Wave Drift Research Articles

Hydrodynamics of a free-floating cylinder in front of an orthogonal vertical wall

ABSTRACT The paper deals with the analytical evaluation of the linearized exciting wave forces; hydrodynamic coefficients and wave drift forces acting on a free-floating vertical cylindrical body placed in front of a reflecting orthogonal vertical wall. Linear potential theory is assumed, and the associated diffraction and radiation problems are solved in the frequency domain. The hydrodynamic interactions among the body and the adjacent breakwater are taken into account by applying a theoretical model based on the method of images, considering the breakwater as a fully reflecting, bottom mounted and water surface piercing wall of infinite length. The theoretical approach is supplemented by a numerical model considering the orthogonal breakwater as a barrier of finite length. The results of both formulations are compared with the ones corresponding to an isolated cylindrical body demonstrating the amplified scattered and reflected waves at specific frequency ranges originating from the presence of the orthogonal breakwater.

Identification of wave drift force QTFs for the INO WINDMOOR floating wind turbine based on model test data and comparison with potential flow predictions

The paper presents a comparison between empirical and numerical quadratic transfer functions (QTFs) of the horizontal wave drift loads on the INO WINDMOOR floating wind turbine. The empirical QTFs are determined from cross bi-spectral analysis of model test data obtained in an ocean basin. Validation of the identified QTF is provided by comparing low frequency motions reconstructed from the empirical QTF with measurements. The numerical QTFs are calculated by a panel code that solves the wave-structure potential flow problem up to the second order. Systematic comparisons between numerical and empirical QTFs allows identification of tendencies of empirical QTFs and limitations of the second order potential flow predictions. The study is limited to hydrodynamic loads from waves only, i.e. without current. For small seastates, the results indicate that the second order potential flow predictions of the surge QTFs agree quite well with the wave drift coefficients identified empirically from the model test data. For moderate and high seastates, second order predictions underestimate the surge wave drift coefficients for all compared diagonals of the QTFs. The discrepancies between predictions and empirical coefficients are not small, especially at the lower frequency range (below around 0.10 Hz) where the potential flow wave drift forces tend to zero.

Investigation of a dynamically positioned floating offshore wind turbine concept

The dynamically positioned wind turbine concept consists of a floating platform equipped with a wind turbine and propellers. In contrast to a conventional floating offshore wind turbine, it has no moorings. Instead, the propellers are used to keep the wind turbine stationary. It may also be equipped with an on-board energy storage system (e.g. batteries, hydrogen, etc.) to avoid grid-connection. This concept is well suited for deployment in the far-offshore, where grid-connection and installation operations are challenging.As the propellers which are used to control the position of the wind turbine require power supply, the aim of this study is to investigate whether and in what conditions there can be a positive net power production. To this end, we have developed a velocity and power prediction program (VPPP) to estimate the power consumed by the propellers and the power generated by the wind turbine, as a function of wind conditions, and design parameters (e.g. diameter of the wind turbine and characteristics of the propellers rotors). The VPPP is based on Newton’s first law of motion. The forces applied on the system are: the wind turbine thrust, the mean wave drift, and the propellers thrust.Inspired by an existing floating offshore wind concept, an example design has been developed. The diameter of the wind turbine’s rotor is 78 m. Its rated power is 2 MW. The wind turbine is mounted on a 40 m square barge. The diameter of the propellers’ rotor is 6 m. Using the VPPP, the power performance of this example design has been investigated as function of wind conditions. The maximum generated power is 0.89 MW. It is obtained for a true wind speed of 13.4 m/s. If deployed in the Northern Atlantic Ocean, this design could achieve a capacity factor of 15%, which is low in comparison to the 70% capacity factor which would be achieved by a moored floating offshore wind turbine if deployed at the same location.

Experimental investigation of a closed vertical cylinder-shaped fish cage in waves

Wave-induced response of a closed floating fish cage consisting of a vertical circular cylinder with an external toroidal floater is studied theoretically and experimentally. A main purpose was to investigate how the internal sloshing would influence the global response of the cage, the interior wave elevation and also the mean drift loads. An ocean basin laboratory was used in order to minimize tank wall effects. An optical system involving eight markers was used to obtain experimental values for radial elastic deformations of the cylindrical part. The closer a coupled natural period between body motions and sloshing is to a corresponding natural sloshing period, the more nonlinear sloshing can be. In the examined case, the highest coupled natural period between surge, pitch and sloshing is 0.8 times the highest natural sloshing period. Linear potential flow theory can, in general, explain experimental transfer functions of rigid-body motions and sloshing due to rigid-body motions obtained by both regular wave and truncated white noise tests. Theoretical second order mean wave drift forces based on a rigid body and potential flow agree also well with experimental results. Resonant 3D sloshing was excited due to ovalizing hydroelastic structural modes in both regular waves and white-noise tests. The closeness between the corresponding structural and sloshing frequencies caused large response. A linear hydroelastic analysis based on WAMIT and LS-DYNA could partly explain the response. Parametric resonant pitch response occurred experimentally at large wave periods partially due to in and out of water motion of portions of the floater and was explained by treating the pitch as uncoupled motion modeled by the Mathieu equation. The pitch motion predicted by linear potential flow theory was, in general, unsatisfactory when the floater was partly out of the water occasionally.

Physically significant wave solutions to the Riemann wave equations and the Landau-Ginsburg-Higgs equation

The nonlinear Riemann wave equations (RWEs) and the Landau-Ginsburg-Higgs (LGH) equation are related to plasma electrostatic waves, ion-cyclotron wave electrostatic potential, superconductivity, and drift coherent ion-cyclotron waves in centrifugally inhomogeneous plasma. In this article, the interactions between the maximum order linear and nonlinear factors are balanced to compute realistic soliton solutions to the formerly stated equations in terms of hyperbolic functions. The linear and nonlinear effects rheostat the structure of the wave profiles, which vary in response to changes in the subjective parameters combined with the solutions. The established solutions to the aforementioned models using the extended tanh scheme are descriptive, typical, and consistent, and include standard soliton shapes such as bright soliton, dark soliton, compacton, peakon, periodic, and others that can be used to analyze in ion-acoustic and magneto-sound waves in plasma, homogeneous, and stationary media, particularly in the propagation of tidal and tsunami waves.

Mean Wave Drift Forces on a Barge-Type Floating Wind Turbine Platform with Moonpools

Barge-type platforms with moonpools are a promising type of foundation for floating offshore wind turbines due to their good seakeeping performance. In this paper, the mean wave drift force on a barge-type vertical-axis floating wind turbine with multiple moonpools was investigated through physical model testing and numerical calculations using WAMIT. The focus was on the characteristics of mean drift load and its optimization potential. The present numerical results indicated that the application of moonpools was useful in reducing horizontal mean drift force at specific frequencies, and the reason was ascribed to the significant radiation effect of the resonant water oscillations in moonpools. The observed reduction effect on mean drift force was shown to be dependent on the viscous damping of moonpool resonance. The experimental results showed that the maximum response of the mean sway drift force was reduced by the gyroscopic effect of rotations of the vertical-axis wind turbine, and this reduction effect became stronger as the rotating speed of the wind turbine increased, but was weakened as wave amplitude increased. The comparisons between experimental data and potential flow predictions indicated that viscous effects should be taken into account to reasonably estimate the mean wave drift forces on barge-type floating wind turbines.

Development of Enhanced Two-Time-Scale Model for Simulation of Ship Maneuvering in Ocean Waves

In this study, a modified two-time-scale model is proposed to overcome the limitations of the existing maneuvering analysis model. To this end, not only wave conditions but also all directions of ship operation velocities are considered in estimating wave drift force and moment. Subsequently, the increment of the drift force and moment induced by steady drift and yaw motion of a ship is imposed up to the first derivative of Taylor series expansion. By introducing this bilinear model, the burden of the drift force computation is reduced so that a more realistic and efficient seakeeping-maneuvering coupling analysis can be performed. A turning circle simulation in a regular short wave is carried out using the modified two-time-scale model. Then, the performance is validated by comparing its results with the direct coupling model. Moreover, quantitative improvement of the present numerical scheme and the influence of the operation velocities on ship maneuvering performance are discussed.

Standing wave drift of hemispherical resonator with quality factor non-uniformity under a ring electrode excitation

Hemispherical Resonator Gyroscope (HRG) is a classical high precision Coriolis Vibration Gyroscope (CVG), which performs attitude estimation of carrier by detecting the precession of standing wave of resonator, thus, the drift of standing wave of resonator has a great influence on the output accuracy of gyroscope, where the quality factor non-uniformity of resonator is one of main error sources. Ring electrode is a classical excitation structure of HRG because the standing wave can precess freely under its excitation, which makes the gyroscope have more accurate scale factor, larger measurement range and better dynamic characteristics. In this paper, the equations of motion of an ideal resonator excited by a ring electrode are derived by the elastic thin shell theory and Lagrange mechanical principle, then the corresponding equivalent mechanical model is established. According to the “average method”, it can be seen that the ideal resonator excited by the ring electrode works in integral mode, and any position in the circumferential direction of resonator can be a working point, which means that the quality factor non-uniformity has a great effect on the drift of standing wave. Therefore, the equations of motion of resonator with quality factor non-uniformity under the ring electrode excitation are deduced by the equivalent mechanical model, and the drift model of standing wave is established by the “average method”, it can be found that both the amplitude of quality factor non-uniformity and angle between the “inherent damping axis” and antinode axis of standing wave can affect the drift rate of standing wave. Moreover, the drift model indicates that if the input angular rate does not reach the threshold, the precession angular rate of standing wave will appear “self-locking” phenomenon, that is, the gyroscope will lose the integral effect.

Response of the International Energy Agency (IEA) Wind 15 MW WindCrete and Activefloat floating wind turbines to wind and second-order waves

Abstract. The EU Horizon 2020 project COREWIND (COst REduction and increase performance of floating WIND technology) has developed two floating platforms for the new International Energy Agency (IEA) Wind 15 MW reference wind turbine. One design – “WindCrete” – is a spar floater, and the other – “Activefloat” – is a semi-submersible floater; both designs are made of concrete. In this work the design of the floaters is introduced with their aero–hydro–servo-elastic numerical models, and the responses of both floaters in both static and dynamic simulations are investigated. The static displacements and natural frequencies are simulated and discussed. Additionally, the effects of the mean wave drift forces and second-order difference-frequency wave forces on the systems' responses are presented. The increase in the turbine's power capacity to 15 MW in IEA Wind model leads to an increase in inertial forces and aerodynamic thrust force when compared to similar floating platforms coupled to the Technical University of Denmark (DTU) 10 MW reference model. The goal of this work is to investigate the floaters' responses for different load cases. The results in this paper suggest that at mild wave loads the motion responses of the 15 MW floating offshore wind turbines (FOWTs) are dominated by low-frequency forces. Therefore, motions are dominated by the wind forces and second-order wave forces rather than the first-order wave forces. After assessing and understanding the models' responses, the two 15 MW FOWT numerical reference models are publicly available to be used in the research and development of floating wind energy.

Estimation of wave-induced steady force using system identification, model tests, and numerical approach

This paper addresses the method for estimating maneuvering mathematical models in waves, and uses captive model tests to verify it. To obtain the wave force and moment, two kinds of captive model tests are performed. One is straight towing tests with different towing directions to consider various incident wave angles, while the other is circular motion tests at different regular wave frequency. These captive model tests provide added resistance and wave-induced steady force considering both different wave direction and ship speed, and different wave drift angles. The wave drift forces and moment obtained are validated by performing the maneuvering simulation in waves, and comparison with the results of free running model tests. This paper introduces the application of the Estimation-Before-Modeling (EBM) approach, one of the System Identification methods, to estimate mathematical models for ship maneuverability targeting KRISO Very Large Crude oil Carrier (KVLCC2). The most important force component for the prediction of the maneuverability of a ship is the accuracy of the wave-induced steady force acting on the ship. Here, the EBM approach is divided into two steps: First, the motion variables and forces are estimated by Extended Kalman Filter and Modified Bryson-Frazier smoother. Second, the wave-induced steady forces are determined by removing the hydrodynamic force acting on the ship during motion. Also, during the second step of the EBM approach, the database consisting of wave length and incident wave angles is constructed. All estimated variables are based on data obtained by free running model tests in regular waves. Finally, the estimated wave-induced steady force is interpolated, added to the hydrodynamic force component of the 3-DoF equations of motion, and the turning simulation of the ship in waves is then performed. Comparison of the results with the results of free running model tests confirms the validity of the established model.

Numerical study of closed rigid fish cages in waves and comparison with experimental data

Closed fish cages have gained increased interest in marine aquaculture. However, knowledge on the seakeeping behaviour of a floating closed cage and the influence of the contained water inside the cage are still limited. In this paper, a coupled numerical model is developed for the simulation of closed rigid cages in waves. Numerical studies are conducted both in the frequency domain and in the time domain, and compared with scaled physical experiments. Special attention has been drawn to the coupling effects of sloshing on cage response and the resulting mooring line forces. The comparative analyses show that sloshing of the contained water has large influence on the coupled surge and pitch motions of the cage. Sloshing is also found to have significant effect on the mean-drift forces in regular waves. In the tested/simulated irregular waves, the mooring forces are found to be dominated by the slow-drift motions, which indicates that the slowly-varying wave drift forces need to be considered in the design of the mooring system for a floating closed cage.

Diurnal continental shelf waves with a permeable coastal boundary: Application to the shelf northwest of Norway

Spatially damped continental shelf waves (CSWs) with diurnal tidal frequency outside Lofoten–Vesterålen in north-west Norway are studied theoretically for an idealized shelf topography. Wave damping is caused by the exchange of fluid on the shelf with an inner archipelago through a permeable coastline. This exchange is modelled by the application of a Robin condition at the coastal boundary. It is shown that CSWs with diurnal frequencies are possible in a small wave number range centred around zero group velocity. By calculating the nonlinear radiation stress components in the spatially damped CSWs, we find the time- and depth averaged Lagrangian mean drift current to second order along the coast. We show that the Lagrangian mean drift current is independent of the value of the damping coefficient, however small, as long as it is nonzero. This illustrates the singular behaviour of the Lagrangian wave drift problem for CSWs.

Coupled dynamics between a turret-moored FPSO and a semi-submersible accommodation platform

In multi-body offshore systems, a telescopic gangway is often adopted for personnel transfer, the feasibility and safety of which are crucial. The coupled dynamics and gangway responses of a turret-moored floating production storage and offloading (FPSO) unit and a semi-submersible accommodation platform (AP) were investigated numerically in this study. Both side-by-side arrangement and the configuration that AP is tandem at the stern of FPSO were considered. The hydrodynamics considering multi-body wave interaction were calculated in frequency domain based on potential theory. The non-linearity of second-order wave drifts, moorings, and turret was fulfilled in time domain. We focused mainly on the effects of multi-body interactions on hydrodynamics and gangway responses. The hydrodynamic interactions have a negligible effect on the global motions of FPSO, whereas it more strongly affects AP. The interference is more intense in side-by-side scenario than in tandem configuration. The gangway responses are governed by relative translational motions between two vessels and are also related to its initial arrangement. Since weathervaning of FPSO can cause a large yaw offset, non-collinear sea states are considered, in addition to cases with different significant wave heights. Extreme gangway responses are predicted according to Weibull distribution, by which the environment criteria are determined.

Experimental and Numerical Analysis of Wave Drift Force on KVLCC2 Moving in Oblique Waves

In this study, experimental and numerical methods were applied to estimate surge and sway wave drift forces and yaw drift moment acting on KVLCC2, advancing in oblique wave. An experiment was carried out in the ocean engineering basin of the Korea Research Institute of Ships and Ocean Engineering (KRISO). A series of regular wave tests under various heading conditions were conducted to investigate ship motion responses and wave drift forces. A Rankine panel method based on potential flow was adopted in the numerical analysis, and the direct pressure integration method that integrates second-order pressure on the hull surface was applied to compute wave drift force. Through this study, validation data of wave drift force acting on KVLCC2 was established, and the computation capability of the potential-based numerical method was systematically analyzed.

Drift and termination of spiral waves in optogenetically modified cardiac tissue at sub-threshold illumination.

The development of new approaches to control cardiac arrhythmias requires a deep understanding of spiral wave dynamics. Optogenetics offers new possibilities for this. Preliminary experiments show that sub-threshold illumination affects electrical wave propagation in the mouse heart. However, a systematic exploration of these effects is technically challenging. Here, we use state-of-the-art computer models to study the dynamic control of spiral waves in a two-dimensional model of the adult mouse ventricle, using stationary and non-stationary patterns of sub-threshold illumination. Our results indicate a light-intensity-dependent increase in cellular resting membrane potentials, which together with diffusive cell-cell coupling leads to the development of spatial voltage gradients over differently illuminated areas. A spiral wave drifts along the positive gradient. These gradients can be strategically applied to ensure drift-induced termination of a spiral wave, both in optogenetics and in conventional methods of electrical defibrillation.

Anti-disturbance control for dynamic positioning system of ships with disturbances

A robust anti-disturbance control (RADC) strategy is investigated for the ship dynamic positioning (DP) systems with unknown time-varying disturbances. The disturbances are brought about by wind, second-order wave drift, ocean currents as well as unmodeled dynamics, which are modelled by the first-order Markov process. The disturbance observer (DO) is established to online estimate disturbances. Then, the anti-disturbance controller for the ship DP system is designed and the stability analysis of the composite system is presented by using stochastic stability theory. The DOBC and the pole placement methods are implemented to improve the robustness against ocean environmental disturbances. The unknown time-varying disturbances can be attenuated such that the yaw angle and position of the ship reach the desired value with high accuracy. Finally, simulation on a supply ship is given to illustrate the validity of the proposed control strategy.

Analytical method for loads determination on floating solar farms in three typical environments

Floating solar energy is an industry with great potential. Farms can be installed on lakes, reservoirs or offshore. Numerous projects are under study or have been realised. This study presents three reference cases for floating solar farms, with adapted environmental data: a small lake (2.5 MWp – Mega Watt Peak - island), a large lake (7.5 MWp island) and offshore (2.5 MWp island). Mooring is one of the biggest challenges of floating solar photovoltaics (PV), compared to ground-mounted solar PV. To date, most mooring designs of industrial projects have been performed by computing environmental loads using an analytical analysis. This study aims to present one of the methodologies currently used in industry to perform a mooring design and to highlight the areas where further research is necessary before continuing developing industrial projects. Wind and current loads are computed with drag forces, considering drag coefficients from norms, wind tunnel tests, computational fluid dynamics modelling and the literature. Waves drift loads are computed with the Maruo formula. Results show that wind loads dominate for all cases, except for the offshore conditions, where waves have a significant contribution to the total load (around 50%). Even though the large lake island is 3 times larger than the offshore island, the total load applied on the offshore island is higher. The main challenges in the mooring design for each case are also underlined.

Added resistance using Salvesen–Tuck–Faltinsen strip theory and the Kochin function

It is now more than half a century since the development of the renowned and well-established strip theory of Salvesen–Tuck–Faltinsen (STF), Salvesen et al. (1970). One of the existing, and widely used, methods for calculating the wave drift force (zero-speed case), or added resistance (forward-speed case), within this strip theory, is a near-field formulation which was developed by Salvesen himself in Salvesen (1974), Salvesen (1978). This method invokes a weak-scatterer assumption to drop one term, and also approximates the exponential terms as constant in the integrals over each two-dimensional ship section. These approximations are essentially a long-wave assumption Salvesen (1974). The main objective of this paper, which has been entirely inspired by the method of Kashiwagi et al. (2010), is to apply a far-field formulation, in the context of STF strip theory, without the above-mentioned assumptions. This far-field method is implemented following Maruo (1960b), Maruo (1963) and employs the Kochin function Kochin (1936) to express the wave kinematics in the far field. The necessary ingredients for this method are obtained by an implementation of STF theory using a low-order Boundary Element Method (BEM) and the two-dimensional free-surface Green function. No weak-scatterer assumption is required as the Kochin function explicitly includes the interaction of the disturbance potentials. Sectional integrals of the Kochin function are calculated analytically, assuming piecewise-constant variation of the potentials. Within this far-field framework all three integrals from Maruo’s relation are treated, and the line integral along the vessel’s length is calculated exactly assuming either a linear or a Fourier-mode decomposition of the non-exponential terms. The outcome is a far-field calculation procedure inside STF theory which compares very well with experimental measurements and relevant reference solutions. This is verified by the calculation of wave drift force and added resistance for six different ship hulls. One notable advantage of the presented framework, in comparison to Salvesen’s method (and also to that of Gerritsma and Beukelman (1972)), is its ability to accurately predict the zero-speed wave drift force. In addition, the long-wave approximate form of the Kochin function method is also discussed. Similar to Salvesen’s method, the wave drift force using this approximation, is expressed in terms of the body motion, the hydrodynamic coefficients and the sectional geometric constants. The approximate form performs well at zero-speed, but deteriorates quickly as the speed increases.

P.845The effect of antipsychotic therapy on the social functioning of patients with paranoid schizophrenia

A ship encounters wave loads in actual seas, it is necessary to estimate the ship's manoeuvring performance in waves for its safe operations. In this study, turning characteristics of a KCS model ship in regular waves were investigated by free-running model tests. 35° port and starboard turning circle tests in regular waves were carried out in KRISO Ocean Engineering Basin with variations of regular wave heights, lengths, directions and model approach speeds. Propeller revolution rate was mostly fixed at the constant value corresponding to the full-scale speed of 16 knots in calm water. Ship's turning behaviours in waves can be divided into initial and steady turn phases. Firstly, during initial turns, the ship's safety which is related to avoiding a fixed front obstacle is focused on. ‘DMINw’ is defined as the minimum distance between the fixed front obstacle and the ship initial trajectory. And safety index ‘STw’ is proposed, which is formulated by using the ratio between DMINw in calm water and in waves. The ship becomes safer in head waves than calm water due to small advances. In starboard beam waves, when the ship turns to starboard, that becomes dangerous due to small transfers. In port beam waves, the ship which turns to starboard is mostly safe. But, in short port beam waves, yaw angle is slowly increased and the advance is relatively large. It is hypothesized that the wave drift yaw moments prevent the ship from turning to starboard. Secondly, drifting distances and angles in steady turns are quantified. The drifting distances increase with decreasing wave lengths, when the wave lengths are varied from 0.5 to 1.0 ship length. The drifting distances are approximately proportional to the wave steepness. Finally, approximate formula of STw is proposed. That is formulated as the function of ship advance and transfer in calm water and waves only. DMINw can be simply obtained if the initial trajectory is approximated as the ellipsoidal quadrant. Based on several parametric simulations, it was confirmed that STw is proportional to the cube of the transfer in waves and is inversely proportional to the advance in waves. STw is formulated so that it can be applied to arbitrary ships.

PTEBEM for wave drift forces based on hydrodynamic pressure integration

Taylor Expansion Boundary Element Method(TEBEM) is an accurate numerical scheme for solving waves and floating bodies related potential problems, especially the induced velocity at the sharp corner. However, the TEBEM method introduces too many unknowns, resulting in a decrease in the computational efficiency. In this paper, a less time consuming method with similar numerical accuracy named Partial Taylor Expansion Boundary Element Method(PTEBEM) is proposed. Firstly, research shows that the singular property at sharp corner panels is stronger than others. Therefore, retain the Taylor expansion related coefficient and the partial derivatives corresponding to the panels only can form a smaller algebraic system. After solving all the velocity potential and the partial derivatives at sharp corner panels, the partial derivatives at smooth boundary panels can be obtained by constant panel method. From the results of KVLCC2, coupled with Extended Boundary Integral Method(EBIM), the irregular frequency is eliminated. And the irregular frequency mainly comes from the water line integral term and the square of velocity term. Applying the Taylor expansion at sharp corner panels only can retain the numerical accuracy of TEBEM, and the computational efficiency is improved.