Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37°27.6′ N, 122°15.1′ E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (ν=0.3−0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.     

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.     

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

1　Introduction　Numerousinvestigationsondeepwaterwindwavespectrumhavebeen performed (Phillips ,195 8;Bretschneider,195 9;PiersonandMoscowitz ,196 4;Hasselmannetal.,1973;Donelanetal.,1985 ;Ban ner ,1990 ;Wenetal.,1999) .Ondimensionalground ,Phillips (195 8)suggestedthattheequilibriumfre quencyspectrumofwindwavesfordeepwatershouldbe proportionaltoω- 5,andthecorrespondingwavenumberspectrumshouldbe proportionaltok- 4,whereωistheangularfrequencyandkisthewavenumber.Forfully developedwindwaves…     

Numerical simulation and validation of ocean waves measured by an Along-Track Interferometric Synthetic Aperture Radar

A new nonlinear integral transform of ocean wave spectra into Along-Track Interferometric Synthetic Aperture Radar （ATI-SAR） image spectra is described. ATI-SAR phase image spectra are calculated for various sea states and radar configurations based on the nonlinear integral transform. The numerical simulations show that the slant range to velocity ratio （R/V）, significant wave height to ocean wavelength ratio （Hi2）, the baseline （2B） and incident angle （0） affect ATI-SAR imaging. The ATI-SAR imaging theory is validated by means of Two X-band, HH-polarized ATI-SAR phase images of ocean waves and eight C-band, HH-polarized ATI-SAR phase image spectra of ocean waves. It is shown that ATI-SAR phase image spectra are in agreement with those calculated by forward mapping in situ directional wave spectra collected simultaneously with available ATI-SAR observations. ATI-SAR spectral correlation coefficients between observed and simulated are greater than 0.6 and are not sensitive to the degree of nonlinearity. However, the ATI-SARoPhase image spectral turns towards the range direction, even if the real ocean wave direction is 30. It is also shown that the ATI-SAR imaging mechanism is significantly affected by the degree of velocity bunching nonlinearity, especially for high values of R/V and H/2.     

A relationship between wave steepness and wave age for wind waves in deep water

Studying the relationship between wave steepness and wave age is important for describing wind wave growth with energy balance equation of significant waves. After invoking the dispersion rela- tion of surface gravity wave in deep water, a new relationship between wave steepness and wave age is revealed based on the “3/2-power law” (Toba, 1972), in which wave steepness is a function of wave age with a drag coefficient as a parameter. With a given wave age, a larger drag coefficient would lead to larger wave steepness. This could be interpreted as the result of interaction between wind and waves. Comparing with previous relationships, the newly proposed one is more consistent with observational data in field and laboratory.     

Wave steepness retrieved from scatterometer data in a genetic algorithm

Wave steepness is an important characteristic of a high sea state, and is widely applied on wave propagations at ports, ships, offshore platforms, and CO2 circulation in the ocean. Obtaining wave steepness is a difficult task that depends heavily on theoretical research on wavelength distribution and direct observations. Development of remote-sensing techniques provides new opportunities to study wave steepness. At present, two formulas are proposed to estimate wave steepness from QuikSCAT and ERS-1/2 scatterometer data. We found that wave steepness retrieving is not affected by radar band, and polarization method, and that relationship of wave steepness with radar backscattering cross section is similar to that with wind. Therefore, we adopted and modified a genetic algorithm for relating wave steepness with radar backscattering cross section. Results show that the root-mean-square error of the wave steepness retrieved is 0.005 in two cases from ERS-1/2 scatterometer data and from QuikSCAT scatterometer data.     

Impacts of wave and current on drag coefficient and wind stress over the tropical and northern Pacific

By taking into consideration the effects of ocean surface wave-induced Stokes drift velocity U,w and current velocityU,c on the drag coefficient,the spatial distributions of drag coefficient and wind stress in 2004 are computed over the tropical andnorthern Pacific using an empirical drag coefficient parameterization formula based on wave steepness and wind speed.The globalocean current field is generated from the Hybrid Coordinate Ocean Model (HYCOM) and the wave data are generated from Wave-watch Ⅲ (WW3).The spatial variability of the drag coefficient and wind stress is analyzed.Preliminary results indicate that theocean surface Stokes drift velocity and current velocity exert an important influence on the wind stress.The results also show thatconsideration of the effects of the ocean surface Stokes drift velocity and current velocity on the wind stress can significantly im-prove the modeling of ocean circulation and air-sea interaction processes.     

A new probability distribution function of wave steepness

Wave steepness is an important characteristic describing the severity of sea state in ocean engineering. In the existing theoretical and experimental studies, wave steepness is often substituted by some related quantities. In this paper, a new probability density function (pdf) of steepness, which is a pdf of the steepness in its original definition, is obtained for narrowband Gaussian processes. The drawback inherent in the previous theoretical pdfs of steepness, that is, the probability density at zero steepness is nonzero, has been eliminated. Laboratory experiments were conducted in a wind-wave flume to measure the wave steepness distribu- tion. Comparisons among laboratory measurements and some theoretical pdfs of steepness show that the new pdf generally fits the data better than the one proposed by Zheng et al. (1999).     

Interaction of Waves, Surface Currents, and Turbulence： the Application of Surface-Following Coordinate Systems

Surface waves comprise an important aspect of the interaction between the atmosphere and the ocean, so a dynamically consistent framework for modelling atmosphere-ocean interaction must take account of surface waves, either implicitly or explicitly. In order to calculate the effect of wind forcing on waves and currents, and vice versa, it is necessary to employ a consistent formula- tion of the energy and momentum balance within the airflow, wave field, and water column. It is very advantageous to apply sur- face-following coordinate systems, whereby the steep gradients in mean flow properties near the air-water interface in the cross-interface direction may be resolved over distances which are much smaller than the height of the waves themselves. We may account for the waves explicitly by employing a numerical spectral wave model, and applying a suitable theory of wave–mean flow interaction. If the mean flow is small compared with the wave phase speed, perturbation expansions of the hydrodynamic equations in a Lagrangian or generalized Lagrangian mean framework are useful: for stronger flows, such as for wind blowing over waves, the presence of critical levels where the mean flow velocity is equal to the wave phase speed necessitates the application of more general types of surface-following coordinate system. The interaction of the flow of air and water and associated differences in temperature and the concentration of various substances (such as gas species) gives rise to a complex boundary-layer structure at a wide range of vertical scales, from the sub-millimetre scales of gaseous diffusion, to several tens of metres for the turbulent Ekman layer. The bal- ance of momentum, heat, and mass is also affected significantly by breaking waves, which act to increase the effective area of the surface for mass transfer, and increase turbulent diffusive fluxes via the conversion of wave energy to turbulent kinetic energy.     

WIND WAVES SIMULATION IN THE NORTH AREA OF THE SOUTH CHINA SEA

A third generation wave model was developed to simulate wind waves in the South China Sea near Hong Kong. The model solves the energy conservation equation of the two dimensional wave spectrum by directly computing the nonlinear energy interaction among waves of different frequencies, thus avoiding the imposition of restrictions on the shape of the predicted spectra. The use of an upwind difference scheme in the advective terms produces an artificial diffusion which partly compensates the dispersive effect due to the phase velocity differences among various wave components. The use of a semi-implicit scheme for the source terms together with a special treatment of the high frequency tail of the spectrum allows a large time integration step. Verification of the model was done for wave hindcasting studies under conditions of two typhoons and two cold fronts in the north part of the South China Sea near Hong Kong . The model results agree well with the field measurements except that the presence of a dista     

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19°35′N, 112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.     

Relationship between wave steepness and wave age in the course of wind wave growth

It is traditionally assumed that the relationship between wave steepness and wave age is independent of the wind wave growth state. In fact, the traditional relationship can not describe the whole course of wind wave growth. This paper assumes that the relationship between wave steepness and wave age changes with the variety of dimensionless fetch. Based on the relationship proposed by Hou and Wen (1990), a new relationship in the course of wind wave growth is revealed. Comparisons between the present study and other previous relationships show that this new relationship explains better the observations than the other existing relationships.In the case of small fetch, wave age value increases more quickly than other models while it is in opposition to that in the case of large fetch. The result in present paper can clearly reflect the whole course of wind wave growth, it is an improvement for traditional results.     

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

1　Introduction1.1　Proposed ModelonDirectionalFrequencySpec trum　ThisisthePartⅡofthetwo papersetondirection alspectraofwindwaves.Anewmodelonthedirec tionalspectrumofwindwavesfordeepwaterispro posedbasedonthestatisticsofwindwavesinthePartⅠ .Substituting (4 5 )ofPartⅠinto (4 0 )andaddingapeak enhancementitemγΓ,weobtainS(ω ,) =0 .0 0 93αaαwD( ,k) ωpω2 ξ- 4g2ω5×exp - 2 ξ+14[bωp +(1-b)ωp]4ω4 γΓ. (1)Here ,αaisthewaveagefactorofspectralcoefficientdefinedbyαa = ω0 .55…     

Experimental Investigation of Wave Load and Run-up on the Composite Bucket Foundation Influenced by Regular Waves

In the design of wind turbine foundations for offshore wind farms, the wave load and run-up slamming on the supporting structure are the quantities that need to be considered. Because of a special arc transition, the interaction between the wave field and the composite bucket foundation(CBF) becomes complicated. In this study, the hydrodynamic characteristics, including wave pressure, load, upwelling, and run-up, around the arc transition of a CBF influenced by regular waves are investigated through physical tests at Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China. The distributions of the wave pressures and upwelling ratios around the CBF are described, and the relationship between the wave load and the wave parameters is discussed. New formulae based on the velocity stagnation head theory with linear wave theory and the second-order Stokes wave theory for wave kinematics are proposed to estimate the wave run-up. Moreover, the multiple regression method with nonlinear technology is employed to deduce an empirical formula for predicting run-up heights. Results show that the non-dimensional wave load increases with the increase in the values of the wave scattering parameter and relative wave height. The wave upwelling height is high in front of the CBF and has the lowest value at an angle of 135? with the incoming wave direction. The performance of the new formulae proposed in this study is compared using statistical indices to demonstrate that a good fit is obtained by the multiple regression method and the analytical model based on the velocity stagnation head theory is underdeveloped.     

INTERNAL WAVE EIGENMODES AND THEIR WEAK NONLINEAR RESONANT INTERACTION IN A NONLINEARLY STRATIFIED FLUID- A PRELIMINARY THEORETICAL AND EXPERIMENTAL STUDY

A preliminary theoretical and experimental study was conducted on internal wave modes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid . An asymptotical solution of the modes and a dispersion relation of internal waves in a stratified fluid with density profile similar to that in our experiment were obtained theoretically . The resonant-interaction mechanism to 2nd order approximation is also discussed . The resonant interaction of the 3rd and 4th mode internal waves excited by the unstable 1st mode wave is analyzed on the basis of data obtained by conductivity probes. The resonant-interaction condition, , is examined . It is shown that the resonant instability increases with pycnocline thickness and wave maker driving frequency .     

Comparison and analysis of Envisat ASAR ocean wave spectra with buoy data in the northern Pacific Ocean

The validation and assessment of Envisat advanced synthetic aperture radar (ASAR) ocean wave spectra products are important to their application in ocean wave numerical predictions. Six-year ASAR wave spectra data are compared with one-dimensional (1D) wave spectra of 55 co-located moored buoy observations in the northern Pacific Ocean. The ASAR wave spectra data are firstly quality control filtered and spatio-temporal matched with buoy data. The comparisons are then performed in terms of 1D wave spectra, significant wave height (SWH) and mean wave period (MWP) in different spatio-temporal offsets respectively. SWH comparison results show the evident dependence of SWH biases on wind speed and the ASAR SWH saturation effect. The ASAR wave spectra tend to underestimate SWH at high wind speeds and overestimate SWH at low wind speeds. MWP comparison results show that MWP has a systematic bias and therefore it should be bias-modified before used. The comparisons of 1D wave spectra show that both wave spectra agree better at low frequencies than at high frequencies, which indicates the ASAR data cannot resolve the high frequency waves.     

Energy cascades in the upper ocean

1 INTRODUCTION Wave-wave interactions play a key role in the evolution of the dynamics of upper ocean phenomena. Even though they conserve total wave energy, these interactions cause energy cascades to occur in which wave-energy is transferred at the surf…     

The efifect of wave breaking on surface wave imaging by Synthetic Aperture Radar

The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions (MTF) of radar was investigated based on Bragg resonance theory and parametric method. The result showed that the additional effect of wave breaking on backscattering cross-section is not more than 20% except for the small incident angle of VV polarized electromagnetic (e.m.) wave but is significant for HH polarized e.m. wave. Breaking waves lead to increase in the modulus of tilt modulation MTF and the larger the wind speed, the faster the increase. For large incident angle, the modulus of tilt modulation MTF with wave breaking decreases quickly with incident angle for HH polarization and approach to that without wave breaking for VV polarization. The hydrodynamic MTF increases 30%-60% when considering wave breaking and the increase is larger for HH polarization than for VV polarization.     

THE DEPENDENCE OF WIND STRESS ON SEA STATE

Based on up to date literature, this paper details the evolution of wave dependence of wind stress.Some typical models of the dependence of wind stress on waves are described in detail. Although there isno universally accepted theory and model, recent studies indicate that the wind strees strongly dependson the development state of sea waves, i. e., young seas are rougher than mature seas, in other words, thewind stress decreases with increasing wave age.     

Numerical analysis of the nonlinear parameterization of waves in currents over a submerged sill with a non-hydrostatic model

An investigation of the effects of a uniform current strength direction (following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using SWASH, a non-hydrostatic numerical wave model. The nonlinear parameters (i.e., asymmetry, skewness, and kurtosis) are calculated, and the empirical formulas for these parameters are presented as a function of the local Ursell number based on the present numerical data measured. In the shoaling area of the submerged sill, the nonlinear characteristics of waves are more obvious when waves propagate in the same direction as the currents than when waves propagate in the opposite direction. Whereas nonlinear parameters grow with the strengthening of the following currents over the crest, they tend to decrease as the adverse current velocity increases over the crest area of the submerged sill.