Directional Spectrum of Wind Waves: Part Ⅱ- Comparison and Confirmation

A model on the directional frequency spectrum of wind waves for deep water is introduced. The comparisons of the proposed model with other existing models show that the proposed model is very close to the JONSWAP model and DHH model for describing the developing waves under the normal spectral bandwidth, and has a better description for the transition of the unidirectional spectrum from ω -4 to ω -5 at a position around 3ω p, i.e., three time the peak frequency. Comparisons also show that the proposed model describes closely both field data measured by a four-frequency radar and a laser-optical sensor, and laboratory data measured by a laser slope gauge and an imaging optical method. The comparisons further demonstrate that the inverse spectral bandwidth as a new wave parameter is robust for describing the spectral steepness. Finally, the formula on the local spectral-peak angular frequency is confirmed using the observed two-dimensional spectra.

Interannual Variability of SST,SLA and Wind Waves in the Hawaii Area and Their Responses to ENSO

Time series of sea surface temperature （SST）, wind speed and significant wave height （SWH） from meteorological buoys of the National Data Buoy Center （NDBC） are useful for studying the interannual variability and trend of these quantities at the buoy areas. The measurements from 4 buoys （B51001, B51002, B51003 and B51004） in the Hawaii area are used to study the responses of the quantities to El Nino and Southern Oscillation （ENSO）. Long-term averages of these data reflect precise seasonal and climatological characteristics of SST, wind speed and SWH around the Hawaii area. Buoy observations from B51001 suggest a significant warming trend which is, however, not very clear from the other three buoys. Compared with the variability of SST and SWH, the wind speeds from the buoy observations show an increasing trend. The impacts of EI Nifio on SST and wind waves are also shown. Sea level data observed by altimeter during October 1992 to September 2006 are analyzed to investigate the variability of sea level in the Hawaii area. The results also show an increasing trend in sea level anomaly （SLA）. The low-passed SLA in the Hawaii area is consistent with the inverse phase of the low-passed SOI （Southern Oscillation Index）. Compared with the low-passed SOl and PDO （Pacific Decadal Oscillation）, the low-passed PNA （Pacific-North America Index） has a better correlation with the low-passed SEA in the Hawaii area.

Low frequency shift of wind waves induced by long waves based on experimental observation data

The influence of long regular waves on wind waves are examined in the laboratory tank. The wave spectra of wind waves are compared when there is and there is not long waves. Besides the widely addressed suppression of wind waves by long waves, it is also found that, the presence of long regular wave induces low frequency shift of wind waves when long wave slope is small and also its frequencyf is quite apart from wind wave crest frequencies fp. The effect of long wave modulation on wind wave spectra is estimated according to Longuet-Higgins ＆ Stewart （1960） （abbreviated as LS60 afterwards）, which is found to be prominent at the large ratio of fp/f l. It＇s also found that, when the limitation of wave breaking on wind wave steepness is taken account of, the LS60 theory can explain the low frequency shift satisfactorily. The work suggests that, at small long wave slope and large ratio of fp/fl, the LS60 modulation mechanism together with the enhanced wave breaking may dominate the influence of long waves on wind waves.

Directional Spectrum of Wind Waves: Part Ⅰ- Model and Derivation

A new model on the directional spectrum of wind waves for deep water is proposed based on the statistics of wind waves. This model contains three parameters: the wave age, the inverse spectral bandwidth and the local spectral-peak angular frequency. The inverse spectral bandwidth is a robust parameter for describing the spectral steepness of wind waves. Using the inverse spectral bandwidth parameter, the proposed model can well describe various observations obtained from the open ocean and laboratory tank.

Numerical simulation of non-gaussian process of wind waves

In this paper further mathematical analysis on 'correlation transfer technique' by Polge el al. is carried out, the tenable conditions and the extent of suitability for the said method are proved as well. In consideration of the influence of skewness of the sea surface elevation on spectral shape, a 'quasi-correlation transfer techique' is developed by the modification of the simulated target spectrum. Meanwhile, the numerical simulation of the non-Gaussian process of wind waves is carried out in view of the two conditions of the surface elevation probability distribution and the spectrum. By using its simulated results, the influence of skewness of the sea surface elevation on two parameters in the distribution of wave heights (which had been fitted by using the Weibull distribution) is analysed. The 'quasi- correlation tranfer technique' is verified and compared with the selection wave data observed in the Jiaozhou Bay in the period of 1980 to 1981. Results make clear (hat, as far as the statistical distribution of the wave heights and the distribution of the maximum (minimum) values of the sea surface elevation are concerned, the said method is obviously superior to the conventional mothed of the linear wave superposition, and that the simulated results are closer to the observation data.

Numerical calculation of drift current in wind waves

-Drift current induced by wind and waves is investigated with phase-averaged Navier-Stokes equation in which the Reynolds stress is closed by k-ε model. The governing equations are solved by the finite volume method in a system of nonorthogonal coordinates which is fitted to the phase-averaged wave surface. The predicted drift current is fairly reasonable and the drag coefficient of sea-surface predicted with the newly developed interface conditions shows good agreement with previous measurements when breaking waves do not exist.

An experimental study of the relations between bispectra and nonlinear apparent features of wind waves

To investigate the nonlinear properties of wind waves, experiments are carried out in a wind-wave flume with slope bottom at different wind speeds and fetches. Both the internal structure and apparent features of the nonlin-earity of wind waves are studied by using bispectral and statistical analysis of surface elevations. The relations between bispectra and nonlinear apparent characteristics of wind waves are established and confirmed.

Rainfall effect on wind waves and the turbulence beneath air-sea interface

Rainfall effects on wind waves and turbulence are investigated through the laboratory experiments in a large wind-wave tank. It is found that the wind waves are damped as a whole at low wind speeds, but are enhanced at high wind speeds. This dual effect of rain on the wind waves increases with the increase of rain rate, while the influence of rainfall-area length is not observable. At the low wind speed, the corresponding turbulence in terms of the turbulent kinetic energy （TKE） dissipation rate is significantly enhanced by rain- fall as the waves are damped severely. At the high wind speed, the augment of the TKE dissipation rate is suppressed while the wind waves are enhanced simultaneously. In the field, however, rainfall usually hin- ders the development of waves. In order to explain this contradiction of rainfall effect on waves, a possibility about energy transfer from turbulence to waves in case of the spectral peak of waves overlapping the inertial subrange of turbulence is assumed. It can be applied to interpret the damping phenomenon of gas trans- fer velocity in the laboratory experiments, and the variation of the TKE dissipation rates near sea surface compared with the law of wall.

On the Spectrum Width of Wind Waves

Based on the universal expression of wind wave spectra, four commonly used definitions of the spectrum width are re-examined. The results show that the non-dimensional spectrum width can measure the width of non-dimensional spectra but it does not reflect the developing state of the spectra. The dimensional spectrum width expresses the degree of concentration of wave energy of the spectrum in the process of wind wave growth. Tests show that the spectrum width presented by Wen et al. can objectively measure the degree of concentration of wave energy of the spectrum, reflect the state of wind wave growth, and provides a better result for practical application, The rules for definition of the spectrum width are discussed.

Observation and analysis of the influence of wind waves on air-sea momentum fluxes

Due to the long-standing lack of understanding the role of wind waves on wind stress at moderate to high wind speeds,a high-frequency turbulence observation system is used in this study to obtain air-sea momentum flux data under pure wind wave conditions based on the tower-based marine meteorological observation platform in the southern Bohai Sea.Moreover,the modulation of wind waves on wind stress under wind speeds greater than 10 m s^(–1)is analyzed.The results indicated that the wind wave states caused by winds from the northwest and northeast are different under the influence of cold air,resulting in different wind stresses and drag coefficients.The wind stress increases with an increasing wind speed,reaching its maximum value when the northwest wind is nearly 20 m s^(–1),while the extreme value of the drag coefficient is basically the same when the northwest wind speed is the maximum and the northeast wind wave significant wave height is the maximum.The drag coefficient increases with an increasing wind speed within the range of 10–15 m s^(–1),reaching saturation at 15 m s^(–1).The critical wind speed is smaller than other observed results.Further analysis showed that wind-induced turbulent stress deviates from the observed values,and the degree of deviation depends on the wind speed and wave state,with a greater deviation caused by strong winds and waves.The wave-induced stress can correct the negative deviation between wind-induced turbulent stress and the observed value,and the drag coefficient calculated based on the modified wind stress tends to be close to the observed value overall.

MEASUREMENTS AND THEORETICAL STUDY ON GROWTH RATES OF TURBULENT WIND WAVES

The spatial growth of turbulent wind waves is investigated theoretically and experimentally. Introduction of wave induced turbulent Reynolds stress, in particu- lar at the average interface, makes great improvement in the prediction of wind wave properties.

Study on the growth of wind wave frequency spectra generated by cold waves in the northern East China Sea

The growth of frequency spectra and spectral parameters of wind waves generated by cold waves, a kind of severe weather system, in the northern East China Sea is studied in this paper. Based on a third-generation wave action model(the Simulating WAves Nearshore model), simulations were developed to analyze the spatiotemporal characteristics of wind waves and to output spectral data. It is shown that the cold wave-induced spectra can be well described by the modified Joint North Sea Wave Project spectral form. The growth of wave spectra is comprehensively reflected by the evolution of the three characteristic parameters: peak frequency, spectral peak and wave energy. Besides, the approximations of dependences between spectral parameters and the three types of universal induced factors are obtained with the least squares method and compared systematically. Fetch and peak frequency turn out to be suitable parameters to describe the spectral parameters, while the dependences on the inverse wave age vary in different sea areas. In general, the derived relationships improve on results from previous studies for better practical application of the wind wave frequency spectrum in the northern East China Sea.

On the Variability of Charleston South Carolina Winds, Atmospheric Temperatures, Water Levels, Waves and Precipitation

Atmospheric winds, air temperatures, water levels, precipitation and oceanic waves in the Charleston South Carolina (SC) coastal zone are evaluated for their intrinsic, internal variability over temporal scales ranging from hours to multi-decades. The purpose of this study was to bring together a plethora of atmospheric and coastal ocean state variable data in a specific locale, to assess temporal variabilities and possible relationships between variables. The questions addressed relate to the concepts of weather and climate. Data comprise the basis of this study. The overall distributions of atmospheric and coastal oceanic state variable variability, including wind speed, direction and kinematic distributions and state variable amplitudes over a variety of time scales are assessed. Annual variability is shown to be highly variable from year to year, making arithmetic means mathematically tractable but physically meaningless. Employing empirical and statistical methodologies, data analyses indicate the same number of intrinsic, internal modes of temporal variability in atmospheric temperatures, coastal wind and coastal water level time series, ranging from hours to days to weeks to seasons, sub-seasons, annual, multi-year, decades, and centennial time scales. This finding demonstrates that the atmosphere and coastal ocean in a southeastern U.S. coastal city are characterized by a set of similar frequency and amplitude modulated phenomena. Kinematic hodograph descriptors of atmospheric winds reveal coherent rotating and rectilinear particle motions. A mathematical statistics-based wind to wave-to-wave algorithm is developed and applied to offshore marine buoy data to create an hour-by-hour forecast capability from 1 to 24 hours;with confidence levels put forward. This affects a different approach to the conventional deterministic model forecasting of waves.

Proton and He^(2+) Temperature Anisotropies in the Solar Wind Driven by Ion Cyclotron Waves

We carried out one-dimensional hybrid simulations of resonant scattering of protons and He2+ ions by ion cyclotron waves in an initially homogeneous, collisionless and magnetized plasma. The initial ion cyclotron waves have a power spectrum and propagate both outward and inward. Due to the resonant interaction with the protons and He2+ ions, the wave power will be depleted in the resonance region. Both the protons and He2+ ions can be resonantly heated in the direction perpendicular to the ambient magnetic field and leading to anisotropic velocity distributions, with the anisotropy higher for the He2+ ions than for the protons. At the same time, the anisotropies of the protons and He2+ ions are inversely correlated with the plasma β||p= 8πnpkBT||p/b02, consistent with the prediction of the quasilinear theory (QLT).

Numerical Simulation of Water Waves’ Modulational Instability under the Effects of Wind’s Stress and Gravity Force Relaxation

The waves driven by the wind do not move on the water as ordinarily done by sailboats. Indeed, the movement of the waves driven by the wind is more complex than the sailboats’ translation movement that we know. The movement of the wave in our particular case results from the chain-job done by wind’s stress and gravity forces: material is collected upstream (erosion phenomenon) and then deposited on the wave’s summit by the wind. This material deposited on the summit of the wave by the wind is then removed and dispatched on the downstream side of the wave by gravity forces. As always happens in any chain-job: if the wind works faster than gravity forces, great accumulation of material will occur at the summit of the wave that will lead to an increase in its (the wave in this case) height. If conversely the wind works more slowly, a deficit in material delivery will occur and gravity force goes directly to remove material on the wave’s summit and lead to a decrease in its height. In terms of Mechanics, we know that the main obstacle that can seriously disturb the work of the wind is the unavailability of water or so its viscosity. Given the complexity of the process to be studied, it seemed necessary for us to make a use of modulational instability theories such as the standard NLSE in order to better understand the contribution of wind and water viscosity to modulations of driven waves’ amplitudes (or phases): modulations which sometimes can accidentally trigger unpredictable rogue waves.

Extreme Responses of An Integrated System with A Semi-Submersible Wind Turbine and Four Torus-Shaped Wave Energy Converters in Different Survival Modes

Offshore wind power is a kind of important clean renewable energy and has attracted increasing attention due to the rapid consumption of non-renewable energy.To reduce the high cost of energy,a possible try is to utilize the combination of wind and wave energy considering their natural correlation.A combined concept consisting of a semi-submersible wind turbine and four torus-shaped wave energy converters was proposed and numerically studied under normal operating conditions.However,the dynamic behavior of the integrated system under extreme sea conditions has not been studied yet.In the present work,extreme responses of the integrated system under two different survival modes are evaluated.Fully coupled time-domain simulations with consideration of interactions between the semi-submersible wind turbine and the torus-shaped wave energy converters are performed to investigate dynamic responses of the integrated system,including mooring tensions,tower bending moments,end stop forces,and contact forces at the Column-Torus interface.It is found that the addition of four tori will reduce the mean motions of the yaw,pitch and surge.When the tori are locked at the still water line,the whole integrated system is more suitable for the survival modes.

An empirical method for joint inversion of wave and wind parameters based on SAR and wave spectrometer data

Synthetic aperture radar(SAR)and wave spectrometers,crucial in microwave remote sensing,play an essential role in monitoring sea surface wind and wave conditions.However,they face inherent limitations in observing sea surface phenomena.SAR systems,for instance,are hindered by an azimuth cut-off phenomenon in sea surface wind field observation.Wave spectrometers,while unaffected by the azimuth cutoff phenomenon,struggle with low azimuth resolution,impacting the capture of detailed wave and wind field data.This study utilizes SAR and surface wave investigation and monitoring(SWIM)data to initially extract key feature parameters,which are then prioritized using the extreme gradient boosting(XGBoost)algorithm.The research further addresses feature collinearity through a combined analysis of feature importance and correlation,leading to the development of an inversion model for wave and wind parameters based on XGBoost.A comparative analysis of this model with ERA5 reanalysis and buoy data for of significant wave height,mean wave period,wind direction,and wind speed reveals root mean square errors of 0.212 m,0.525 s,27.446°,and 1.092 m/s,compared to 0.314 m,0.888 s,27.698°,and 1.315 m/s from buoy data,respectively.These results demonstrate the model’s effective retrieval of wave and wind parameters.Finally,the model,incorporating altimeter and scatterometer data,is evaluated against SAR/SWIM single and dual payload inversion methods across different wind speeds.This comparison highlights the model’s superior inversion accuracy over other methods.

Comparison of spectral partitioning techniques for wind wave and swell

The ocean waves are generally mixed with wind wave and swell. In order to separate these two kinds of ocean waves, many wave spectral partitioning techniques have been proposed. In this study, a two-dimensional（2D） and three one-dimensional （1D） wave spectral partitioning techniques （denoted as PM, WH, and JP） are examined based on the model simulations and in-situ observations. It is shown that the 2D technique could provide the most reliable results as a whole. Compared with 2D technique, PM and JP techniques obviously overestimate the wind-wave components, and the same situation happens for WH technique at low wind speed. With the adjustment of the partitioning frequency ratio, the 1D PM technique is modified, in which the result agree well with that of the 2D scheme.

New Interpretation of Dependence of Wind Stress on Wave State

Based on observations from buoys, it is found that the wave age is well correlated with the nondimensional wave height, and this correlation is best described by a 3/5-power law. This similarity law is valid in the cases of wind waves as well as swells under natural sea states. On the basis of the 3/5-power law combined with the well-known 3/2-power law I it is shown that the wave-induced wind stress increases rapidly with wave age, indicating that the traditional observations or analytic techniques have only given the turbulent Reynolds stress induced by short wind waves, but excluded the long-wave-induced wind stress. The latter constitutes a small fraction to the total wind stress when the wave age is smaller than 1.0. The increase of sea-surface roughness with wave age can be attributed to wave breaking.

Analysis of Energy Overshoot of High Frequency Waves with Wavelet Transform

A study is made on the overshoot phenomena in wind-generated waves. The surface displacements of time-growing. waves are measured at four fetches in a wind wave channel. The evolution of high frequency waves is displayed with wavelet transform. The results are compared with Sutherland's. It is found that high frequency wave components experience much stronger energy overshoot in the evolution. The energy of high frequency waves decreases greatly after overshoot.