Pierson-Moskowitz Research Articles

A Synthetic Aperture Radar Imaging Simulation Method for Sea Surface Scenes Combined with Electromagnetic Scattering Characteristics

Synthetic aperture radar (SAR) simulation is a vital tool for planning SAR missions, interpreting SAR images, and extracting valuable information. SAR imaging is essential for analyzing sea scenes, and the accuracy of sea surface and scattering models is crucial for effective SAR simulations. Traditional methods typically employ empirical formulas to fit sea surface scattering, which are not closely aligned with the principles of electromagnetic scattering. This paper introduces a novel approach by constructing multiple sea surface models based on the Pierson–Moskowitz (P-M) sea spectrum, integrated with the stereo wave observation projection (SWOP) expansion function to thoroughly account for the influence of wave fluctuation characteristics on radar scattering. Utilizing the shooting and bouncing ray-physical optics (SBR-PO) method, which adheres to the principles of electromagnetic scattering, this study not only analyzes sea surface scattering characteristics under various sea conditions but also facilitates the computation of scattering coupling between multiple targets. By constructing detailed scattering distribution data, the method achieves high-precision SAR simulation results. The scattering model developed using the SBR-PO method provides a more nuanced description of sea surface scenes compared to traditional methods, achieving an optimal balance between efficiency and accuracy, thus significantly enhancing sea surface SAR imaging simulations.

Effect of turbulence driven by wind on sediment suspension under different submerged vegetation density in Lake Taihu

Wind direction and velocitydetermines the hydrodynamic structure in the shallow lakes. Notably, submerged vegetation also affect the hydrodynamic structure of the thermocline region of the lake which in turn affects the resuspension of benthic sediments. Therefore, based on meteorological and high-frequency hydrodynamic data, this study analyses the effect of wind field on the vertical shear of the flow field. Besides, study used Pierson–Moskowitz (PM) spectra to strip wind and surge waves to elucidate the response mechanism of turbulence in Meiliang Bay of Taihu Lake. Based on indoor experiments, we simulate the “wind value” (joint effect of wind speed and direction) on hydrodynamics and sediment release under different hydrophyte density cover. The results show that both wind and wave fields affect the hydrodynamic structure. In summer, the vertical shear layer of the flow field will shift downwards due to the wind field. The wave field consists of wind waves and surge waves, the wind waves having a greater impact on turbulence energy. A characteristic quantity 'wind value' is constructed using trigonometric functions which can characterize wind speed and wind direction of arbitrary magnitude. The correlation between 'wind value' and near-bottom turbulence is significantly better than that of wind speed alone, indicating that the effect of wind direction on turbulence cannot be ignored. Although, within a certain range, sediment re-suspension is not necessarily proportional to flow velocity but to turbulent kinetic energy due to the effect of wind direction. High-density submerged vegetation can form a wall boundary protection, which changes the flow pattern of the lake from mixed laminar flow to boundary laminar flow, reducing the intensity of turbulence and impeding sediment re-suspension. Findings of this study can provide a reference for endogenous control and aquatic ecological restoration in shallow lakes.

Wave spectrum analysis for southern Caspian Sea

The general form of spectrum S(ω)=Aω−pexp(−Bω−q) was used in the present study to mathematically describe the spectrum of the Caspian Sea waves, and its fit to observations was obtained by assigning different values to pair (p,q). For this purpose, five spectral models, including Donelan, Pierson-Moskowitz (PM), Krylov, Davidan, and Neumann were considered corresponding to (4,4), (5,4), (7,4), (6.5,5.5), and (6,2). In the first step, the default coefficients were found to lack the required accuracy, therefore, they were optimized. The performance comparison of these five models showed that the spectral width index (ν) provides a good insight into the performance of the models such that the Krylov model exhibited the highest accuracy for narrow spectra (ν < 0.4). For broad (ν > 0.45) and medium-width spectra (0.4 < ν < 0.45), the Donelan model and PM model yielded the best result, respectively. The highest rate of error was related to the Davidan model; therefore, it was excluded from the study. The Neumann model had similar performance to the Donelan model. Additionally, it was observed that the models are sometimes incapable of accurately estimating the spectrum in high frequency band. In validation of Philips (∼ω−5) and Toba (∼ω−4) theories, the frequency dependence of spectrum in the equilibrium range was found to take the form of ω−7, ω−4, and ω−5 in narrow, broad and medium-width spectra, respectively.

Wind-sea and swell separation of 1D wave spectrum by deep learning

In this study, three existing methods to separate wind-sea and swell from 1D wave spectra, namely the Pierson–Moskowitz (PM) method, the steepness method (HP method), and the overshooting method (JP method), were evaluated statistically using data from 38 meteorological buoys from National Data Buoy Center (NDBC) over the period 2010–2020. Among the three methods, the PM method shows the best agreement with the 2D separation method, because it uses the wind speed information as an input term. Using these buoy data, a new 1D wind-sea-swell separation method based on deep learning is proposed. This new method can directly compute the wind-sea or swell significant wave height (SWH) from a 1D wave spectrum with or without wind speed data as input. When the wind speed is used as an input term, the overall root-mean-square error (RMSE) of the method for wind-sea/swell SWH is 0.27/0.36 m compared to the 2D separation method, which outperforms all existing 1D separation methods. When there is no wind speed data, the RMSE of wind-sea/swell SWH can still reach 0.36/0.41 m, which is similar to the accuracy of the PM method uses wind speed as input. Both methods are robust and have no significant geographical dependence.

A frequency domain study on deck isolation effectiveness in control of wave-induced vibration of offshore jacket platform

A frequency domain-based investigation is carried out on the effectiveness of deck isolation under wave-induced vibrations of offshore jacket platforms. The deck isolation layer comprises laminated rubber bearings and supplemental damping in the form of linear viscous dampers. The jacket platform is modelled by a multi-degree-of-freedom lumped mass system. The frequency response functions (FRFs) are formulated and then presented for an example jacket platform, with and without deck isolation. The power spectral density functions of the deck and jacket cap responses are obtained for the Pierson-Moskowitz (PM) wave spectrum. The effects of deck isolation are studied for several combinations of isolation layer flexibility and damping. The chief deduction from the study is that by providing adequate damping in the isolation layer, the value of which for a given jacket platform is determined by parameters such as the isolation layer flexibility and the intensity of wave loading, the wave-induced vibrations of the deck may be significantly mitigated, even under extreme sea states. Here, the isolation layer damping prevents response amplification from taking place, which is possible as deck isolation causes the structural frequencies to be nearer to that of the wave loading.

Hydrodynamics of an OWC Device in Irregular Incident Waves Using RANS Model

This research examines the hydrodynamic performance of an oscillating water column device placed over a sloping seabed under the influence of irregular incident waves. The numerical model is based on the Reynolds-veraged Navier–Stokes (RANS) equations with a modified k−ω turbulence model and uses the volume-of-fluid (VOF) approach to monitor the air–water interface. To explore the hydrodynamic performance of the OWC device in actual ocean conditions, the Pierson–Moskowitz (P-M) spectrum was used as the incident wave spectrum, together with the four distinct sea states which occur most often along the western coast of Portugal. The numerical simulation offers a comprehensive velocity vector and streamline profiles inside the OWC device’s chamber during an entire cycle of pressure fluctuation. In addition, the impact of the irregular wave conditions on the free-surface elevation at various places, the pressure drop between the chamber and the outside, and the airflow rate via the orifice per unit width of the OWC device are investigated in detail. The results demonstrate that the amplitudes of the inward and outward velocities via the orifice, free-surface elevations, and flow characteristics are greater for more significant wave heights. Further, it is noticed that the power generation and capture efficiency are higher for a seabed having moderate slopes.

Acoustic scattering from dynamic rough ocean surfaces using finite-difference time-domain modeling techniques

Established models for underwater acoustic propagation and scattering typically assume the sea-surface to be either perfectly smooth or rough but static in time. When the sea-surface is rough and moving, received signals show anomalies such as additional transmission losses (due to scattering) and Doppler effects (due to surface motion). Understanding the mechanisms behind these anomalies leads to better sonar system designs without having to perform expensive at-sea experiments. The Finite-Difference Time-Domain (FDTD) method is ideal to predict these physical phenomena. This work presents a FDTD method implemented to model the impact of both sea-surface roughness and motion on underwater acoustic propagation. The FDTD method allows an arbitrary function to define the rough sea-surface and its time evolution. The surface characteristics are modeled using a Pierson-Moskowitz (PM) frequency spectrum. The PM surface model is simple to implement and fully defined by wind speed and direction. Time-domain results from FDTD simulations of static rough sea-surfaces are compared to an established Helmholtz integral equation (HIE) method to establish the validity of the approach. Broadband signals are used as the source waveform. Results demonstrate the anomalous transmission loss and Doppler in received signals. [Work supported by the Office of Naval Research.]

Semi-active control of jacket structure using MR damper and a deformation enhancement device under random ocean waves

The effect of a lever arm arrangement on the dynamic response of jacket structure installed with a Magneto-Rheological (MR) damper is investigated in this study. The structure is excited by random ocean waves for significant wave heights of 5 m, 8 m, and 10 m using the Pierson–Moskowitz (PM) spectrum. MR dampers of capacity 1000 kN, 500 kN, and 200 kN are used to study the effect of the lever arm on the control performances of the structure. The jacket structure is numerically modeled using the Finite Element Method (FEM), and the dynamics of MR damper is represented using the phenomenological Bouc-Wen model. The Fuzzy Logic Controller (FLC) that provides the command voltage to the MR damper is optimized using the Genetic Algorithm (GA) with a fitness function based on Root Mean Square (RMS) values of tip displacement and acceleration. The lever arm arrangement was found to enhance the control force, which further aids in reducing the damper capacity although maintaining the same percentage of control. For a 30% lever ratio, the percentage control in RMS displacement achieved for 200 kN, 500 kN, and 1000 kN dampers are 31.9%, 45.2%, and 47%, respectively. The percentage control on RMS displacement was nearly constant for different significant wave heights because of the lever arm arrangement. The numerical results show that the FLC successfully controls the response of the structure, and the lever arm configuration helps in improving damper efficiency

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.

Deep Learning-Based Timing Offset Estimation for Deep-Sea Vertical Underwater Acoustic Communications

This study proposes a novel receiver structure for underwater vertical acoustic communication in which the bias in the correlation-based estimation for the timing offset is learned and then estimated by a deep neural network (DNN) to an accuracy that renders subsequent use of equalizers unnecessary. For a duration of 7 s, 15 timing offsets of the linear frequency modulation (LFM) signals obtained by the correlation were fed into the DNN. The model was based on the Pierson–Moskowitz (PM) random surface height model with a moderate wind speed and was further verified under various wind speeds and experimental waveforms. This receiver, embedded with the DNN model, demonstrated lower complexity and better performance than the adaptive equalizer-based receiver. The 5000 m depth deep-sea experimental data show the superiority of the proposed combination of DNN-based synchronization and the time-invariant equalizer.

Offshore Electromagnetic Spectrum Distribution Prediction Algorithm Based on Ray Tracing Method

The detection and management of electromagnetic spectrum resources is becoming more and more important. It is difficult to predict the electromagnetic spectrum distribution accurately in complex maritime environment. In this letter, the offshore environment model is described in conjunction with the Pierson–Moskowitz (PM) wave spectrum and antenna attitude. Then, we establish the offshore electromagnetic spectrum distribution prediction model. The offshore electromagnetic wave propagation is divided into the sight straight-line ray propagation and rough sea surface reflecting-line ray propagation. Combined with the antenna directional pattern, we propose the effective angle to accelerate effective rays distribution estimation. In the simulation, the ray distribution is obtained based on the instantaneous PM wave spectrum data, and the final field strength of the effective ray at the receiving point is calculated. The experimental results show that the prediction model based on ray tracing method can accurately estimate the offshore electromagnetic spectrum distribution.

The effect of swell on wave spectra of extreme sea states offshore Sarawak, Malaysia

Wave spectra specified for the design of offshore structures are often expressed in terms of the Pierson Moskowitz (PM) and JONSWAP formulations, which describe the frequency spectrum of fully-developed and fetch-limited wind-seas, respectively. At locations offshore Sarawak, Malaysia, measurements of extreme sea states have spectral shapes with characteristics of a wind-sea, but the frequencies of the spectral peaks are substantially too low to be supported by the measured local winds.As extreme sea states offshore Sarawak are predominantly produced by northeast monsoon surges in the South China Sea, we dissect the wind and wave fields of such an event, by examining the winds and the wave spectra from a hindcast of the event, together with measured wave spectra at a location offshore Sarawak, Malaysia, with the specific aim of identifying the nature of the underlying wave field that produces the spectral shape of the measured extreme sea states.It is found that while the wave spectra of extreme sea states offshore Sarawak have unimodal shapes like those of wind-seas, the wave field is dominated by swell energy located at and around the spectral peak frequency, with a comparatively small wind-sea component at higher frequency.

Research on a Method for Simulating Multiview Ocean Wave Synchronization Data by Networked SAR Satellites

It is expected that the problem of the azimuth cutoff wavelength in single-satellite synthetic aperture radar (SAR) observations can be solved by means of the cooperative observation of networked SAR satellites. Multiview SAR wave synchronization data are required in the process. However, most of the current orbiting satellites are geosynchronous orbit satellites; the simultaneous observation by multiple SARs in the same sea area cannot be achieved, and multiview synchronization data cannot be obtained. Therefore, this paper studies the simulation of the multiview SAR wave synchronization data. Ocean wave spectra were simulated by using the Pierson Moskowitz (PM) spectrum. The Monte Carlo method was used to simulate two-dimensional (2D) ocean surfaces at different wind speeds. The two-scale electromagnetic scattering model was used to calculate the ocean surface backscattering coefficient, and the time-domain echo algorithm was used to generate echo signals. The echo signals were processed by the Range–Doppler (RD) imaging algorithm to obtain ocean SAR data. Based on the obtained single-SAR wave data, networked satellites consisting of three SARs were simulated, and the SAR wave data were synchronized. The results show that when SARs are used to observe the same sea area from different observation directions, the clarity of the wave fringes in the SAR images are different. For different azimuth angles, the degrees of azimuth cutoff are different. These results reflect the influences of different degrees of azimuth cutoff on SAR images. The simulated wave synchronization data can be used as the basic data source for subsequent azimuth cutoff wavelength compensation.

Acoustic wave scattering from dynamic rough sea-surfaces using the finite-difference time-domain method

Numeric models for underwater acoustic propagation typically assume the sea-surface to be either perfectly smooth or rough but “frozen” in time. For long sonar signals on the order of tens of seconds, the sea-surface can interact at many different wave displacements over its duration. This causes anomalies in the received signal which introduces additional transmission losses and Doppler effects. The impact of including roughness and motion of the sea-surface on sonar systems is investigated using the finite-difference time-domain (FDTD) method. The FDTD method is a numeric technique that is well suited for modeling boundary roughness and motion. This is due to its ability to directly configure complex boundary conditions in the surrounding simulation grid and full pressure wave propagation in the time-domain. The rough, time-evolving sea-surface is modeled using a Pierson-Moskowitz (PM) frequency spectrum which is simple to implement and defined using just wind speed and direction. The results from FDTD simulations of static rough sea-surfaces are compared to a previously established integral solution method to evaluate the validity of the approach. Agreement is also demonstrated for FDTD simulations of a dynamic rough sea-surface and a theoretic statistical model. [Work supported by the Office of Naval Research.] Numeric models for underwater acoustic propagation typically assume the sea-surface to be either perfectly smooth or rough but “frozen” in time. For long sonar signals on the order of tens of seconds, the sea-surface can interact at many different wave displacements over its duration. This causes anomalies in the received signal which introduces additional transmission losses and Doppler effects. The impact of including roughness and motion of the sea-surface on sonar systems is investigated using the finite-difference time-domain (FDTD) method. The FDTD method is a numeric technique that is well suited for modeling boundary roughness and motion. This is due to its ability to directly configure complex boundary conditions in the surrounding simulation grid and full pressure wave propagation in the time-domain. The rough, time-evolving sea-surface is modeled using a Pierson-Moskowitz (PM) frequency spectrum which is simple to implement and defined using just wind speed and direction. The results from FDTD...

Study on Energy Spectrum Instability in the Processes of Propagating and Breaking of Focusing Waves

Based on phase focusing theory, focusing waves with different spectral types and breaking severities were generated in a wave flume. The time series of surface elevation fluctuation along the flume were obtained by utilizing 22 wave probes mounted along the mid-stream of the flume. Based on the wave spectrum obtained using fast Fourier transform (FFT), the instability characteristics of the energy spectrum were reported in this paper. By analyzing the variation of total spectral energy, the total spectral energy after wave breaking was found to clearly decrease, and the loss value and ratio gradually increased and tended to stabilize with the enhancement of breaking severity for different spectral types. When wave breaking occurred, the energy loss was primarily in a high-frequency range of f/fp>1.0, and energy gain was primarily in a low-frequency range of f/fp<1.0. As the breaking severity increased, the energy gain-loss ratio decreased gradually, which demonstrates that the energy was mostly dissipated. For plunging waves, the energy gain-loss ratio reached 24% for the constant wave steepness (CWS) spectrum, and was slightly larger at approximately 30% for the constant wave amplitude (CWA) spectrum, and was the largest at approximately 42% for the Pierson-Moskowitz (PM) spectrum.

Offshore Electromagnetic Spectrum Distribution Prediction Model Based on Ray Tracing Method and PM Wave Spectrum

Electromagnetic spectrum distribution prediction is the basis for the development of wireless communication technology. Due to the high randomness of the rough sea surface, it is difficult to accurately predict the offshore electromagnetic spectrum distribution. We present a prediction model of offshore electromagnetic spectrum distribution based on ray tracing method and Pierson-Moskowitz (PM) wave spectrum model. Based on the antenna attitude and the antenna directional pattern, the field strength calculation formulas of the electromagnetic wave sight line ray (SLR) propagation and the electromagnetic wave reflecting line ray (RLR) propagation off the sea surface are established. As the sea surface and the antenna attitude change, the effective rays from the transmitting antenna to the receiving antenna also change. This paper focus on the electromagnetic spectrum distribution prediction by calculating the effective angle (EA) of the transmitting antenna. We relate the EA to the antenna tilt angle and the antenna directional pattern, and combine the PM wave spectrum to establish the offshore electromagnetic spectrum distribution prediction models. Finally, we simulated the electromagnetic spectrum distribution prediction based on specific PM wave spectrum data.

Methodology for assessment of operational limits including uncertainties in wave spectral energy distribution for safe execution of marine operations

Marine operations need to be executed in a cost-effective and safe manner. Safety depends on safety margins that are included in the operational limits. These operational limits are normally given in terms of sea state parameters, i.e. significant wave height (Hs) and peak period (Tp), here denoted as Hs(Tp). Safety margins on Hs(Tp) should account for various sources of uncertainties in weather forecasts, wave spectral shape, numerical models, etc. Wave spectra at an offshore site may be multi-modal and not necessarily resemble analytical spectra, such as Joint North Sea Wave Project (JONSWAP) or Pierson-Moskowitz (PM) models. Since floating vessels are sensitive to wave spectral energy distribution, Hs(Tp) operational limits should account for this source of uncertainty. This paper provides a general methodology to assess the uncertainty in Hs(Tp) limits due to variability in wave spectral energy distribution. This is important for safe execution of marine operations. The methodology uses response-based operational limits, directional (2D) hindcast wave spectra and dynamic coupled models of marine operation activities. A case study of an offshore wind turbine transition piece installation is shown to illustrate the proposed methodology.

Experimental Generation of Focusing Wave Groups on Following and Adverse-Sheared Currents in a Wave-Current Flume

Focused waves are often used in physical and numerical studies as a representative condition for extreme waves or as a means to generate very steep and breaking waves at a prescribed location in space and time. They have also been combined with depth-varying currents in investigations of incipient wave breaking, wave breaking–induced energy dissipation, and wave–current induced loads on marine structures. A focused wave is created when all the components in a transient wave group come into phase. In the past, linear wave theory and iterative methodologies coupled with the linear Doppler-shifted dispersion relationship have been suggested to account for the presence of a current and achieve the required phase and amplitude focusing. In the majority of cases, linear or constant steepness spectra are used, which, compared to measured or theoretical spectra like the Joint North Sea Wave Project (JONSWAP), Gaussian, and Pierson-Moskowitz (PM) can be termed unrealistic. The effectiveness of these methodologies also decreases as the nonlinearity increases; therefore, in most studies, either weakly nonlinear conditions are used or the focus location is determined empirically. Here, an iterative methodology is suggested that can focus waves of any height at a predetermined temporal and spatial location even for wave groups propagating on a strong following or adverse current. An experimental apparatus developed to generate relatively stable sheared velocity profiles is also described. The depth-varying profile of the resulting currents diverges from that of classical wind-driven currents and comes closer to profiles measured in field sites important for the deployment of, for instance, tidal and wind energy converters. The methodology is successfully applied to wave groups traveling on still water, following, and adverse currents, and the results presented refer to linear, weakly nonlinear, and strongly nonlinear–focused waves generated for a range of realistic target spectra. The capability to generate wave groups with the same amplitude spectrum at a fixed location for a variety of flow conditions—still water, following, and adverse sheared currents—is also illustrated.

Electromagnetic scattering of coated objects over sea surface based on SBR-SDFSM

An efficient approach to analyze the electromagnetic (EM) scattering from coated objects above a three-dimensional (3-D) dielectric random rough surface is proposed in this paper. The electric and magnetic current densities on the sea surface are analytically realized using the semi-deterministic facet scattering model (SDFSM). Considering Fresnel reflection coefficient, a scheme combining the shooting and bouncing rays (SBR) and the physical theory of diffraction (PTD) is developed to calculate the scattering of the coated objects. Simulation results obtained with the combined method are verified by comparison with exact simulations using the multilevel fast multiple method (MLFMM). Scattering of large coated objects over sea surface composite model are too large and complex to be calculated using exact methods. With the asymptotic approach in this paper, the scattering performance can be analyzed with rather moderate computational efforts. Numerical results of composite scattering from an electric large three-dimensional model, e.g. an airplane target over a randomly rough surface with Pierson Moskowitz (PM) spectrum are presented and discussed.

High-Performance Time-Code Diversity Scheme for Shore-to-Sea Maritime Visible-Light Communication

This paper presents a novel shore-to-sea maritime data transmission system based on time-code diversity, using visible light in maritime environments to overcome the limitations of conventional maritime wireless communications. The proposed system is primarily comprised of existing LED-based lighthouses and maritime transceivers (marine beacons, buoys, etc.), and thus is considered cost-effective in terms of implementation. We first analyze maritime visible-light communications on the basis of the unique properties of a maritime environment, i.e. sea states (wave height, wind speed, etc.), plus atmospheric turbulence, using the Pierson-Moskowitz (PM) and JONSWAP (JS) spectrum models. It is found that the JS model outperforms the PM model, and that the coverage distance depends on the LED power and sea states. To combat maritime fading conditions that significantly degrade performance and coverage distance, we propose a time-code diversity (TCD) scheme in which the delayed versions of the original data are retransmitted using orthogonal Walsh codes. This TCD scheme is found to be superior, in that it offers three orders of magnitude in terms of BER performance, compared to a conventional (non-TCD) transmission scheme. The proposed scheme is robust and efficient in overcoming the effect of impairments present in maritime environments with a BER of approximately $10^{-5}$ and a data rate of 100 Kbps at a distance of 1 km.