JONSWAP Spectrum Research Articles

Simulation of time-invariant three-dimensional Freak waves and their scattering identification based on the JONSWAP spectrum and Donelan direction function

Abstract The results of recent maritime accident investigations show that many maritime accidents are related to the attack of freak waves, which can sink ships instantaneously with colossal energy. To identify and forecast freak waves accurately and avoid the danger of freak waves to marine structures and people, we have conducted further research on freak waves. In this paper, we propose an efficient time-invariant three-dimensional (3-D) freak wave computational model to study the scattering characteristics of time-invarian 3-D freak waves and obtain a more explicit identification of their scattering differences. First, this paper adopts linear superposition method to simulate a 3-D random rough sea surface based on the JONSWAP wave spectrum and Donelan directional distribution function. Moreover, we analyze the effect of different angular frequencies on the simulated sea surface. At the same time, the Monte Carlo method is used to further simulate the capillary waves based on the random sea surface, and this method vastly improves the computational accuracy of the random sea surface. Then, based on the two-wave train superposition wave energy focusing mode, a numerical calculation method of time-invariant 3-D freak waves is proposed, and the time-series evolution process of 3-D freak waves is simulated. Finally, the backscattering coefficients of the 3-D freak wave surface are calculated using the two-scale method, and the electromagnetic scattering characteristics of the freak wave surface under different evolution stages, wind speeds, and radar incidence angles are analyzed. By this method, we conclude that the recognition of freak waves is more accurate under medium-high wind speed and significant incidence angle conditions. The experiments show that the research in this paper can identify and predict freak waves more effectively, further improve the forecast accuracy of future freak waves, and also have some application value for freak wave risk warnings.

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.

Fuzzy disturbance observer-based fuzzy swing suppression control of a ‘mooring-heavy lift crane-cargo’ coupled system

In this paper, an adaptive fuzzy disturbance observer (FDO)-based control is proposed for the swing suppression of the mooring-heavy lift crane (HLC)-cargo system in the presence of a wave disturbance. First, the dynamic model of the HLC system is determined by employing the Lagrangian method, and the wave force is modeled as an exosystem with unknown terms based on the Jonswap spectrum. Then, based on the HLC model and the wave force exosystem, an FDO is established to determine the wave disturbances, and a fuzzy approximator is developed to estimate the unknown terms. A novel disturbance estimation error observer is first developed to facilitate the parameter adaptive updating law. Subsequently, by augmenting the HLC system and disturbance estimation error system, an FDO-based fuzzy antiswing control method is proposed in terms of the linear matrix inequality technique to suppress the swing. The closed-loop system stability is examined by using the Lyapunov method. Finally, the effectiveness of the proposed method is validated by numerical simulation.

Experimental and numerical investigation of breakwater-integrated heaving point absorber device under irregular waves

Integrating wave energy devices with coastal structures is a promising solution to reduce the cost of wave energy development along with additional shared benefits. In this study, the performance of a heaving spherical point absorber wave energy converter model in irregular waves is analysed and compared experimentally and numerically. After the fundamental investigation of models in regular waves, it is important to advance the testing in more realistic conditions before the sea trial phase. The investigations are conducted in irregular waves on a 1:30 scale model under two scenarios, (1) model heaving alone and (2) model heaving in a chambered breakwater. Irregular waves are generated based on the JONSWAP spectrum with modified parameters to suit the Indian coastal conditions. Results indicate that the wave energy converter model in the chambered breakwater produces 40.25 % higher power than the model heaving alone in irregular sea conditions. The performance of the model is found to be less compared to that in regular waves.

Statistical Parameters Extracted from Radar Sea Clutter Simulated under Different Operational Conditions.

A complete framework of predicting the attributes of sea clutter under different operational conditions, specified by wind speed, wind direction, grazing angle, and polarization, is proposed for the first time. This framework is composed of empirical spectra to characterize sea-surface profiles under different wind speeds, the Monte Carlo method to generate realizations of sea-surface profiles, the physical-optics method to compute the normalized radar cross-sections (NRCSs) from individual sea-surface realizations, and regression of NRCS data (sea clutter) with an empirical probability density function (PDF) characterized by a few statistical parameters. JONSWAP and Hwang ocean-wave spectra are adopted to generate realizations of sea-surface profiles at low and high wind speeds, respectively. The probability density functions of NRCSs are regressed with K and Weibull distributions, each characterized by two parameters. The probability density functions in the outlier regions of weak and strong signals are regressed with a power-law distribution, each characterized by an index. The statistical parameters and power-law indices of the K and Weibull distributions are derived for the first time under different operational conditions. The study reveals succinct information of sea clutter that can be used to improve the radar performance in a wide variety of complicated ocean environments. The proposed framework can be used as a reference or guidelines for designing future measurement tasks to enhance the existing empirical models on ocean-wave spectra, normalized radar cross-sections, and so on.

Numerical investigation of the response of the hybrid wave energy converter including oscillating water column and horizontal floating cylinder to irregular waves

The main goal of this research is to investigate the effect of some geometrical parameters on an onshore Hybrid Wave Energy Converter (HWEC) including an onshore Oscillating Water Column (OWC) and a Horizontal Floating Cylinder (HFC) under regular and irregular waves. The TMA spectrum is the basis of this study. The wave spectrum is used to generate irregular waves in a numerical wave tank using Ansys-fluent software based on URANS equations. Active wave absorption is used to avoid the effect of reflected waves. Also, the SST k−ω turbulence model and the VOF scheme are used for turbulence modeling and interface tracking, respectively. The results confirm that the efficiency of the HWEC is higher than the efficiency of an OWC and the efficiency of an HFC in both regular and irregular waves. Besides, the efficiency of the HWEC in irregular waves is lower than its efficiency in regular waves. A comparison of the TMA and JONSWAP spectrum on HWEC performance shows that HWEC performance is lower on the JOANSWAP spectrum. This study shows that the use of irregular waves is essential to obtain more realistic results from analyses of the onshore HWEC performance, despite their need for high computational cost.

Energy harvest on TSUSUCA DOLPHIN under irregular waves: Experimental studies

Finding sustainable and infinite green energy options in a world that relies primarily on fossil fuels is crucial as traditional sources decline. Wave energy is an excellent example of an environmentally friendly power source. A multi-utility bio-inspired floating device consisting of two TSUSUCA (TSUnami Protection Solar Utilization and other Coastal Applications) Dolphin-shaped bodies integrated with a linear motion electricity generator (LMEG) connected to a rigid deck by a hinged connection is tested experimentally under irregular waves. This novel and innovative multi-utility floating offshore device can function as a tsunami barrier and a wave energy extraction device. Its performance and operating mechanism are investigated under 8 different sets of irregular waves. The examined sea states are represented by JONSWAP and PM wave spectra with a range of significant wave heights (0.05–0.20 m) and peak periods (1.5 and 2.0 s). The experimental results show that the overall electrical power efficiency of LMEG coupled to each Dolphin obtained for set 6 is 32.04 % and 30.81 % for both JONSWAP and PM spectrums, respectively. This bio-inspired device and its performance confirms the proof-of-concept while the presented study shall become a prime factor towards the development of more similar devices to harness wave energy.

An investigation on the vibrations of a flexible net excited by irregular waves and irregular boundary deformations

Aquaculture cages located in offshore areas typically contain frames and flexible nets. The cages are typically subjected to irregular waves and the frames may deform irregularly over time. Since the nets are tied on the frames, when the frames deform over time, the boundaries of the nets change. In this study, a large flexible net subjected to irregular waves and irregular boundary deformations is theoretically simulated. The irregular waves are simulated using the modified Jonswap spectrum, while the irregular boundary deformations are described by superimposing a series of cosine functions that follow a Gaussian distribution. The dynamic responses of a flexible net are solved numerically. The proposed model is validated by comparison with experimental results. When the boundaries of the net irregularly deformed in the vertical direction, the vibrations of the net in the vertical direction are significantly affected, while the vibrations in the horizontal direction are slightly affected, which are mainly dominated by irregular waves.

Optimal multiple tuned mass dampers for monopile supported offshore wind turbines using Genetic Algorithm

This study investigates the parametric optimization of multiple-tuned mass dampers (MTMDs) deployed along the length of a tower and monopile structure subjected to stochastic wind and wave forces. The structural components, comprising the tower and monopile, are conceptualized as Euler–Bernoulli beams. The interaction with the soil is modeled through viscoelastic springs distributed along the monopile. The rotor nacelle assembly (RNA) and blades are abstracted into a concentrated mass at the tower’s apex. The MTMDs are characterized as spring–mass–dashpot systems strategically positioned at intervals along the tower and monopile. The investigation involves a random vibration analysis under wind and wave loads, employing the Kaimal spectrum for wind and the JONSWAP spectrum for waves. The study focuses on optimizing the TMD parameters using H2 optimization techniques, with the optimization criteria being the minimization of the standard deviation of the tower’s top displacement response. Additionally, meta-heuristic algorithms like the genetic algorithm (GA) are utilized to refine the determination of these optimal parameters. A key aspect of the research includes a parametric study that reveals variations in optimal parameters as the number of TMDs is altered, maintaining a consistent total mass across the MTMDs.

Laboratory and non-hydrostatic modelling of focused wave group evolution over fringing reef

This paper presents physical experiments and numerical simulations to study the propagation of focused waves group across hypothetical fringing reef profiles. A wave flume is 69 m long and 1.0 m deep, and the reef cross section is made up of a reef face, a reef flat and a vertical wall. A reef crest of 0.085 m is optionally constructed on the outside to replicate the reef crown. By focusing wave trains of the JONSWAP or constant wave amplitude spectrum, the transient wave group is generated on the reef slope. Free surface elevations and flow velocity are measured over time along the flume's centreline. The focused wave process and the development of higher harmonics as a result of the nonlinear interaction over the reef face are clearly visible in the wavelet and FFT analyses of the observed free surface elevation. Low frequency wave is increasing on the reef flat while these short-period wave motions are primarily absorbed by rapid breaking on reef edge and crest. On the flat, it is discovered that reef crest has the effect of reducing short-period wave motion and increasing long-period wave motion. A numerical multi-layer non-hydrostatic wave model is employed and its ability to describe the propagation of focused wave groups over fringing reef profiles is assessed.

A numerical study of added resistance performance and hydrodynamics of KCS hull in oblique regular waves and estimation of resistance in short-crested irregular waves through spectral method

Research on multidirectional waves is increasing as studies on added resistance advance. In this study, the added resistance of the multidirectional regular waves of the KCS hull was estimated by numerical analysis. The direction of the grid was changed according to the heading angle to consider waves in multiple directions. In addition, the method in which the entire domain moved along the movement of the hull was used without using the overset method to minimize the numerical errors. The added resistance and motion RAOs for each angle and the flow characteristics were compared to support the results. For fluid dynamics, time-averaged stern dynamics pressure, boundary layer, and nominal wake for each heading angle were compared, and differences compared to calm water were also reviewed. Based on the bow quartering sea condition analysis results, the added resistance in long-crested and short-crested irregular wave conditions was estimated using the spectral method. The JONSWAP spectrum was used as the target wave spectrum, and the cos-power type was considered the directional spreading function.

Analysis of Unidirectional Wave Spectral Characteristics in the Northeastern Waters of Taiwan

Marine energy development has been actively promoted in recent years. Analyzing wave data in the surrounding sea areas is crucial for improving wave power generator efficiency. This study collected unidirectional wave spectrum data from the northeast coastal area of Taiwan (e.g., Pengjia Islet, Fugui Cape, and NTOU). It aimed to analyze the main wave types (i.e., wind waves, swell, or mixed sea) and their proportions during the northeast and non-northeast monsoon periods. The results indicate that swell waves dominate at the NTOU buoy, while wind waves dominate at the other two stations. In addition, the analysis of wave spectra ratios revealed a low percentage of unimodal spectra (only about 0.5%), and bimodal and unformed spectra presented as predominant. Furthermore, this study also introduced a brand new JW-J wave spectrum, which combines the JW and JONSWAP spectra to describe low-frequency (swell) and high-frequency (wind wave) systems, showing superior performance compared to the Torsethaugen spectrum. Finally, this research analyzed the JW-J spectrum parameters from the Pengjia Islet and Fugui Cape stations and applied these results to the NTOU bouy for effectively describing wind/swell wave variations.

Variable cross-sectional effect on bi-directional blades–tower–soil–structure dynamic interaction on offshore wind turbine subject to wind–wave loads

BackgroundThis study introduces a numerical model designed to simulate interactions occurring between a wind turbine's tower and the surrounding soil, as well as between the nacelle, blades, and the surrounding environment. This simulation accounts for both fore–aft and side-to-side movements. To describe these interactions, the model leverages the Euler–Lagrange equations. It calculates wave loads utilizing the Morison equation, with wave data generated based on the JONSWAP spectrum. Furthermore, aerodynamic loads are determined using the blade element moment theory, and the wind spectrum is generated using the Von Karman turbulence model. The tower is represented as a variable cross-sectional beam, employing a two-noded Euler beam element with two degrees of freedom: transverse displacement and rotation, and utilizing Hermite polynomial shape functions.ResultsIn a comparative analysis against experimental data, this modified model demonstrates significant enhancements in accurately reproducing the dynamic behavior of wind turbines with variable cross-sectional towers, outperforming models that approximate the tower with a constant cross section. Our findings reveal that the modified model achieves a remarkable improvement of 15% in replicating the tower's dynamic response when compared to the constant cross-sectional models. As a case study, a 5 MW monopile wind turbine with a flexible foundation, specifically the one provided by the National Renewable Energy Laboratory (NREL), is employed to simulate its dynamic response.ConclusionsThis research presents a robust numerical model for simulating wind turbine behavior in various environmental conditions. The incorporation of variable cross-sectional tower representation significantly improves the model's accuracy, making it a valuable tool for assessing wind turbine dynamics. The study's findings highlight the importance of considering tower flexibility in wind turbine simulations to enhance their real-world applicability.

Groupiness effect on irregular wave train propagation and impact on cylinder

A wave flume based on solving the Reynolds-averaged Navier-Stokes equation is modelled to simulate the irregular wave group interacting with a cylinder. The irregular wave groups are generated based on the wave envelope spectrum and the improved JONSWAP spectrum. The wave-making boundary and the momentum source term for wave-making and wave dissipation are developed based on the irregular wave theory. To suppress excessive growth of turbulent viscosity, a modified formula for turbulent viscosity is implemented in the shear stress transport turbulence model. Several sets of irregular waves with different groupiness factors are simulated. The effects of groupiness on the wave parameters, wave run-up height and wave force on the cylinder are investigated. The results show that the wave parameters increase as the groupiness increase. The group height factor has a larger influence on the significant wave height than the group length factor. The group length factor mainly influences the average wave period and average wavelength. When the average wavelength is larger than the diameter of the cylinder, the increase in wave group length results in a decrease in wave run-up height and wave force on the cylinder.

Comparison of a spectral wave model with a fully nonlinear potential flow wave model

This study evaluates the performance of the MIKE 21 Spectral Wave (SW) model by comparing the evolution of the spectrum with the fully nonlinear potential flow model OceanWave3D. We test only the shoaling, nonlinear wave–wave interaction and whitecapping terms by considering a two-dimensional shoaling problem on a mild slope bottom without wind, or bottom friction effects and before reaching the breaking zone at the beach. A JONSWAP spectrum is introduced at the deep-water boundary and allowed to propagate freely up to a relatively shallow shelf. The peak wave is in relative water depth kh=4 at the deep water boundary where k=2π/λ is the wave number, λ the wavelength and h the water depth. For the peak relative water depth greater than about kh=0.8, the spectrum agrees well with the fully nonlinear results, but below this value significant differences appear. In particular, the long-wave difference frequency effects are mostly absent, indicating a need for improvement in the SW triad interaction model.

Multi-scale calibration of a non-hydrostatic model for wave runup simulation

Modeling wave runup on beaches and structures is an important step toward accurate coastal flood prediction. Depth-averaged non-hydrostatic models such as XBNH (XBeach Non-Hydrostatic) are computationally cost-effective yet accurate tools to numerically simulate random wave runup. XBNH includes a number of calibration parameters, which are determined on a case-study basis. This study aims to investigate the range of XBNH input parameters that results in accurate predictions regardless of the application scale, benefiting future applications of XBNH that lack the measurements needed for model calibration. The study performs calibration and sensitivity analysis to investigate the model response to the input parameters for applications with different spatial scales, including small- and large-scale laboratory wave runup experiments and a real-scale field experiment. A Grid search method is utilized to perform a multi-scale calibration of the input parameters used in the parametrization of the wave breaking process in XBNH. The effect of parameters in the JONSWAP spectrum used to generate the offshore boundary conditions is investigated. Results show that using a single combination of calibrated input parameters, the model is able to capture random wave runup on beach, beach-dune, and beach-seawall systems with various spatial scales. Moreover, wave spectrum parameters can highly influence the model performance, and calibration of these parameters makes the model more robust to replicate the actual water surface fluctuations.

Analysis of FPSO Motion Response under Different Wave Spectra

A variety of floating structures at sea play a vital role in the exploitation and utilization of marine resources. The study about interactions between waves and structures is necessary for the impact of the harsh marine environment on the motion and service life of structures. Currently, most studies about the seakeeping of structures are based on simplified regular waves. Because the regular waves do not truly restore the actual wave conditions at sea, the simulation of irregular waves has great practical importance to the study of interactions between waves and structures. Based on the potential flow theory and high-order boundary element method (HOBEM), a Fortran code is developed in this paper and named as SWBI (Solver for Wave–Body Interactions). This program consists of the following two parts: a time–domain numerical model about interactions between waves and 3D structures is based on weakly nonlinear method, and a numerical model about simulation of the nonlinear regular waves, the long-crested irregular waves, and the short-crested irregular waves. This Fortran code is used to simulate the motion of Floating Production Storage and Offloading (FPSO) under three different ocean wave spectra (including ITTC two-parameters spectrum, JONSWAP spectrum and the most likely spectral form of Ochi-Hubble) and found that: To a certain extent, the difference in the motion of FPSO under different wave spectra have a connection with different type of wave, sea conditions and incident angle. The difference in roll of FPSO is quite significant in short-crested irregular waves. The range of FPOS’s roll under the JONSWAP spectrum is the largest when the incident angle is 30°, and range of FPOS’s roll under the most likely spectral form of Ochi-Hubble is the largest when the incident angle is 90°.

Maximum power point tracking control based on inertia force for underwater direct-drive wave energy converter

Underwater direct-drive wave energy converter (UDDWEC) using linear-rotating axial flux permanent magnet generator (LR-AFPMG) can change form of energy conversion and improve conversion efficiency. This paper proposed a maximum power point tracking (MPPT) control based on inertia force in electromagnetic force for UDDWEC which can control the form and magnitude of electromagnetic force including damping force, spring force and inertia force. By adding inertia force in electromagnetic force, the pole location and dynamic response performance can be changed and adjusted. This paper studied the influence of inertial force in electromagnetic force and system response in detail. The research also involved the influence of buoys with different shapes on wave energy capture, the expression of q-axial reference current when inertia force is considered, the necessity of additional damping in the system and power capture width in different sea conditions. According to the hydrodynamic parameters and wave characteristics, the proposed MPPT control was verified through simulation in regular wave and JONSWAP spectrum and the results showed that MPPT control based on inertia force can capture the maximum wave energy and achieve maximum power capture width. Above on this, this control strategy can be a decent candidate for UDDWEC. Finally, a series of flume experiments were carried out to verify the accuracy of hydrodynamic parameters of underwater buoy.

Estimation of a five-parameter JONSWAP spectra with an improved particle swarm optimization

An improved particle swarm optimization (PSO) algorithm is presented to estimate a five-parameter JONSWAP spectrum for modeling of certain wave states, including normal events and extreme events at deep-water and shallow-water stations, respectively. The choices of spectral parameters (energy scale coefficient α, peak enhancement coefficient γ, and shape parameter σ) through vast amounts of in situ observations and spectral nonlinear factors are of significant importance for safety of marine structures and activities. Several experiments are carried out for five JONSWAP spectral parameters (α, γa, γb, σa, and σb) using relatively unimpaired and long series significant wave height, dominant wave period, average wave period, maximal spectral value, and ratio of dominant period and average period. And the choices of γ from γa and γb, as well as σ from σa and σb depend on the relationships between current frequency and the peak frequency. Two improvements of PSO algorithm are made, one is the fitness function, another is that the population average replacing particle’s individual optimum in the updating step. Well fitted spectra and statistic results show that the improved PSO model is more suitable to be applied to estimate the wave spectrum at a given record time. This heuristic model can be used without restrictions of water depth and sea state with its intuitive background, easy-programming and portable feature.

Study of Diameter-to-Draft Ratio of Pitch Point Absorber as Wave Energy Converter in Indonesia Waters Based on Boundary Element Method

Recently, harnessing the energy from low wave energy density areas is concerned to deal with renewable energy targets. The previous study proposed a pitch point absorber with a submerged sectional equivalent area as the design parameter. However, that parameter did not suggest the best sectional area and did not directly correlate with the theory of structure hydrodynamic. Thus, this research proposes the diameter-to-draft ratio as a design parameter for the pitch point absorber. The study was conducted numerically using Boundary Element Method software to investigate diffraction characteristics of the device and analyze structure response in irregular waves. The model was modified with five different diameters and ratios. JONSWAP Spectrum was used to generate wave elevation with a 2-m significant wave height and 10-second peak period. The time domain simulation was set at 10.800 seconds. The result of this study showed that the highest responses occurred when the diameter-to-draft ratio was 5 because it has the closest structure natural frequency to assumed wave frequency, which makes it easier to resonate. In all diameters, the higher ratio affects the range of the structure natural frequency getting farther from the assumed wave, so the responses become smaller.