Wave Spectral Shape Research Articles

Uncertainty of Wave Spectral Shape and Parameters Associated with the Spectral Estimation

The uncertainty in estimating the wave spectrum from the records of wave elevation by heave–pitch–roll buoys is studied, considering the effects of the estimation method and the spectral resolution adopted in the process. This investigation utilizes measurements from a wave buoy moored in deep water in the South Atlantic Ocean. First, the spectra are computed using the autocorrelation function and the direct Fourier method. Second, the spectral resolution is tested in terms of degrees of freedom. The degrees of freedom are varied, and the resulting spectra and integrated parameters are computed, showing significant variability. A simple and robust methodology for determining the wave spectrum is suggested, which involves calculating the average energy density in each frequency band. The results of this methodology reduce the variability of the estimated parameters, improving overall accuracy while preserving frequency resolution, which is crucial in complex sea states. Additionally, to demonstrate the feasibility of the implemented approach, the final spectrum is fitted using an empirical model ideal for that type of spectrum. Finally, the performance and the goodness of the fit process for the final averaged curve are checked by widely used statistical metrics, such as R2 = 0.97 and root mean square error = 0.49.

Observations of coastal infragravity wave characteristics under swell-dominated conditions

This study analyzed the characteristics of infragravity (hereafter IG) waves under a microtidal and swell-dominated wave climate based on the field observations collected in the nearshore waters (water depth: ∼ 13 m) of southern Sri Lanka. The main focus is on the dependence of nearshore IG waves on the incident short wave parameters, with particular attention to the influence of the short wave spectral shape on the IG wave characteristics. The observation results indicate that IG waves are primarily locally excited by incident swell wave energy, and accurate prediction of the IG wave height can be achieved using the parameter HS2Tm−1,0, which represents the short wave energy flux. Bound IG wave energy is much smaller than the free IG wave under conventional sea states but becomes significant under high-energy swell sea states.Higher levels of IG wave energy are found to be forced under narrower spectral shapes and smaller directional spreading short wave conditions, and these conditions typically correspond to stronger coupling strengths in the bound IG wave theory. Compared to the single-peaked spectra wave condition, the forced IG wave energy decreases under the double-peaked spectra wave condition. This is likely mainly because the latter tends to have a broader spectrum and a larger directional spreading. On the other hand, under the narrow-banded spectral short wave conditions, IG wave energy is inclined to be distributed over a lower and smaller frequency range. This is noteworthy because lower-frequency IG waves tend to be more difficult to break. In addition, the bound IG wave energy was found to increase at low tide, but for the intermediate water depths in which the observation site is located in this study, the influence of the small tidal range in the study area on the IG wave energy was not significant.

Global 3-hourly wind-wave and swell data for wave climate and wave energy resource research from 1950 to 2100

Ocean wave climate, including wind waves and swells, is essential to human marine activities and global or regional climate systems, and is highly related to harnessing wave energy resources. In this study, a global 3-hourly instantaneous wave dataset was established with the third-generation wave model MASNUM-WAM and wind forcings derived from the products of the First Institute of Oceanography-Earth System Model version 2.0, the climate model coupled with wave model, under the unified framework of the Coupled Model Intercomparison Project phase 6. This dataset contains 17 wave parameters, including the information associated with wave energy and spectral shape geometries, from one historical (1950–2014) simulation and three future (2015–2100) scenario experiments (ssp125, ssp245, and ssp585). Moreover, all the parameters can be accessed separately in the form of wind waves and swells. The historical results show that the simulated wave characteristics agree well with satellite observations and the ERA5 reanalysis products. This dataset can provide the community with a unique and informative data source for wave climate and wave energy resource research.

A Study on Omnidirectional Ocean Wave Spectral Shape with Bimodal Index

A Study on Omnidirectional Ocean Wave Spectral Shape with Bimodal Index

A numerical study on nonlinear surface wave evolution over viscoelastic mud

Accurate prediction of wave energy dissipation over mud is essential for understanding nearshore circulation, sediment transport processes, and design of engineering projects along muddy coasts. It is desirable to be able to simulate wave propagation over a wide range of mud behaviors as wave evolution is highly dependent on mud rheological characteristics. In this study, we develop a numerical model to simulate surface wave evolution over viscoelastic muds. This new wave-mud interaction model is comprised of a frequency-domain phase-resolving model for wave propagation that explicitly solves nonlinear wave-wave interactions, and a model for mud-induced surface wave dissipation and modulation. Model results show satisfactory agreement with laboratory measurements of wave height and attenuation rates over mud, and shows improvement over the model with a viscous mud mechanism. The model is then used to investigate the combined effect of mud viscoelasticity and nonlinear wave-wave interactions on surface wave evolution. Cnoidal and random wave simulations are conducted. In general, qualitative measures such as shape of cnoidal waves or pattern of variation in Hrms of random waves are dictated by direct mud-induced damping which due to resonance effects, has a substantially different structure over viscoelastic mud compared to viscous mud. Nonlinear interactions affect spectral shape and distribution of energy loss across the spectrum. Subharmonic interactions cause indirect damping of high frequencies but ameliorate damping of harmonics around mud’s resonance frequency. Therefore, neglecting mud elasticity can result in significant errors in estimation of bulk wave characteristics and spectral shape.

FIELD MEASUREMENTS AND SWASH PARAMETERIZATION ON BEACHES

The wave runup, defined as the vertical oscillation of the water edge at the coast, is commonly used as criterion for coastal design projects and flooding/erosion risk analysis. Due to the complexity of nearshore wave processes, most runup studies are based on empirical approaches which directly relate these oscillations to the beach and offshore wave characteristics. However, there is still considerable debate about just how runup is related to these environmental parameters, as well as about the range of application of empirical models due to site specific conditions. Recent works emphasized the importance of including site specific conditions to reduce the scatter in available parameterizations. Parameters related to beach characteristics like the sediment size, the amount of reflection, wave spectral shape and morphodynamic beach state may improve runup predictions (Poate et al., 2016, Guza and Feddersen, 2012).

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.

Reproduction of ocean waves for large-scale model seakeeping measurement: The case of coastal waves in Puerto Rico & Virgin Islands and Gulf of Maine

The novel testing technique for ship seakeeping behavior, which includes conducting large-scale model trial in realistic sea waves, has been given special attention by naval architects in recent years. Large-scale model measurement provides obvious advantages in the investigation of ship hydrodynamics in many aspects. However, there still exist some challenges that need addressing to improve this kind of testing technique. One of the great challenges is the reproduction of full-scale ocean waves when conducting downscaled model experiments in natural sea environment. This paper aims to explore the possibility of reproduction of full-scale wave states in coastal sea areas. Criteria, such as significant wave height, mean period, spectral shape and directional spreading, are involved in the wave similarity judgment. Various factors including season, climate, model scaling, coastal space and time are taken into account to determine suitable waves for model measurement. The wave selection principle and methodology proposed in this paper are demonstrated through a case study using coastal wave data of the Puerto Rico & Virgin Islands and the Gulf of Maine.

Wave spectral shapes in the coastal waters based on measured data off Karwar on the western coast of India

Abstract. An understanding of the wave spectral shapes is of primary importance for the design of marine facilities. In this paper, the wave spectra collected from January 2011 to December 2015 in the coastal waters of the eastern Arabian Sea using the moored directional waverider buoy are examined to determine the temporal variations in the wave spectral shape. Over an annual cycle for 31.15 % of the time, the peak frequency is between 0.08 and 0.10 Hz; the significant wave height is also relatively high (∼ 1.55 m) for waves in this class. The slope of the high-frequency tail of the monthly average wave spectra is high during the Indian summer monsoon period (June–September) compared to other months, and it increases with an increase in significant wave height. There is not much interannual variation in the slope for swell-dominated spectra during the monsoon, while in the non-monsoon period when wind-seas have a high level of influence, the slope varies significantly. Since the exponent of the high-frequency part of the wave spectrum is within the range of −4 to −3 during the monsoon period, the Donelan spectrum shows a better fit for the high-frequency part of the wave spectra in monsoon months compared to other months.

Storm overwash of a gravel barrier: Field measurements and XBeach-G modelling

Gravel barriers provide a natural form of coastal protection and flood defence for many sites around the UK and worldwide. Predicting their vulnerability to different storm impact regimes that cause overtopping and overwash is crucial as these processes can lead to hazardous consequences such as inundation of the back of the barrier or breaching. This paper presents the first field measurements of storm overwash events on a gravel beach (Loe Bar, Cornwall, England). High frequency in-situ observations (2Hz) were performed using a 2D laser-scanner and allowed a complete characterization of the overwash flows (velocity and depth) and morphological response along a cross-shore section of the barrier. These novel measurements are used to validate the numerical model XBeach-G, to forecast overwash discharge. Several simulations were performed with XBeach-G to investigate the thresholds for the different storm impact regimes, given a variety of water levels and wave heights. Wave period and wave spectral shape are found to significantly affect these thresholds. While short period waves dissipate most of their energy by breaking before reaching the swash zone and produce short runup excursions, long period waves due to their low steepness arrive at the swash zone unbroken with enhanced heights (due to shoaling) thus promoting large runup excursions. When the offshore wave spectrum has a bimodal shape, wave transformation in shallow water causes the long period peak to dominate the swash giving large runup excursions. Long period waves or strongly bimodal waves result in enhanced runup thereby reducing the thresholds for barrier overtopping or overwashing.

Water surface slope spectra in nearshore and river mouth environments

With the ever-growing interest in satellite remote sensing, direct observations of short wave characteristics are needed along coastal margins. These zones are characterized by a diversity of physical processes that can affect sea surface topography. Here we present connections made between ocean wave spectral shape and wind forcing in coastal waters using polarimetric slope sensing and eddy covariance methods; this is based on data collected in the vicinity of the mouth of the Columbia River (MCR) on the Oregon-Washington border. These results provide insights into the behavior of short waves in coastal environments under variable wind forcing; this characterization of wave spectra is an important step towards improving the use of radar remote sensing to sample these dynamic coastal waters. High wavenumber spectral peaks are found to appear for U10 > 6 m/s but vanish for τ > 0.1 N/m2, indicating a stark difference between how wind speed and wind stress are related to the short-scale structure of the ocean surface. Near-capillary regime spectral shape is found to be less steep than in past observations and to show no discernable sensitivity to wind forcing.

A study on the optimal equation of the continuous wave spectrum

Waves can be expressed in terms of a spectrum; that is, the energy density distribution of a representative wave can be determined using statistical analysis. The JONSWAP, PM and BM spectra have been widely used for the specific target wave data set during storms. In this case, the extracted wave data are usually discontinuous and independent and cover a very short period of the total data-recording period. Previous studies on the continuous wave spectrum have focused on wave deformation in shallow water conditions and cannot be generalized for deep water conditions. In this study, the Generalized Extreme Value (GEV) function is proposed as a more-optimal function for the fitting of the con-tinuous wave spectral shape based on long-term monitored point wave data in deep waters. The GEV function was found to be able to accurately reproduce the wave spectral shape, except for discontinuous waves of greater than 4m in height.

파랑 스펙트럼 형상에 따른 처오름 특성

파랑 스펙트럼 형상에 따른 처오름 특성

Nanodust detection near 1 AU from spectral analysis of Cassini/Radio and Plasma Wave Science data

AbstractNanodust grains of a few nanometers in size are produced near the Sun by collisional breakup of larger grains and picked up by the magnetized solar wind. They have so far been detected at 1 AU by only the two STEREO spacecraft. Here we analyze the spectra measured by the radio and plasma wave instrument onboard Cassini during the cruise phase close to Earth orbit; they exhibit bursty signatures similar to those observed by the same instrument in association with nanodust stream impacts on Cassini near Jupiter. The observed wave level and spectral shape reveal impacts of nanoparticles at about 300 km/s, with an average flux compatible with that observed by the radio and plasma wave instrument onboard STEREO and with the interplanetary flux models.

Detecting nanoparticles at radio frequencies: Jovian dust stream impacts on Cassini/RPWS

We analyse wave observations by the Cassini/RPWS instrument performed during the Jovian fly‐by, when the on‐board dust analyser recorded dust streams which were interpreted as nanoparticles moving at about the solar wind speed. The observed wave pulses are produced by ionisation of dust grains impacting the spacecraft. Nanoparticles are detected because they move fast and the voltage produced by impact ionisation increases very fast with speed, so that they produce wave pulses as high as do much larger grains of smaller speeds. The observed wave level and spectral shape are compatible with those expected for the streams deduced from the dust analyser observations, and the impact rates observed on both instruments appear to vary similarly. The present result is the first wave detection simultaneous with a conventional detection by a dust analyser attributed to nanoparticles.

Gravity wave dynamics and effects in the middle atmosphere

Atmospheric gravity waves have been a subject of intense research activity in recent years because of their myriad effects and their major contributions to atmospheric circulation, structure, and variability. Apart from occasionally strong lower‐atmospheric effects, the major wave influences occur in the middle atmosphere, between ∼ 10 and 110 km altitudes because of decreasing density and increasing wave amplitudes with altitude. Theoretical, numerical, and observational studies have advanced our understanding of gravity waves on many fronts since the review by Fritts [1984a]; the present review will focus on these more recent contributions. Progress includes a better appreciation of gravity wave sources and characteristics, the evolution of the gravity wave spectrum with altitude and with variations of wind and stability, the character and implications of observed climatologies, and the wave interaction and instability processes that constrain wave amplitudes and spectral shape. Recent studies have also expanded dramatically our understanding of gravity wave influences on the large‐scale circulation and the thermal and constituent structures of the middle atmosphere. These advances have led to a number of parameterizations of gravity wave effects which are enabling ever more realistic descriptions of gravity wave forcing in large‐scale models. There remain, nevertheless, a number of areas in which further progress is needed in refining our understanding of and our ability to describe and predict gravity wave influences in the middle atmosphere. Our view of these unknowns and needs is also offered.

Ocean wave extraction from RADARSAT synthetic aperture radar inter-look image cross-spectra

This study is concerned with the extraction of directional ocean wave spectra from synthetic aperture radar (SAR) image spectra. The statistical estimation problem underlying the wave-SAR inverse problem is examined in detail in order to properly quantify the wave information content of SAR. As a concrete focus, a data set is considered comprising six RADARSAT SAR images co-located with a directional wave buoy off the east coast of Canada. These SAR data are transformed into inter-look image cross-spectra based on two looks at the same ocean scene separated by 0.4 s. The general problem of wave extraction from SAR is cast in terms of a statistical estimation problem that includes the observed SAR spectra, the wave-SAR transform, and prior spectral wave information. The central role of the weighting functions (inverse of the error covariances) is demonstrated, as well as the consequence of approximate (based on the quasilinear wave-SAR transform) versus exact linearizations on the convergence properties of the algorithm. Error estimates are derived and discussed. This statistical framework is applied to the extraction of spectral wave information from observed RADARSAT SAR image cross-spectra. A modified wave-SAR transform is used to account for case-specific geophysical and imaging effects. Analysis of the residual error of simulated and observed SAR spectra motivates a canonical form for the SAR observation error covariance. Wave estimates are then extracted from the SAR spectra, including wavenumber dependent error estimates and explicit identification of spectral null spaces where the SAR contains no wave information. Band-limited SAR wave information is also combined with prior (buoy) spectral wave estimates through parameterization of the wave spectral shape and use of regularization.

Gravity's rainbow

The temperature anisotropy of the cosmic microwave background may be partially the imprint left by gravitational waves. Measuring the gravitational wave component and spectral shape of the anisotropy is a critical test of inflationary cosmology and theories of large-scale structure formation.

Stability of the seaward slope of berm breakwaters

An extensive research on stability of statically and dynamically stable rock slopes and gravel beaches was reanalysed and focussed on berm breakwaters. Berm breakwaters are initially dynamically stable under severe wave attack, but become more or less statically stable after reshaping. The effects on the seaward profile of wave height, period, storm duration, spectral shape, initial slope, rock size, rock shape and grading, water depth and angle of wave attack, are described in a qualitative way. Relationships between these variables and the profile parameters are described, leading to a computer program. This program was verified with independent data of berm breakwaters from various international institutes. The program showed to give a good prediction of the behaviour of the seaward slope of berm breakwaters and can, therefore, be used as a conceptual design tool.

A statistical study of ELF‐VLF plasma waves at the magnetopause

A statistical study of the broadband ELF‐VLF plasma waves at the magnetopause has been performed using ISEE 1 plasma wave data. It is found that enhanced wave intensities are detected at 85% of all magnetopause crossings. Although wave amplitudes are highly variable from event to event and even within an event (particularly during high‐intensity events), the wave spectra averaged over many passes are remarkably similar at dawn, noon, and dusk local hours. Thus to first order, the average wave intensity and spectral shape are independent of local time. At select frequencies, the intensities are 10−8, 10−13, and 3 × 10−17 V2/m2 Hz at 101, 103, and 105 Hz and 3 × 10−4 and 5 × 10−8 nT2/Hz at 101 and 102 Hz, respectively. The average wave intensity is independent of latitude, magnetosheath field strength, and magnetopause position. The only parameter found to be correlated with wave intensity is the magnitude of the Z component of the magnetosheath magnetic field. The broadband wave intensities increase with increasing negative Bz. These observational results put strong constraints on any proposed generation mechanism for the broadband magnetopause boundary layer waves. Reasonable mechanisms should be able to explain the lack of local time, latitude, and interplanetary parameter dependences. The dependence of IMF Bz and possible correlation with magnetic reconnection should be a principal feature in the model. These observations support the conjecture that cross‐field diffusion of magnetosheath plasma by wave particle interaction with these waves (Tsurutani and Thorne, 1982) is the steady state source of the low‐latitude boundary layer, and that pitch angle scattering and the consequential particle precipitation into the ionosphere is the mechanism for the dayside aurora. For cyclotron resonant interaction with E>100 eV electrons during southward IMF Bz events, a total precipitation rate of 1.0 to 1.2 ergs/cm2 s is determined.