Pierson-Moskowitz Spectrum Research Articles

The Application of Short-Term Deterministic Wave Prediction to Offshore Electricity Generation.

The field of wave energy extraction from the oceans is moving from the realm of drawing board dreams to the reality of device farms in the open ocean. Several devices are now at the stage of full scale testing and methods of increasing their economic potential are required. Maximum energy capture from a given sea state is one such way of increasing production and for devices to achieve this an accurate prediction of the sea surface elevation in the vicinity of these devices is required. The method proposed is based on the work of Belmont [1] and Zhang [2], extending from unidirectional modelling to directional. Preliminary simulations for a unidirectional buoy excited by a Pierson-Moskowitz spectrum are given and the proposed method for directional modelling is then set forth.

Study application of an unmoored ocean wave energy harvester with harmonic and random excitation

Vibration-based Energy Harvesting offers a promising technique for generating sustainable energy for electronic devices by converting ambient kinetic energy into predictable electrical energy. On the other hand, these systems can be considered as a replacement for the battery, which of course should be portable. Ocean wave energy is a rich source of ambient energy that is often underutilized for vibration energy generation due to the low frequency of ocean waves. Although ocean wave energy harvesters are considered by many researchers, unmoored vibration-based ocean wave energy harvesters with low frequency and random excitation have not been studied. This study proposes and examines a new energy harvesting system that unlike usual ocean wave energy harvesters is not anchored to the seabed and can use both roll and pitch motions of the ocean waves. The dynamic behavior of the energy harvester, which consists of an inverted pendulum and a mechanical rectifier, is formulated, and experimentally validated. In order to do this, the damping of the rectifier is experimentally determined and considered as part of the equivalent damping of the whole system. Then the effect of changing the nondimensional mass and geometry of the floater on the oscillatory behavior of the system under harmonic and random excitation is investigated. To do so, using the strip theory method, equivalent dynamic parameters of the different floater are calculated. It is shown that optimizing the non-dimensional mass of the energy harvester can lead to an energy harvester that produces relatively equal power under both random and harmonic excitation. To study the random behavior of ocean waves, Pierson-Moskowitz Spectrum is used. The relevant design recommendations for the presented energy harvester are summarized in a table. Finally, it is shown that the presented system is flexible in the choice of design parameters and can generate large amounts of energy.

Modeling sea state induced atmospheric sound transmission loss

This work presents a numerical study on atmospheric sound propagation over rough rigid surfaces. The intent is to simulate acoustic propagation over water. Methods to estimate sea state induced atmospheric sound transmission loss and relative uncertainties are evaluated. In previous studies, a flat surface with an equivalent impedance was used to account for the effect of surface roughness on sound transmission loss. Equivalent impedances were estimated based on time-domain numerical simulations of atmospheric sound propagation above pseudorandom sea surfaces coherent with a Pierson-Moskowitz spectra. Estimation of equivalent impedances using time- and frequency- domain approaches are compared for cases up to sea state 4. Acoustic excess attenuation due to propagation over a rough surface was predicted by the authors, in a previous work, by correcting the excess attenuation of a propagation over a flat, perfectly reflecting surface. The correction factor was frequency and sea state dependent and included an additional term to account for the uncertainties characteristic of different sea states. Excess attenuation predictions estimated using the equivalent impedance approach are compared with those obtained from the authors’ previous study. Implications of the use of these methods for source detectability determinations are discussed.

Use of Magnetostrictive Actuators for Wave Energy Conversion with Improvised Structures

This paper presents work on a wave energy device with an on-board power take-off based on a magnetostrictively actuated deformable structure. Such devices potentially could be used in low-cost, short-term expeditionary operations. The paper discusses an analytical model that describes the heave oscillations of a buoy with two inclined, overhanging beams with magnetostrictive strips affixed to them. This work comprises the first steps toward an analytical model that would enable potential users to obtain quick power estimates at the planning stage. Here, the fully nonlinear magneto-mechanical-electrical constitutive relations are linearized about a desirable operating point, and a coupled dynamic model is derived using a variational formulation that includes buoy heave, flexural oscillations of the two beams, and the voltage response of the magnetostrictive strips. Energy conversion performance in wind-sea-dominated Pierson–Moskowitz spectra is found to be modest. However, present results also indicate that performance could be improved with suitable mechanical modifications.

Formula for wave transmission at submerged homogeneous porous breakwaters

A new formula is introduced to determine the wave transmission at submerged porous breakwaters highlighting the effect of the wave-induced pore pressure distribution inside the breakwater, applicable for both regular and random waves. A CFD numerical wave flume based on the Stokes-Cnoidal wave theory for regular waves and Pierson-Moskowitz spectrum theory for random waves combined with the Forchheimer formula is calibrated using an experimental dataset from Calabrese et al. (2002). The proposed formula for the wave transmission coefficient has been obtained by means of dimensional analysis and incomplete self-similarity, and it has been calibrated using the results of the numerical experiments. The new formula has been verified using a large database on wave transmission coefficient yield fairing good predictions for a wide range of wave conditions and breakwater geometries.The proposed formula has been compared with other existing formulae applying to 2336 data of the existing wave transmission coefficient dataset where the proposed formula giving the minimum root mean square error Erms = 12.6% showed the maximum accuracy among all other existing formulae for determining the wave transmission coefficient over the submerged porous breakwaters.

An Accurate Maritime Radio Propagation Loss Prediction Approach Employing Neural Networks

The radio propagation loss prediction model is essential for maritime communication. The oceanic tropospheric duct is much more complicated than the atmospheric structure on land due to the rough sea surface influence, and it leads to difficulties in loss prediction. Classical radio wave propagation loss prediction models are either based on complicated electromagnetic wave theories or rely on empirical data. Consequently, they suffer from low accuracy and a limited range of application. To address this issue, a novel maritime propagation loss prediction approach is proposed, which fully exploits the data for training. In this new approach, 3D sea surface contour profiles are generated based on the Pierson–Moskowitz spectrum theory and the direction expansion formula Stereo Wave Observation Program (SWOP), by sweeping the parameters. The full-wave propagation procedure of radio signals over the sea surface is simulated by commercial EM analysis software CST Studio Suite. Based on the large quantity of simulated data, the BP neural network is employed to fit the radio propagation loss and obtain the sea surface radio wave propagation prediction model. Other classical machine learning methods are also compared to validate the proposed approach. Traditional empirical model construction relies on observation data. This approach, for the first time, proposed an automatic scheme which covers the whole procedure from the data generation to prediction model training. It avoids the requirements for on-site observation, as well as significantly decreases the cost of experiments. The application scope of the prediction model such as propagation distance range and working frequency range could be adaptive through adjustments for simulated sea size and simulated working frequency. This approach is validated to save 99% of prediction time in comparison with the full-wave simulations. The prediction model trained via our proposed method could obtain the coefficient of determination R2 which is over 0.92, demonstrating the superiority of this method.

Power output estimation of WEC with HF radar measured complex representative sea states

Wave tank model testing has been widely used to assess the performance of Wave Energy Converters (WEC) in different technology readiness levels (TRL). At early stage the use of simple wave conditions such as regular waves and parametric wave spectrum JONSWAP or Pierson-Moskowitz spectrum is acceptable. However at later stages there is a need to use site specific complex wave conditions representative of potential prototype deployment sites. In previous research, 10 different regrouping methods on HF radar measured wave spectrum were tested to find out the most representative sea states for tank testing. It has been shown that by using the K-means clustering technique, the characteristics of wave conditions can be well preserved. In order to assess the power capture performance of a typical WEC in these representative sea states, the RM3 point absorber has been simulated. By analysing how well the average power output predicted from different representative sea-state selection methods compares with the total power output prediction, it is shown that the non-directional wave spectrum K-means clustering method provides the most representative sea states and, for a point absorber, with a very accurate estimation of the total power output, which is not the case by using a traditional binning method. The importance of using the complex site-specific sea states rather than simplified parametric JONSWAP sea states to obtain the accurate total power estimation has also been shown.

Ocean wave autocorrelation function

Certain models for ocean wave spectra, including the Bretschneider and Pierson-Moskowitz spectra, have spectral densities in the form of the Fréchet probability density. The autocorrelation function (ACF) of the waves is the Fourier cosine transform of the spectral density. Mellin transforms are applied to obtain the ACF in the form of a Fox H-function. If the Fréchet shape parameter is rational, the ACF may also be expressed as a Meijer G-function. These generalised functions are difficult to compute, so power series and saddle point approximations are derived to compute the ACF. The speed and accuracy of these methods is assessed.

Infrared Ocean Image Simulation Algorithm Based on Pierson–Moskowitz Spectrum and Bidirectional Reflectance Distribution Function

Infrared ocean image simulation has been widely used in water-pollution prevention, meteorological observation and melting-ice monitoring. However, in actual remote sensing observation scenes, the simulation images provided by conventional algorithms are lacking sufficient wave details because the viewing angle and the scale of simulation images are simplex. In this paper, an infrared ocean image simulation algorithm based on the Pierson–Moskowitz spectrum and a bidirectional reflectance distribution function is proposed. First, a 3D model of ocean surface is set up based on Pierson–Moskowitz spectrum. Then, the imaging position is calculated by the pinhole camera imaging method, which describes how each point of the 3D model is mapping to the 2D image. Next, by using a bidirectional reflectance distribution function, the radiation intensity from every point of the ocean model to the camera is computed. Finally, we figure up the sum of the radiation intensity received by every point of the detector and obtain the infrared simulation ocean image by quantizing the radiation intensity sum to grayscale. The entropy of the simulation images is 2.725, which is, respectively, improved by 71.86% and 16.83% compared with two other algorithms. The Kullback–Leibler divergence of the simulation images is 11.446, which is improved by 0.54% and 0.59% compared with other algorithms. The quantitative experimental results prove that the authenticity and clarity of the presented simulation images have remarkable advantages over conventional algorithms.

CFD Modeling of Regular and Irregular Waves Generated by Flap Type Wave Maker

The improvement of wave generation in numerical tanks represents the key factor in ocean engineering development to save time and effort in research concerned with wave energy conversion. For this purpose, this paper introduces a numerical simulation method to generate both regular and irregular waves using Flap-Type wave maker. A 2D numerical wave tank model is constructed with a numerical beach technique, the independence of the numerical beach slope is tested to reduce the wave reflections. The different governing parameters of the Flap type wave maker were studied such as periodic time dependency and length of the flap stroke. The linear wave generated was validated against the wave maker theory WMT, the numerical results agreed with WMT. The Pierson-Moskowitz model is used to generate irregular waves with different frequencies and amplitudes. The numerical model succeeded to generate irregular waves which was validated against published experimental data and with Pierson-Moskowitz spectrum model using Fourier expansion theory in the frequency domain. Useful results are presented in this paper based on the numerical simulation to understand the characteristics of the waves. This paper produces a full guide to generate both regular and irregular waves numerically using ANSYS-CFX approach to solve the 2D Unsteady Reynolds Averaged Navier-Stokes Equation (URANS).

Effects of Weakly Nonlinear Waves on Acoustic Scattering from the Ocean Surface

The elevation of ocean waves is always modeled in linear theory as a superposition of the sinusoidal components with crests and troughs of identical heights. However, under some circumstances, the wave amplitude is outside the linear range and presents as a weakly nonlinear asymmetrical waveform with sharper crests and shallower troughs. We studied the impact of the weakly nonlinear effect of ocean waves in deep and intermediate waters on acoustic scattering from the surface of the ocean using two rough surface models with fractal geometry and power law spectral behavior in the equilibrium range. The classic Weierstrass–Mandelbrot function was used to model the linear waves and a new fractal function, the fractional Weierstrass function developed in studies of electromagnetism, was used to model the weakly nonlinear waves. We evaluated these two models using the Pierson–Moskowitz spectrum and the incident wavelength. The bistatic scattering strength was obtained via a numerical method based on the “exact” solution of the integral equation. The weakly nonlinear phenomenon led to a very small reduction in the narrow area around the specular reflection angle and a small increase in the remaining wide area, including the backpropagation area with a scattering angle [Formula: see text]. The differences in backscattering strength between the two models were similar to the bistatic scattering strength in the backpropagation area and did not depend on the incident grazing angle.

Performance of an OWC device placed over multi-stepped bottom in random waves environment

The performance of an OWC device placed over multi-stepped bottom is analyzed in random incident waves environment. To model the irregular local wave climate, the Pierson-Moskowitz spectrum along with two different sea states are considered. The effect of chamber width, lip-wall thickness and draft, and turbine damping coefficient of the OWC device on the performance and efficiency are discussed in a detailed manner. It is observed that the OWC device parameters and the local wave climate play a crucial role on the performance and efficiency of the OWC device.

Performance of an OWC device placed over stepped bottom in random waves environment

The performance of an OWC device placed over stepped bottom is analyzed in random waves environment. To model the random local wave climate, the Pierson-Moskowitz spectrum along with two different sea states are considered. The effect of front wall draft, wall thickness, device chamber length and turbine damping coefficient on the efficiency of the device are discussed in details. It is observed that the local wave climate plays a vital role on the performance and efficiency of the OWC device along with the variation in device parameters.

Deterministic wave forecasting with the Zakharov equation

Abstract

Aerodynamic behaviour of double hinged articulated loading platforms

Articulated loading platforms (ALPs) belongs to a class of offshore structures known as compliant. ALP motions have time periods falling in the wind excitation frequency range due to their compliant behaviour. This paper deals with the dynamic behavior of a double hinged ALP subjected to low-frequency wind forces with random waves. Nonlinear effects due to variable submergence, fluctuating buoyancy, variable added mass, and hydrodynamic forces are considered in the analysis. The random sea state is characterized by the Pierson-Moskowitz (P-M) spectrum. The wave forces on the submerged elements of the platform's shaft are calculated using Morison's Equation with Airy's linear wave theory ignoring diffraction effects. The fluctuating wind load has been estimated using Ochi and Shin wind velocity spectrum for offshore structures. The nonlinear dynamic equation of motion is solved in the time domain by the Wilson-e method. The wind-structure interactions, along with the effect of various other parameters on the platform response, are investigated. The effect of offset of aerodynamic center (A.C.) with the center of gravity (C.G.) of platform superstructure has also been investigated. The outcome of the analyses indicates that low-frequency wind forces affect the response of ALP to a large extent, which otherwise is not enhanced in the presence of only waves. The mean wind modifies the mean position of the platform surge response to the positive side, causing an offset. Various power spectral densities (PSDs) under high and moderate sea states show that apart from the significant peak occurring at the two natural frequencies, other prominent peaks also appear at very low frequencies showing the influence of wind on the response.

Online Prediction of Ship Roll Motion in Waves Based on Auto-Moving Gird Search-Least Square Support Vector Machine

A novel method based on auto-moving grid search-least square support vector machine (AGS-LSSVM) is proposed for online predicting ship roll motion in waves. To verify the method, simulation data are used, which are obtained by solving the second-order nonlinear differential equation of ship roll motion using the fourth-order Runge–Kutta method, while the Pierson–Moskowitz spectrum (P–M spectrum) is used to simulate the irregular waves. Combining the sliding time window with the least square support vector machine (LS-SVM), the samples in the time window are used to train the LS-SVM model, and the model hyperparameters are optimized online by the auto-moving grid search (AGS) method. The trained model is used to predict the roll motion in the next 30 seconds, and the prediction results are compared with the simulation data. It is shown that the AGS-LSSVM is an effective method for online predicting ship roll motion in waves.

A new design concept for ocean nuclear power plants using tension leg platform

This paper presents a new design concept for ocean nuclear power plants (ONPPs) using a tension leg platform (TLP). The system-integrated modular advanced reactor, which is one of the successful small modular reactors, is mounted for demonstration. The authors define the design requirements and parameters, modularize and rearrange the nuclear and other facilities, and propose a new total general arrangement. The most fundamental level of design results for the platform and tendon system are provided, and the construction procedure and safety features are discussed. The integrated passive safety system developed for the gravity based structure-type ONPP is also available in the TLP-type ONPP with minor modifications. The safety system fully utilizes the benefits of the ocean environment, and enhances the safety features of the proposed concept. For the verification of the design concept, hydrodynamic analyses are performed using the commercial software ANSYS AQWA with the Pierson-Moskowitz and JONSWAP wave spectra that represent various ocean environments and the results are discussed.

Wave asymmetry and particle orbits in irregular wave models

Abstract

Effect of current on the dynamic response of a bi-articulated offshore tower

Wind and wave loadings have a predominant role in the design of articulated offshore towers for its successful service and survival. Such towers are very sensitive to the dynamic effect of environmental loads. The compliant nature of these towers with environmental loads introduces geometric nonlinearity due to large displacements, which becomes an important consideration in the analysis of these towers. This article deals with the dynamic response of a bi-articulated offshore tower to wind, wave, and current forces. The exposed portion of the tower is subjected to the action of wind, while the submerged portion is acted upon by random wave and current forces. Wind load is modeled by Ochi and Shin spectrum, while the wave load is characterized by Pierson–Moskowitz spectrum. The nonlinear dynamic equations of motion are derived by Hamilton’s principle. Response of the tower is determined by a time domain iterative (Wilson-θ) method. Power spectral density of important parameters such as surge, tilting motion, hinge shear, and bending moment are presented under high and low sea states. It is observed that response of tower due to current modifies the peak energy of power spectral density functions.

Test Bench Algorithms for Catamaran Roll Simulation

Creation of seaworthiness catamaran system required two stages: computer simulation and prototyping of software and hardware. To commit second stage we made test bench to perform catamaran roll, calculations and collecting experiment data. Possibility of making calculation like on real onboard vessel deck is required. Thus test bench is a Stewart platform which performs catamaran deck roll and computer connected to the platform performs calculations. 3-DOF sensor mounted on movable plate of platform give us roll and pitch. Using transfer function approximation of Pierson-Moskowitz spectrum and Runge-Kutta 4-order method with constant step size we make software for sea-wave simulation, catamaran roll generation, filtering data and general calculation. Software we make is a set of command-line applications performing their tasks. Test bench allows us repeat experiments and debug software and algorithms, compare recorded and simulated data.