Statistical distribution of nonlinear random water wave surface elevation

This study deals with the development of statistical modeling for water wave surface elevation by using a method that combines a dynamic solution with random process statistics. Ocean wave data taken from four NOAA (National Oceanic and Atmospheric Administration) buoys moored in the northeast Pacific were used to validate the model. The results indicated that the nonlinear probability density distribution of ocean wave surface elevation derived from the model described the measurements much better than Gaussian distribution and Longuet-Higgins distribution.     

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.     

Comparison of TOPEX/POSEIDON altimeter derived wave period with ocean buoy data in the East China Sea and South China Sea

Altimeter wave period data obtained from continental shelf seas are analyzed in this paper. Empirical models are introduced for zero up-crossing and peak wave period calculation with TOPEX/POSEIDON data. Their performances are assessed using independent validation dataset in four sites in the open ocean of China. To provide more accurate wave period estimation, new coefficients are applied to reliable in situ data. Comparison of our estimated the wave periods with new linear calibrations based on independent data of Seapac 2100 deployed in the East China Sea and South China Sea showed that the accuracy was improved over estimates determined from earlier empirical models. Regional analysis indicated that the wave period model works better under wind sea condition.     

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.     

Comparison of retrieving methods of ocean wave periods from satellite altimeter with buoy measurements

For validating the results of retrieved mean wave period, four empirical algorithms established previously are introduced. Based on the data of over five years derived from TOPEX satellite altimeter for the entire East China Sea, ocean wave periods were calculated and statistical comparison among them was performed. The retrieved mean wave period obtained with our new distribution parameters showed better agreement with the wave period TB measured by buoy than that calculated by other three algorithms. The difference between the mean values of and that of TB is 0.16 s and the RMSE (root mean square error) of is the lowest value (0.48).     

Low frequency oscillations of the heat distribution in the global upper ocean layers

The heat distributions in the upper layers of the ocean have been studied and some important low frequency oscillations （LFOs） are already found and quantified by using various characteristic factors. In this paper, the ‘heat center＇ of a sea area is defined with a simple method. Then the temperature data set of the upper layer of the global ocean （from surface down to 400 m, 1955-2003） is analyzed to detect the possible LFOs. Not only some zonal LFOs, which were reported early, but also some strong LFOs of the vertical and meridional heat distribution, which might imply some physical sense, are detected. It should be noted that the similar vertical oscillation pattern can be found in the Pacific Ocean, Atlantic Ocean and Indian Ocean. Results from some preliminary studies show that the vertical LFO might be caused by the solar irradiance anomalies. This study may help reveal some unknown dynamical processes in the global oceans and may also benefit other related studies.     

Wave breaking on turbulent energy budget in the ocean surface mixed layer

As an important physical process at the air-sea interface, wave movement and breaking have a significant effect on the ocean surface mixed layer （OSML）. When breaking waves occur at the ocean surface, turbulent kinetic energy （TKE） is input downwards, and a sublayer is formed near the surface and turbulence vertical mixing is intensively enhanced. A one-dimensional ocean model including the Mellor-Yamada level 2.5 turbulence closure equations was employed in our research on variations in turbulent energy budget within OSML. The influence of wave breaking could be introduced into the model by modifying an existing surface boundary condition of the TKE equation and specifying its input. The vertical diffusion and dissipation of TKE were effectively enhanced in the sublayer when wave breaking was considered. Turbulent energy dissipated in the sublayer was about 92.0% of the total depth-integrated dissipated TKE, which is twice higher than that of non-wave breaking. The shear production of TKE decreased by 3.5% because the mean flow fields tended to be uniform due to wave-enhanced turbulent mixing. As a result, a new local equilibrium between diffusion and dissipation of TKE was reached in the wave-enhanced layer. Below the sublayer, the local equilibrium between shear production and dissipation of TKE agreed with the conclusion drawn from the classical law-of-the-wall （Craig and Banner, 1994）.     

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.     

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 …     

An estimation of internal soliton forces on a pile in the ocean

Internal soliton forces on oil-platform piles in the ocean are estimated with the Morison Formula. Different from sur- face wave forces, which change only in magnitude along a pile, internal soliton forces can be distributed over the entire pile in the water and they change not only in magnitude but also in direction with depth. Our calculations show that the maximum total force caused by a soliton with its associated current of 2.1 m s-1 is nearly equal to the maximum total force exerted by a surface wave with a wavelength of 300 m and a wave-height of 18 m. The total internal soliton force is large enough to affect the operations of marine oil platforms and other facilities. Therefore, the influence of internal solitons should not be neglected in the design of oil platforms.     

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'(…     

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).     

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…     

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…     

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…     

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.     

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.     

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.     

Modeling vertical heat transport in the wave affected surface layer of the ocean

In considering the vertical heat transport problems in the upper ocean, the flat upper boundary approximation for the free surface and the horizontal homogenous hypothesis are usually applied. However, due to the existence of the wave motion, the application of this approximation may result in some errors to the solar irradiation since it decays quickly in respect to the actual thickness of the water layer below the surface; on the other hand, due to the fluctuation of the water layer depth, it is improper to neglect the effects of the horizontal advection and turbulent diffusion since they also contribute to the vertical heat transport. A new model is constructed in this study to reflect these effects. The corresponding numerical simulations show that the wave motion may remarkably accelerate the vertical heat transferring process and the variation of the temperature in the wave affected layer appears in an oscillating manner. Supported by the National High Technology Research and Development Program of China (863 Program, No. 2006AA09A309); China Postdoctoral Science Foundation (No. 20070411111) and the Fund of Shandong Province for the Excellent Post-Doctors (No. 200603056)