in a sandy seabed was physically simulated with a large wave flume. The breaking-wave was generated by superimposing a series of longer waves onto the foregoing shorter waves at a specified location. Water surface elevations and the corresponding pore pressure in the process of wave breaking were measured simultaneously at three typical locations, i.e., at the rear, just at, and in front of the wave breaking location. Based on test results, characterization parameters are proposed for the wave surface elevations and the corresponding pore-pressures. Flume observations indicate that the wave height was greatly diminished during wave breaking, which further affected the pore-pressure responses. Moreover, the measured values of the characteristic time parameters for the breaking-wave induced pore-pressure are larger than those for the free surface elevation of breaking-waves. Under the action of incipient-breaking or broken waves, the measured values of the amplitude of transient pore-pressures are generally smaller than the predicted results with the analytical solution by Yamamoto et al. (1978) for non-breaking regular waves with equivalent values of characteristic wave height and wave period.

Validation of the dynamic load characteristics on a Tidal Stream Turbine when subjected to wave and current interaction

A comparison of a tidal turbine's performance and structural loads is conducted using lab-scale numerical models and experimental testing under multiple current-only and wave-current conditions at the IFREMER wave-current flume. Experimental testing, used to validate CFD models, was accomplished using a 0.9 m diameter, 3-bladed tidal turbine and had a blockage ratio of 8% while the turbine was submerged. Initial investigations analysed the performance and loads on the turbine under uniform and profiled current-only conditions. The presence of a profiled velocity gradient was found to have a negligible effect on the average performance characteristics; however, transient thrust, torque and out of plane bending moment loads experienced much greater variations. These load fluctuations were further increased with increasing levels of shear in the velocity profile, while peaks in the turbine loads coincided with its rotational frequency. The addition of regular, Stokes 2nd Order Theory waves added to the complexity of the flow conditions experienced by the turbine. The effect on the average performance characteristics were negligible while the total turbine thrust and torque fluctuations increased by 35 times that of the current-only cases. Peaks in the loads aligned with the wave surface elevation, indicating the importance of transient analyses of dynamic loads.

An extended nonlinear Schrödinger equation for water waves with linear shear flow, wind, and dissipation

Based on potential flow theory, governing equations are developed for surface gravity waves affected by wind, dissipation, and a linear shear flow (LSF). The LSF is composed of a uniform flow and a shear flow with constant vorticity. Using the multiple-scale analysis method, a two-dimensional nonlinear Schrödinger equation (NLSE) describing the evolution of freak waves in water of finite depth is derived by solving the governing equations. The modulational instability (MI) of the NLSE is analyzed, and it is shown that uniform up-flow and positive vorticity require a lower angular frequency to sustain the MI than uniform down-flow and negative vorticity. Moreover, the low-frequency section requires stronger wind velocity to sustain the MI than the high-frequency section. In other words, young waves are more sensitive to the MI than old waves. In addition, the free surface elevation of freak waves as a function of time is examined for different uniform flows, vorticities, and wind forcing, and the results are compared with a measured freak-wave time series from the North Sea. It is found that the theory agrees with the observations. Furthermore, the LSF affects the height and steepness of freak waves, while wind forcing affects their symmetry. Hence, the MI, wave–current interactions, and wind–wave interactions may be responsible for generating freak waves in realistic ocean scenarios.

Sensitivity Study on Influencing Factors of Coupled Motion Characteristics for Truss Spar

In the absence of mooring condition, the heave and pitch coupled equations are established considering the effect of static stability and wave surface elevation for a truss spar platform. The influence of the change of the pitch period and the external excitation force (combined wave loads and wind loads together) on the stability of the heave-pitch coupling motion is studied by means of numerical iteration method. The results show that when the wave frequency is close to the natural heave frequency besides the heave-pitch frequency ratio is close to 2: 1, both of the amplitude of heave and pitch motion are increased considering the wind loads. It is about 12 percent increase for heave motion, while 8 percent for pitch motion. Meanwhile, there is a penetration phenomenon between heave and pitch. And the wind load play a more important role in pitch motion, the characteristic frequency of pitch motion will have an obvious change between 1/2 times sub harmonic motion frequency component and 1 time forced motion frequency component considering the wind load.

Rotational Speed Control Using ANN-Based MPPT for OWC Based on Surface Elevation Measurements

This paper presents an ANN-based rotational speed control to avoid the stalling behavior in Oscillating Water Columns composed of a Doubly Fed Induction Generator driven by a Wells turbine. This control strategy uses rotational speed reference provided by an ANN-based Maximum Power Point Tracking. The ANN-based MPPT predicts the optimal rotational speed reference from wave amplitude and period. The neural network has been trained and uses wave surface elevation measurements gathered by an acoustic Doppler current profiler. The implemented ANN-based rotational speed control has been tested with two different wave conditions and results prove the effectiveness of avoiding the stall effect which improved the power generation.

Estimation of velocity potential of water waves using a Luenberger-like observer

We propose a Luenberger-like observer for a water wave system. The water wave dynamics are assumed to be governed by the linearized water wave equation (LWWE). Our proposed observer estimates the velocity potential of water waves by measuring only the surface wave elevation. The information of the water-wave velocity field is then extracted from the gradient of the velocity potential. It is shown that the estimation error of the observer converges exponentially to zero as time tends to infinity. Furthermore, we numerically solve the LWWE and observer equation by the finite difference method. The efficiency of our proposed numerical scheme and the performance of the observer are validated by numerical simulation results.

Experimental and numerical investigation of a jacket structure subject to steep and breaking regular waves

Jacket structures installed in shallow water less than 50 m for offshore wind turbines are frequently exposed to steep and even breaking waves, which may result in severe damage of the structure. However, the models for calculating wave loads were primarily developed for monopile structures, and may not be suitable for jacket structures. The aim of this paper is to improve the understanding of extreme wave loads on jacket structures exposed to steep and breaking waves, based on a combination of numerical modeling and large scale experiments. The experiments with a 1:8 scaled jacket structure exposed to controlled regular waves were conducted in the WaveSlam project. In this study, the measured wave surface elevations and water particle velocities from the experiments are reproduced using a fully nonlinear potential flow solver with a fairly good agreement. Furthermore, the validity of the Morison equation applied to jacket structures is investigated. A reasonably good agreement is achieved for the steep waves without occurrence of breaking. In terms of the breaking waves, the calculated hydrodynamic forcing is examined by subdividing it into a quasi-static and an impulsive slamming force component. The quasi-static force is well reproduced by the Morison equation given the fully nonlinear wave kinematics. Furthermore, eleven degrees of parameterization of the slamming force history are statistically analyzed for a better understanding of the slamming force characteristics. Significant variabilities are presented in these parameters, as a result of the inherent uncertainties in the wave breaking process. In the end, practical implications of the proposed slamming force description to load assessment of a realistic offshore wind jacket structure are discussed.

Experimental investigation of directional hydrodynamic coefficients and the effects on wave force due to spreading angles

Abstract Assessment of wave forces in the design of marine structures considering real ocean properties were reported better represented by short-crested wave statistics. Henceforth, this paper aims to investigate the effect of directional spreading angles for short-crested wave on the prediction of wave forces and hydrodynamic coefficients. The wave surface elevation and forces exerted on bottom fixed vertical cylindrical models in the wave tank by waves with directional spreading angles ranging from 0 to 45 deg were measured experimentally. Based on the measured data, directional hydrodynamic coefficients as function of Keulegan-Carpenter (KC) numbers were derived numerically by the least square method and its effects were analyzed. Force reduction was found due to the directional spreading angles, whereby 1.20 percent of total wave force were reduced with every one deg of angle incremental. Overall, greater reductions are expected for bigger angles as the wave energy distribution area is expected to be increased.

Effects of wave-field nonlinearity on motions of ship advancing in irregular waves using HOS method

The effects of incident-wave nonlinearity on motions of ships advancing in irregular waves are investigated here in statistical sense. The study is carried out by exploiting the combination of HOS method (High Order Spectral method) and time-domain Rankine source method incorporated with HOBEM (Higher-order Boundary Element Method). In the proposed model, HOS method is employed to simulate nonlinear irregular wave fields in cubic order and Rankine source method incorporated with HOBEM is applied to compute ship wave potential as well as disturbed potential, the equations of motions of ship advancing with constant forward speed in nonlinear waves are further established. Instead of employing simplified steady flow models such as uniform stream, steady ship wave potential is computed beforehand and applied to solve ship motions. Weakly nonlinear scheme considering nonlinear F–K (Froude-Krylov) and restoring forces is adopted.The proposed model is first validated in the case of linear regular and irregular waves via comparisons to experiment data and then applied to three different irregular sea states defined by spectrum with respective BFIs (Benjamin-Feir index). A series of long-time numerical simulations are carried out for both linear wave cases and nonlinear ones, and the statistical properties of nonlinear incident waves and the induced influence on ship motions are investigated and further analyzed. The analysis reveals that with large BFI, the skewness and kurtosis of wave surface elevation manifest departures from Gaussian values and the probability density function (p.d.f.) of the surface elevation performs departures from Gaussian behavior. In nonlinear cases, p.d.f. of instantaneous motions and motion amplitudes as well as exceedance probability of motion amplitudes are notably different from their linear counterparts. Higher possibilities for large motions occur in nonlinear cases.

On the Estimation of the Surface Elevation of Regular and Irregular Waves Using the Velocity Field of Bubbles

This paper describes a new set of experiments focused on estimating time series of the free surface elevation of water (FSEW) from velocities recorded by submerged air bubbles under regular and irregular waves using a low-cost non-intrusive technique. The main purpose is to compute wave heights and periods using time series of velocities recorded at any depth. The velocities were taken from the tracking of a bubble curtain with only one high-speed digital video camera and a bubble generator. These experiments eliminate the need of intrusive instruments while the methodology can also be applied if the free surface is not visible or even if only part of the depth can be recorded. The estimation of the FSEW was successful for regular waves and reasonably accurate for irregular waves. Moreover, the algorithm to reconstruct the FSEW showed better results for larger wave amplitudes.

Analysis of water wave interaction with a submerged fluid-filled semi-circular membrane breakwater

This study investigates the hydroelastic interaction between water waves and a submerged fluid-filled semi-circular membrane breakwater based on potential theory. An analytical solution for wave interaction with the membrane breakwater is developed. The series solutions for velocity potentials in the external and internal fluid domains of the breakwater are obtained using the multipole expansions and the separation of variables, respectively. The unknowns in the series solutions are determined by the boundary conditions on the surface and at the two ends of the semi-circular membrane. In addition, a numerical solution for wave interaction with a submerged fluid-filled circular-arc membrane breakwater is developed using the multi-domain boundary element method (BEM). In the numerical solution, the boundary condition on the membrane's surface is directly discretized by expressing the membrane deflection as an integral representation involving the unknown dynamic pressure jump across the membrane. The calculation results from the present analytical solution and the numerical solution are in good agreement. The present numerical results also show reasonable agreement with the numerical and experimental results in literature. Calculation examples are presented to examine the basic features of the hydrodynamic quantities (reflection and transmission coefficients, wave surface elevation and membrane deflection) for the fluid-filled membrane breakwater. Valuable results are given for the engineering design.

Wave Excitation Force Estimation Using an Electrical-Based Extended Kalman Filter for Point Absorber Wave Energy Converters

Accurate real-time knowledge of the wave excitation force affecting a wave energy converter (WEC) – either through measurement or by estimation – is crucial for implementing effective control strategies that ensure optimum power absorption, system reliability, and durability. The estimation of the excitation force using other readily available measurements is deemed a cost-effective solution given the technical difficulties associated with directly measuring the excitation force on the WEC’s floater hull. In this study, an electrical-based extended Kalman filter (E-EKF) estimator for estimating the wave excitation force, floater’s heave displacement, and velocity is proposed. The estimator is derived using a holistic nonlinear wave-to-wire model of a direct-drive heaving WEC. A continuous and differentiable approximation of the well-known Tustin friction model is utilized to incorporate the friction force model into the estimator. The proposed E-EKF estimator requires only the measurement of the three-phase permanent magnet linear generator stator currents using current transducers. A practical approach is provided to overcome the need for measuring the wave surface elevation and velocity. Simulations are conducted to assess the goodness of the proposed E-EKF under various sea-state conditions, modeling mismatches, and electric loading scenarios. For the sake of comparison, the performance of the E-EKF estimator is measured against mechanical-based extended Kalman filter and linearized mechanical Kalman filter estimators. The E-EKF estimator exhibits superior performance in terms of nearly all performance metrics, with an excitation energy percentage error score not exceeding 9 %, while being immune to measurement noise.

Computational Model of Unsteady Hydromechanics of Large Amplitude Gerstner Waves

The computational experiments in the ship fluid mechanics involve the nonstationary interaction of a ship hull with wave surfaces that include the formation of vortices, surfaces of jet discontinuities, and discontinuities in the fluid under the influence of negative pressure. These physical phenomena occur not only near the ship hull, but also at a distance where the waves break as a result of the interference of the sea waves with waves reflected from the hull. In the study reported here we simulate the wave breaking and reflection near the ship hull. The problem reduces to determining the wave kinematics on the moving boundary of a ship hull and the free boundary of the computational domain. We build a grid of large particles having the form of a parallelepiped and, in the wave equation instead of the velocity field we integrate streams of fluid represented by functions as smooth as the wave surface elevation field. We assume that within the boundaries of the computational domain the waves do not disperse, i.e. their length and period stay the same. Under this assumption, we simulate trochoidal Gerstner waves of a particular period. This approach allows to simulate the wave breaking and reflection near the ship hull. The goal of the research is to develop a new method of taking the wave reflection into account in the ship motion simulations as an alternative to the classic method which uses added masses.

Rip current reduction at the open inlet between double submerged breakwaters by installing a drainage channel

In this study, we performed two-dimensional hydraulic experiments to analyze the hydrodynamic characteristics of wave height, surface elevation, and flow around single submerged breakwater with a drainage channel under regular waves corresponding to storm and normal conditions. On the basis of the two-dimensional experimental results, we also performed three-dimensional numerical simulations to specifically analyze hydrodynamic characteristics around double submerged breakwaters with the drainage channel, and compare the numerical results with the experimental results. Compared the numerical results with the experimental results, the numerical results agree well with the experimental results. The numerical and experimental results reveal that the proposed single and double submerged breakwaters with the drainage channel reduces the surface elevation behind the submerged breakwater and rip currents flowing offshore through the open inlet between double submerged breakwaters. Therefore, we see that, the rip currents, that cause scour around the lower part of the open inlet and affect the stability of the submerged breakwaters, can be reduced by installing a drainage channel.

Boundary element model for investigation of the effects of various porous baffles on liquid sloshing in the two dimensional rectangular tank

The liquid sloshing resonance may cause the structural instability even damage of vessel walls. The porous baffles have the ability to dissipate the energy of sloshing motion and suppress the sloshing force on the container walls. The liquid is assumed to be incompressible and inviscid, oscillations amplitudes of liquid are treated to be small, and the walls of tank are chosen as rigid. The fluid domain should be divided into several regions by the porous baffles and the virtual boundaries. The fluxes across those porous baffles satisfy continuity, and the difference of pressure between each baffle's sides is linearly proportional to the flow velocity through the baffles. The porous baffles are fixed at the container in this paper, and the external excitation acting on the porous baffles with flow velocity form also should be added to the boundary conditions. Meanwhile, the normal velocity and pressure of virtual boundary named matching boundary between each region sides should remain continuous. The boundary element method (BEM) with Green's theorem based on the potential flow is conducted with the governing equation and the corresponding to the boundaries of each region. The final entire equation of liquid motion is formulated by assembling the equation of each region. The numerical model is validated by comparing the results with those of the available literatures, good agreement is achieved. The results are proposed for the two dimensional rectangular tank with the top or bottom-mounted vertical porous baffles, multiple mounted two-sided porous baffles, middle-mounted circle porous baffle, top or bottom-mounted semicircle porous baffles, top or bottom-mounted T-shaped porous baffle, and center-mounted cosine-shaped porous baffle. The effects of the porous baffle length, porosity and design on the sloshing force, wave surface elevation, and velocity field are studied and some conclusions are obtained.

Multi-lens stereo reconstruction of wave surface in a wave basin

A new method is developed to measure the wave surface elevation in a wave basin. A thin film of tiny granules floating on the free surface ensures the formation of the dot grid pattern on the wave surface. The dot grid pattern is generated by a high-brightness projector. The granule film has little influence on the wave propagation in a wave basin. The measuring system is validated by the experiments of the propagation of solitary wave in water of uniform depth. It turns out that the time series of the surface elevation measured by the multi-lens stereo reconstruction method agree well with that measured by wave gauges. The errors of the measuring system are discussed. This work sheds a light on measuring the local wave field with high precision and efficiency in laboratory.