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.     

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).     

CALCULATIONS OF WAVE BREAKING PROBABILITY AND DISTRIBUTION OF BREAKING WAVE HEIGHTS IN DEEP WATER

lareODUcrI0NThephenomenonofbreakingwavesintheoasnoocurswheneveramomentahiyhighcrestmecheSanunstablecondition.It0ccursintendtimhy,andtheoccurrencefre-qUencydePendsonthescastate.ManystudAshaddricaniedoutontheoccurmcefre-qUencyofbrmkingwavesindeepweter.0chiandTsai(l983),LongueHiggins(l975)andVanD0mandPamn(l975)nadstheptalictonofbrmkingwavesoccurrenceindeePwater,usingabaskingcriterionforindividualwavesbasedonthewavesmpness.ThecriterioncanbeexpmeedintennSofthewaVehdghtHandperiodTasH>PgT'(…     

Crest-height distribution of nonlinear random waves

The wave crest is an important factor for the design of both fixed and floating marine structures. Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damage. Many empirical and theoretical distribution functions for wave crest heights have been proposed, but there is a lack of agreement between them. It is of significance to develop a better new nonlinear wave crest height distribution model. The progress in the research of wave crest heights is reviewed in this paper. Based on Stokes’ wave theory, an approximate nonlinear wave crest-height distribution formula with simple parameters is derived. Two sets of measured data are presented and compared with various theoretical distributions of wave crests obtained from nonlinear wave models and analysis of the comparison is given in detail. The new crest-height distribution model agrees well with observations. Also, the new theoretical distribution is more accurate than the other methods cited in this paper and has a greater range of applications.     

Empirical formula for wave length of ocean wave in finite depth water

In this paper, function characteristics of dispersion of ocean wave in finite depth water were analyzed systematically. The functional form of the fitting function is reasonably proposed, in which the parameters are optimally determined by the least square method （LSM）. For infinitely deep and extremely shallow water,the fitting function fits strictly the dispersion to be fitted. A new technique is presented in application of LSM.An empirical formula with maximum error of less than 0.5% for computing wavelength in finite depth water is presented for practical applications.     

A wave modulation model of ripples over long surface waves

A study is presented on the modulation of ripples induced by a long surface wave (LW) and a new theoretical modulation model is proposed. In this model, the wind surface stress modulation is related to the modulation of ripple spectrum. The model results show that in the case of LW propagating in the wind direction with the wave age parameter of LW increasing, the area with enhanced shear stress shifts from the region near the LW crest on the upwind slope to the LW trough. With a smaller wave age parameter of LW, the ripple modulation has the maximum on the upwind slope in the vicinity of LW crest, while with a larger parameter the enhancement of ripple spectrum does not occur in that region. At low winds the amplitude of ripple modulation transfer function (MTF) is larger in the gravity wave range, while at moderate or high winds it changes little in the range from short gravity waves to capillary waves.     

A WEAKLY NONLINEAR WATER WAVE MODEL TAKING INTO ACCOUNT DISPERSION OF WAVE PHASE VELOCITY

This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges‘ (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase ve-locity is rational and in good agreement with experiment data.     

STUDY ON METHOD OF NUMERICAL SIMULATION OF NONLINEAR RANDOM WAVES

This new method can simulate the nonlinear random wavcs processes by computer if the higherorder moments of the probability distribution of the sea surface elevation reflecting the nonlinearity ofthe sea wave are given. Compared with other methods, this method has greater accuracy andflexibility, wider application and faster simulation. Statistical analysis of the sea surface elevationdistribution of the simulated wave process showed obviously the Gram-Charlier series can be used to depictthe distribution of the sea surface elevation.     

Numerical simulation of 3-D wave crests

1　Introduction　Anefficientwaytostudywaveforceonoffshorestructuresisthroughphysicalandnumericalwavesim ulation .Althoughmanysimulationsof 2 Dregularorirregularwaveshavesuccessfullybeencarriedoutinlaboratorythroughwindandwavegenerator ,itisstillratherdifficulttosimulate 3 Drandomwavesinlabo ratory .Therefore ,numericalsimulationiswidelyusedinsuchstudies (Baietal.,2 0 0 0 ;Zhuetal.,1999) .Tobuildlargeoffshorestructureslikemarineairports ,itisofinteresttostudytheeffectof 3 Dwaves .Goda(1994 …     

Contrast validation test for retrieval method of high frequency ground wave radar

1 INTRODUCTION Ocean wave and sea wind, are important oce-anic dynamic phenomena having great influence on the development of marine economy, exploitation of marine resources, and location selection, planning and designing, construction and operation of marine projects; so study on measuring methods of ocean wave and sea wind is important. High frequency ground wave radar (HF radar) was a technique developed in the last decades for the detection of oceanic environment. Long radio wave (mu…     

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.     

STATISTICAL PROPERTIES OF WAVE GROUPS DESCRIBED BY GROUP-INDUCED LONG WAVES

A new method using group-induced second-order long waves (GSLW) to describe wave groups is presented in this paper on the basis of the GSLW theory by Longuet- Higgins and Steward (1964) . In the method , the parabolic relationship between GSLW and the wave envelope is first deduced , and then the distribution function of GSLW amplitude is derived . Thus, the formulae in terms of the moments of GSLW and short wave spectra for the average time duration and the mean length of runs of wave heights exceeding a certain level can be derived . A new groupiness factor equivalent to half the mean wave number in wave groups is defined by taking into account the widths of spectra of GSLW and short waves . Compared with theoretical results of others , ours are closer to measured wave data .     

STATISTICAL PROPERTIES OF HIGH-FREQUENCY INTERNAL WAVES IN QINGDAO OFFSHORE AREA OF THE YELLOW SEA

Densely-sampled thermistor chain data obtained from a shallow-water acoustics experiment in the Yellow Sea off the coast of Qingdao were analyzed to examine the statistical properties of the 6 to 520 cpd frequency band internal waves observed. The negative skewness coefficients and the greaterthan-3 kurtosis coefficients indicated non-Gaussianity of the internal waves. The probability distributions were negatively skewed and abnormally high peaks. Nonlinear properties, as exemplified by the asymmetric waveshapes of the internal waves in the offshore area are described quantitatively.     

Ocean wave diffraction in near-shore regions observed by Synthetic Aperture Radar

Observation and analysis of ocean wave diffraction in near-shore and near-island region was performed with Synthetic Aperture Radar (SAR) data, using an optimized retrieval method named parameterized first-guess spectrum retrieval method. The results retrieved from ERS-SAR and ENVISAT-ASAR images showed that, in the region sheltered by land jut, the energy of long waves is reduced by 10%-20% and that the propagation direction of long waves is changed due to the effect of topography. In the shadow zone behind the island, ocean wave can propagate along the seashore instead of perpendicular to the coastline, as shown by SAR images.     

Analysis on monthly-averaged distribution of sea surface wind and wave over the seas southeast of Asia using ERS-2 scatterometer data

The wind system over the seas southeast of Asia (SSEA) plays an important role in China's climate variation. In this paper, ERS scatterometer winds covering the period from January 2000 to December 2000 and the area of 2-41 °N, 105- 130°E were analyzed with a distance-weighting interpolation method and the monthly mean distribution of the sea surface wind speed were given. The seasonal characteristics of winds in the SSEA were analyzed. Based on WAVEWATCH Ⅲ model, distribution of significant wave height was calculated.     

A temporal sliding procedure for ocean wave variational data assimilation and its application

For sequential performance of wave variational data assimilation, we proposed a temporal sliding method in which the temporal overlap is considered. The advantage of this method is that the initial wave spectrum of the optimization process is modified by the observations in latter and former times. This temporal sliding procedure is important for marginal region, such as the China seas, where the duration of assimilation effectiveness is 2-3 days. Experiments were performed in the whole course of Cyclone 9403 (Russ). Around the cyclone center, the maximum value of wave elements did not change much by assimilation, because the extreme value was determined by wind energy input that was not yet optimized. In the area outside the cyclone center, this modification is evident especially for wind wave growth.     

Quadratic correction to the linear wave spectrum of two-dimensional random waves

ImooUcrIONAtfrequendesseveraltirathatofthespeCtralpcak,thewaveelevationhigherordercomPonentS'contributionstothewavespatrumaremoresignificantthanthosefromthelinearcomPonentS.Tick(l959)firstproposedandevaluatedtheserendxidespodrumofunidindionalrandomwaves.TheexpnaionderivedbyDingPingxingetal.(l994)forthesecondxirderspeCtmmisanimProvernentofTick's.TickandDingPingxingetal.didnotaanuntforthirdxirderperturbations,althoughthethirdxirdersolutionefhaonthequadraticspeCtrumisofthesameorderofmagnit…     

Wave extraction with portable high-frequency surface wave radar OSMAR-S

High frequency surface wave radar (HFSWR) has now gained more and more attention in real-time monitoring of sea surface states such as current, waves and wind. Normally a small-aperture antenna array is preferred to a large-aperture one due to the easiness and low cost to set up. However, the large beam-width and the corresponding incorrect division of the first- and second-order Doppler spectral regions often lead to big errors in wave height and period estimations. Therefore, for the HFSWR with a compact cross-loop/monopole antenna (CMA), a new algorithm involving improved beam-forming (BF) and spectral division techniques is proposed. On one hand, the cross-spectrum of the output sequence by the conventional beam-forming (CBF) with all the three elements and the output with only the two loops is used in place of the CMA output self-spectrum to achieve a decreased beam-width; on the other hand, the better null seeking process is included to improve the division accuracy of the first- and second-order regions. The algorithm is used to reprocess the data collected by the portable HFSWR OSMAR-S during the Sailing Competition of the 16th Asian Games held in Shanwei in November 2010, and the improvements of both the correlation coefficients and root-mean-square (RMS) errors between the wave height and period estimations and in situ buoy measurements are obvious. The algorithm has greatly enhanced the capabilities of OSMAR-S in wave measurements.     

Dynamic responses of top tensioned riser under combined excitation of internal solitary wave, surface wave and vessel motion

An investigation on the dynamic response of a top tensioned riser (TTR) under combined excitation of internal solitary wave, surface wave and vessel motion is presented in this paper. The riser is idealized as a tensioned slender beam with dynamic boundary conditions. The KdV-mKdV equation is chosen to simulate the internal solitary wave, and the vessel motion is analysed by using the method proposed by Sexton. Using finite element method, the governing equation is solved in time domain with Newmark-β method. The computation programs for solving the differential equations in time domain are compiled and numerical results are obtained, including dimensionless displacement and stress. The action of internal solitary wave on the riser is like a slow powerful impact, and is much larger than those of surface wave and vessel motion. When the riser is under combined excitation, it vibrates at frequencies of both surface wave and vessel motion, and the vibration is dominated by internal solitary wave. As the internal solitary wave crest passes by the centre of the riser, the maximum displacement and stress along the riser occur. Compared to the lower part, the displacement and stress of the riser in the upper part are much larger.     

A background error covariance model of significant wave height employing Monte Carlo simulation

The quality of background error statistics is one of the key components for successful assimilation of observations in a numerical model.The background error covariance(BEC) of ocean waves is generally estimated under an assumption that it is stationary over a period of time and uniform over a domain.However,error statistics are in fact functions of the physical processes governing the meteorological situation and vary with the wave condition.In this paper,we simulated the BEC of the significant wave height(SWH) employing Monte Carlo methods.An interesting result is that the BEC varies consistently with the mean wave direction(MWD).In the model domain,the BEC of the SWH decreases significantly when the MWD changes abruptly.A new BEC model of the SWH based on the correlation between the BEC and MWD was then developed.A case study of regional data assimilation was performed,where the SWH observations of buoy 22001 were used to assess the SWH hindcast.The results show that the new BEC model benefits wave prediction and allows reasonable approximations of anisotropy and inhomogeneous errors.