Irregular Waves Research Articles

Assessment of ADIS 16364 for the Examination of Ship Motions in the Free-Running Model

The ADIS 16364 instrument is frequently employed for direct measurement of ship motion on ships. However, the validation process for ADIS 16364, to assure its reliability in monitoring ship motion, has not yet been completed. The ship motion model test conducted at the hydrodynamics laboratory utilizes the free-running test technique in conjunction with the QUALISYS motion capture system and the ADIS 16364 device. The purpose of this assessment is to ascertain the instrument's appropriateness for performing ship motion testing. The ADIS device is composed of two components: an accelerometer and a gyroscope. These components are employed to quantify the acceleration of the ship's heave motion and the rotational velocity of its pitch and roll motions, respectively. Utilizing a motion capture system, the QUALISYS Motion Capture System records the motion of a ship model. The examination evaluates two discrete waves produced, comprising two cases of regular waves measuring 10 centimetres in height and 1.5 seconds in period and two cases of irregular waves measuring 16 centimetres in height and 1.75 seconds in period. The elevation motion data in the time domain is acquired from the measurements of the instrument via a wireless system. Following this, various numerical processing methods are implemented, including the moving average filter and cumulative trapezoidal numerical integration. As a result, the root mean square percentage error (RMSPE) discrepancies between the two measuring instruments for regular waves are restricted to a maximum of 5.7% for roll motion and fall below 4% for heave and pitch motions. In the results of the model test response, every movement in both the regular wave and irregular wave scenarios is the same because it does not have an RMSPE of more than 5%.

Fully Coupled Analysis of a 10 MW Floating Wind Turbine Integrated with Multiple Wave Energy Converters for Joint Wind and Wave Utilization

The study focuses on a semi-submersible wind-wave integrated power-generation platform, which consists of an OO-Star semi-submersible platform equipped with a DTU 10 MW wind turbine and a set of wave energy converters. A hydrodynamic model was established using ANSYS-AQWA (2023 R1), and by incorporating upper wind loads and utilizing the open-source program F2A, a fully coupled time-domain model of the integrated power-generation platform was constructed. The primary objective is to explore the interaction mechanisms between the upper wind turbine and the lower wave energy devices under the combined effects of irregular waves and turbulent wind through a series of operational conditions. Additionally, the safety of the mooring system was assessed. The results indicate that, compared to the wave period, the power generation of the lower wave energy devices is more significantly affected by wave height. Overall, the integrated power-generation platform demonstrates optimal performance under the third operational condition. In survival conditions, the introduction of oscillating buoys can improve the motion responses of the platform in terms of sway, roll, pitch, and yaw to a certain extent, but it also increases the surge and heave motion responses and the associated mooring loads. The mooring system can ensure the safety of the integrated power-generation platform under extreme sea conditions.

Effect of shoaling length on rogue wave occurrence

The impact of shoaling on linear water waves is well known, but it has only been recently found to significantly amplify both the intensity and frequency of rogue waves in nonlinear irregular wave trains atop coastal shoals. At least qualitatively, this effect has been partially attributed to the ‘rapid’ nature of the shoaling process, i.e. shoaling occurs over a distance far shorter than that required for waves to modulate themselves and adapt to the reduced water depth. Through a theoretical model and highly accurate nonlinear simulations, we disentangle the respective effects of the length and angle of a shoal's slope. We investigate the effects of the shoaling process rapidness on the evolution of key statistical and spectral sea-state parameters. We let the wave field evolve over a slope with constant angle in all cases while we vary the slope length. Our results indicate that the non-equilibrium dynamics is not affected by the slope length, because further extending the slope length does not influence the magnitude of the statistical and spectral measures as long as the non-equilibrium dynamics dominates the wave evolution. Thus, the shoaling effect on rogue waves is deduced to be mainly driven by the slope magnitude rather than the slope length.

Numerical investigation of the effects of short-crested irregular waves on the performance of a floating power capture platform

This paper presents a novel power capture platform concept consisting of a semi-submersible platform and multiple point-absorber wave energy converters (WECs). The primary objective of the current study is to investigate the dynamic behavior of the power capture platform under short-crested irregular wave conditions. A spreading function is used to modify the JONSWAP spectrum into a wave spectrum that accounts for both frequency and direction. To ensure the reliability of the numerical analysis, three-dimensional potential flow theory and boundary element method (BEM) are utilized to perform mesh convergence analysis and hydrodynamic validation of the platform and WEC models. Time-domain simulations are conducted to evaluate the effects of wave directionality on the platform motion, mooring line tension, and power absorption of the WEC array. In addition, three models, “single WEC”, “WEC array” and “fixed power capture platform” are defined. The influence of hydrodynamic interactions and platform motion are predicted by comparing the power absorption of individual WEC, WEC row, and WEC array among these models. The results show that the effects of wave directionality on the performance of the floating power capture platform cannot be ignored. The findings of this study may provide some insights into the design of power capture platforms. Meanwhile, it is recommended to determine the wave characteristics of the target operational area in advance, in order to find out the optimal design for system stability and power absorption.

Scotch yoke structure inspired piezoelectric-electromagnetic hybrid harvester for wave energy harvesting

This paper presents a piezoelectric-electromagnetic hybrid harvester for wave energy harvesting inspired by a scotch yoke structure for obtaining energy from irregular and low-frequency waves. Through simplification of the energy harvester model, the kinematic equations of the scotch yoke are established. One of the advantages of the harvester is that the wave energy can be harvested by an up-conversion mechanism, The piezoelectric transducer (PZT) and electromagnetic generator (EMG) transform the wave excitation into electricity, and by utilizing the frequency up-conversion mechanism, the PZTs’ harvesting efficiency is increased, the influencing factors of the output power of the harvester are explored by simulation and experimental studies, The results of the experiment demonstrate that this harvester could generate an ultimate output power of 286.36 mW at ultra-low frequency (1.4 Hz) operating frequency. This study offers a practical solution for harvesting low-frequency and disordered wave energy and makes significant progress in harvesting low-frequency and irregular wave energy.

Study on the Prediction of Motion Response of Offshore Platforms Based on ResCNN-LSTM

In the random sea environment, offshore platforms are influenced by factors such as wind, waves, and currents, as well as their interactions, leading to complex motion phenomena that affect the safety of offshore platform operations. Consequently, accurately predicting the motion response of offshore platforms has long been a key focus in the fields of naval architecture and ocean engineering. This paper utilizes STAR-CCM+ to simulate time-history data of offshore platform motion responses under both regular and irregular waves. Furthermore, a predictive model combining residual convolutional neural networks and long short-term memory neural networks using neural network technology is also studied. This model utilizes an autoregressive approach to predict the motion responses of offshore platforms, with its predictive accuracy validated through comprehensive evaluations. Under regular wave conditions, the coefficient of determination (R2) for the platform’s heave and pitch responses consistently exceeds 0.99. Meanwhile, under irregular wave conditions, the R2 values remain generally above 0.4. Additionally, the model exhibits commendable performance in terms of Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) metrics. The aim of this study is to present a novel approach to predicting offshore platform motion responses, while providing a more scientific basis for decision-making in offshore platform operations.

The influence of toe geometry on toe armour stability for conventional rubble mound breakwaters

Rubble mound breakwaters have toe structures that provide support to the armour layer and prevent damage to the structure from scouring. In this way, toe failure may be regarded as one of the primary failure modes of rubble mound breakwaters. Several formulae have been proposed for toe stability with conflicting results owing to the neglect of factors such as storm duration and armour layer slope. In the present study, a statically stable rubble mound with rock armoured toe was tested under irregular waves. The effects of wave height, wave period, armour layer slope, water height in front of the structure, water height above the toe, and toe width on the hydraulic stability of a toe structure are investigated. Toe width was found to be ineffective on toe stability, while the relative depth was found as an effective parameter for the toe stability. Greater toe damage was observed by increasing wave height and storm duration. The results highlighted the necessity for a new stability number involving the type of wave breaker on the armour slope with a critical Iribarren value of 4.1. Based on the data from the present study and the findings of another study, new formulae have been developed for estimating toe damage in rubble mound breakwaters. Evaluating the proposed formula using other researchers’ data and formulae highlighted its strengths.

Nonlinear Model Predictive Control of Heaving Wave Energy Converter with Nonlinear Froude–Krylov Forces

Wave energy holds significant promise as a renewable energy source due to the consistent and predictable nature of ocean waves. However, optimizing wave energy devices is essential for achieving competitive viability in the energy market. This paper presents the application of a nonlinear model predictive controller (MPC) to enhance the energy extraction of a heaving point absorber. The wave energy converter (WEC) model accounts for the nonlinear dynamics and static Froude–Krylov forces, which are essential in accurately representing the system’s behavior. The nonlinear MPC is tested under irregular wave conditions within the power production region, where constraints on displacement and the power take-off (PTO) force are enforced to ensure the WEC’s safety while maximizing energy absorption. A comparison is made with a linear MPC, which uses a linear approximation of the Froude–Krylov forces. The study comprehensively compares power performance and computational costs between the linear and nonlinear MPC approaches. Both MPC variants determine the optimal PTO force to maximize energy absorption, utilizing (1) a linear WEC model (LMPC) for state predictions and (2) a nonlinear model (NLMPC) incorporating exact Froude–Krylov forces. Additionally, the study analyzes four controller configurations, varying the MPC prediction horizon and re-optimization time. The results indicate that, in general, the NLMPC achieves higher energy absorption than the LMPC. The nonlinear model also better adheres to system constraints, with the linear model showing some displacement violations. This paper further discusses the computational load and power generation implications of adjusting the prediction horizon and re-optimization time parameters in the NLMPC.

Experimental Implementation of Reinforcement Learning Applied to Maximise Energy from a Wave Energy Converter

Wave energy has the potential to provide a sustainable solution for global energy demands, particularly in coastal regions. This study explores the use of reinforcement learning (RL), specifically the Q-learning algorithm, to optimise the energy extraction capabilities of a wave energy converter (WEC) using a single-body point absorber with resistive control. Experimental validation demonstrated that Q-learning effectively optimises the power take-off (PTO) damping coefficient, leading to an energy output that closely aligns with theoretical predictions. The stability observed after approximately 40 episodes highlights the capability of Q-learning for real-time optimisation, even under irregular wave conditions. The results also showed an improvement in efficiency of 12% for the theoretical case and 11.3% for the experimental case from the initial to the optimised state, underscoring the effectiveness of the RL strategy. The simplicity of the resistive control strategy makes it a viable solution for practical engineering applications, reducing the complexity and cost of deployment. This study provides a significant step towards bridging the gap between the theoretical modelling and experimental implementation of RL-based WEC systems, contributing to the advancement of sustainable ocean energy technologies.

Numerical Modelling of Fish Cage Structural Responses in Regular and Irregular Waves Using Modified XPBD

Abstract The structural response of gravity-type fish cages in waves and current is numerically investigated. A Morison model is adopted to compute the hydrodynamic forces acting on the net ropes of the aquaculture nets and a screen model is used to compute the hydrodynamic forces on the net twines of the fish cages. The irregular waves are created based on the JONSWAP wave spectrum. The structure of the aquaculture nets is modeled using a modified extended position-based dynamics (XPBD) algorithm. The proposed method is effectively validated against the published experiment data to ensure its accuracy and reliability. The static response of the fish cage at various current speeds and the dynamic responses of the fish cage in regular and irregular waves are analyzed. Results show that the volume of the investigated fish cage is reduced by 30% in a current of 0.5m/s. The tension at the bottom net can reach about five times of maximum tension of the case without current. In the regular or irregular waves, the drag force of the fish cage is higher than that in a uniform flow with the same current speed and the fish cage volume decreases. The increase in drag force rises from the coupling between the waves and current. Therefore, the hydrodynamic model including the regular and irregular modeling, Morison model and screen model is successfully implemented into the framework of the present modified XPBD algorithm to provide the structural response of fish cages in waves and current.

An adaptive internal mass source wave-maker for short wave generation

The mass source wave-maker is commonly employed for generating water waves in numerical simulations, during which a correct amount of mass is introduced or subtracted from the internal flow region to produce target waves. The method has proven to be effective in producing waves in shallow and intermediate water depths, while its efficiency is declined for short wave generation. The main reason for this efficiency declination is that the internal mass source in deeper water region is not effective to generate short waves with their motions primarily on water surface. In order to overcome this shortcoming, many of the previous numerical treatments have introduced various enhancement factors into the source functions, which are empirically obtained and also violate the law of mass conservation. In this study, we develop a new adaptive internal wave-maker model that can be self-adjusted to suit different wave conditions. The line source starts from the bottom and extends to the computational cell right beneath free surface at each time step. The depth dependent weighting coefficient is introduced to the source function based on the linear wave theory for each wave component. No empirical coefficients are necessary, and the mass conservation is strictly and explicitly enforced. In principle, the method can be applied to all types of linear waves in the entire range of kh. The numerical experiments show that the present method can produce very good results for linear waves with kh up to 16.11, adequate for most of wave conditions in coastal engineering. For generation of fifth-order Stokes waves, the method can be extended straightforwardly for each of five wave components. For irregular waves composed of many linear wave components, different weighting coefficients can be readily calculated for each of them, respectively. As a result, the new model can generate irregular waves with overall better performance of reproducing wave spectrum, whose high-frequency part has been underestimated by previous methods. The numerical experiments also show that the new model can produce better results for focused waves where many linear waves of different frequencies start from the same point with specific phase angles, due to its capability of generating shorter wave components.

Experimental Investigation of Wave Pressure on Breakwater-Integrated Oscillating Water Column Devices with a Perforated Wall

This study investigates the wave pressure on an Oscillating Water Column (OWC) device, which features a perforated wall positioned in front of the OWC chamber and is integrated with a caisson breakwater. The perforated wall is designed to mitigate wave impacts on the OWC device under storm wave conditions. To achieve this, a series of laboratory experiments were conducted using a 1:25 scale model, considering both regular and irregular waves. Wave pressure measurements and analyses were performed on various configurations to assess the effects of the perforated wall on the wave pressure exerted against the front wall of the OWC chamber and the caisson breakwater. The results indicate that the perforated wall effectively reduces the amplitude of water column oscillations within the OWC chamber during storm conditions, thereby significantly reducing wave pressure on the OWC chamber wall by approximately 14% and on the breakwater by about 20.3%.

Performance assessment of a Triple Coaxial-Cylinder Wave-Energy Converter (TCWEC)

We propose a novel Triple Coaxial-cylinder Wave-Energy Converter (TCWEC) system, as an evolution of the commonly deployed dual-coaxial cylinder WEC (DCWEC). TCWEC consists of one inner cylinder and two concentric outer cylinders, characterized by two coupled resonant frequencies, improving wave power absorption. A semi-analytical model, based on potential flow theory and matched eigenfunction expansions, is developed to analyze the 3-Degrees of Freedom (DOF) system. The viscous drag coefficients are determined by Computational Fluid Dynamics (CFD) simulations and employed as equivalent linear damping. Analysis of impact of the viscous flow-separation factor fvis on the capture width indicates that the higher energy-absorption capability of TCWEC is not merely attributed to a smaller fvis value, but rather a planned split of the outer cylinder in DCWEC design into two cylinders in TCWEC, so as to produce an effectively broader resonance property. Under identical sea conditions, it is found that, compared to DCWEC, the optimal capture width of TCWEC is increased by as much as 77% in regular waves. In irregular waves, the optimal capture width is increased up to 40% across the entire frequency range. These findings suggest that the energy absorption efficiency of TCWEC is promising and its potential for real-world applications.

Effects of nonlinearity on the crest shape of extreme irregular sea waves: Nonlinear harmonic separation and analysis

This work highlights the effects of nonlinearity on the crest shape of extreme directional water wave events in infinite and finite water depths. HOS-ocean, a High-Order Spectral code developed for solving the deterministic propagation of nonlinear wavefields in open ocean [Ducrozet et al., “HOS-ocean: Open-source solver for nonlinear waves in open ocean based on High-Order Spectral method,” Comput. Phys. Commun. 203, 245–254 (2016)], is used for comparisons with linear simulations. Nonlinear wave harmonics were extracted combining and extending previous methods [Fitzgerald et al., “Phase manipulation and the harmonic components of ringing forces on a surface-piercing column,” Proc. R. Soc. A 470, 20130847 (2014) and Hann et al., “A new set of focused wave linear combinations to extract non-linear wave harmonics,” in Proceedings of 29th International Workshop on Water Waves and Floating Bodies, 2014], showing the contribution of various orders of nonlinearity. The work shows that “walls of water,” [Adcock et al., “Nonlinear dynamics of wave-groups in random seas: Unexpected walls of water in the open ocean,” Proc. R. Soc. A 471, 20150660 (2015) and Adcock et al., “On the shape of large wave-groups on deep water—The influence of bandwidth and spreading,” Phys. Fluids 28, 106601 (2016)], a significant increase in the crest width, are also formulated in finite water depths. Mainly responsible for this is the first order harmonic, with significant energy transfers away from components propagating at an angle, which are more pronounced in finite water depths. As nonlinearity increases, higher order harmonics (>second) become, as expected, more significant. In deep water, rapid energy transfers lead to a broadening of the spectrum which is reflected in the increase in the first order amplitude sum and hence increased crest elevations at the point of the large event. However, in finite water depths, energy transfers are gradually leading to a narrowing of the spectrum around the spectral peak and to a general broadening of the spectrum at the higher harmonics; reflected in the significant decrease in the first order amplitude sum and hence a decrease in crest elevations at the point of the large event, also aided by the larger increase in the out-of-phase difference terms (zeroth harmonic).

Wave Resonance in the Narrow Gap between Two Boxes under Irregular Wave Actions

Wave Resonance in the Narrow Gap between Two Boxes under Irregular Wave Actions

GWECS: An indicator to describe the energy absorption characteristics of wave energy converter arrays in real sea states

Grouping wave energy converters (WECs) into an array has become a trend to improve power production and achieve economies of scale. Therefore, the performance of a WEC array in real sea states is of vital importance. To intuitively reflect an array's frequency-based energy absorption characteristics instead of only the total extractable power in given irregular wave conditions, a new indicator of group wave energy capture spectrum (GWECS) is proposed by extending the concept of wave energy capture spectrum (WECS) to an array. A practical method to measure the indicator by estimating the absorbed wave surface from the array's power signal is also given. Simulations in two-dimensional conditions with a 2-cuboid WEC array and in three-dimensional conditions with a 2-cylinder WEC array are conducted to study the concept. The results examine the consistency in capture efficiency between the newly proposed indicator and conventional ones, and present the effect of various parameters, including linear power take-off (PTO) damping, buoy permutation, separation distance, and incident wave angle on the GWECS.

Multi-dimensional modeling of solitary wave–structure interaction problems by using a [formula omitted]-LES-SPH model

The interaction mechanisms between waves and marine structures are a popular research topic. This paper applies the weakly compressible smoothed particle hydrodynamics (WCSPH) method to study the dynamics of green water overtopping. To enhance the accuracy of the simulations, the SPH method coupled with the large eddy simulation (LES) model is employed for numerical investigations. Initially, we validate the effectiveness of the model by simulating the generation of solitary waves and irregular waves, as well as numerically reproducing the water surface morphology during the interaction between solitary waves and the deck. Subsequently, the validated model is used to study the dynamic characteristics of different types of waves overtopping, revealing significant variations in their motion. Furthermore, we investigate the effect of deck roughness during the entire green water overtopping process in terms of both protrusions extent and distribution, confirming that a reasonable setting of the protrusions can greatly reduce the wave impact loads on the deck, thereby protecting the structure. Additionally, a three-dimensional model is developed to study the green water problem, and we find that the turbulence phenomenon is more pronounced in the three-dimensional scenario.

A study into the correlation between single array-hull configurations and wave spectrum for floating solar photovoltaic systems

Floating photovoltaic (FPV) systems offer a viable renewable energy solution due to easy installation and cost-effectiveness compared to other renewable energy generation methods. On the other hand, land-based solar photovoltaics face challenges such as space scarcity and environmental impacts. Shifting to nearshore locations unlocks vast ocean space potential, though waves expose significant challenges to FPV systems. Several novel FPV system designs are proposed, inspired by high-speed vessel multihulls, including catamaran, trimaran, quadrimaran, and pentamaran configurations, as floating supports for solar panels. Simulations were conducted to determine Response Amplitude Operators (RAOs) under various irregular wave spectrum conditions in a free-floating initial state. The FPV motion problem was solved using linear potential-flow theory with the Boundary Element Method (BEM) with Green-Function approach. Superposition of wave spectral energy and motion RAOs was used to obtain spectral structural responses. Motion in heave, roll, and pitch modes was evaluated across wave spectrum types. Results show that adding hulls reduces the significant amplitude response in all motion modes. In summary, valuable insights into floater designs and the hydrodynamic evaluation of FPV systems are presented.

The Hydrodynamic Similarity between Different Power Levels and a Dynamic Analysis of Ocean Current Energy Converter–Platform Systems with a Novel Pulley–Traction Rope Design for Irregular Typhoon Waves and Currents

In the future, the power of a commercial ocean current energy convertor will be able to reach the MW class, and its corresponding mooring rope tension will be very good. However, the power of convertors currently being researched is still at the KW class, which can bear less rope tension. The main mooring rope usually has a single cable and a single foundation. To investigate the dynamic response and rope tension of an MW-class ocean current generator mooring system, here, a similarity rule is proposed for (1) coefficients without any fluid–structure interaction (FSI) using the Buckingham theorem and (2) ones with FSI. The overall hydrodynamic drag and moment including the hydrodynamic coefficients in these two situations are represented in a Taylor series. Assuming similarity between the commercial MW-class and KW-class ocean current convertors, all hydrodynamic parameters of the MW-class system are estimated based on the known KW-class parameters and based on the similarity formula. In order to overcome the extreme tension of the MW-class system and to provide good stability, in this paper, we propose a pulley–rope design to replace the traditional single-traction-rope design. The static and dynamic mathematical models of this mooring system subjected to the impact of typhoon waves and currents are proposed, and analytical solutions are obtained. We find that the pulley–rope design can significantly reduce the dynamic rope tensions of the mooring system. The effect of the length ratio of the main traction rope, rope A, to the seabed depth on the dynamic tension of stabilizing converter rope D is significant. The length ratio is within a safe range, and the maximum rope dynamic tension is less than the fracture strength. In addition, if the rope length ratio is over the critical value, the larger the ratio, the higher the safety factor of the rope. In summary, the pulley–rope design can be safely used in an MW-level ocean current generator system.

Hydrodynamic and energy-harvesting performances of a compact-array OWC device: An experimental study

This study proposed and evaluated a compact-array oscillating water column device called “Rainbow”, which is expected to adapt to the nearshore wave climate characteristics in China, and satisfy the quick response requirements to coastal and offshore electricity. The proposed device employs a bent-duct buoy concept, with an open mouth in two opposite directions, and embraced a moon pool in a ring shape. Moreover, models under a scale ratio of 1:10 are designed and manufactured, which are fixed on the bottom and tested in regular and irregular wave scenarios in a wave tank. The time histories of critical performance parameters, hydrodynamic and aerodynamic performances, and capture width ratios in different modules were recorded and analyzed to reveal the operating mechanisms of the model. The various module arrangement topologies were found to cause significant differences in the value distribution characteristics of the capture width ratio in different modules, peaking at 0.26. The experimental results can be employed as critical benchmark cases for further designs and optimizations.