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.     

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.     

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.     

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.     

Theoretical and experimental investigation on nonlinear interaction among wave groups

Wave group is important in ocean wave theory and applications. In the past, nonlinear interaction among wave groups has been studied on the basis of the nonlinear Schr?dinger equation. Using this theoretical approach, we found that the nonlinear interaction among wave groups causes asymmetry in the shape of the wave envelope (steeper in the front of the curve of the envelope). An important consequence of this asymmetry is that the highest wave in a wave group appears one individual wave length ahead of the center of the wave group. Further results show that the degree of envelope asymmetry increases with increasing spectral width and the wave steepness. This theoretical analysis has been supplemented by a systematic experimental study of wind waves. Laboratory and some open sea wave data were analyzed. The results show that the shape of the wind wave envelope of wind waves has the same asymmetry predicted by the theoretical approach. The observed degree of deformation of the envelope also increases with increasing spectral width and the wave steepness as predicted by theory. These conclusions have important ramifications for practical applications of ocean wave theory.     

A new approach to estimating the T-year return-period wave height

The paper introduces a new approach to estimating the T-year return-period wave height (TRPW), i.e. the wave height expected to occur in T-year, from two sets of observed extreme data and on the basis of the maximum entropy principle. The main points of the approach are as follows. 1) A maximum entropy probability density function (PDF) for the extreme wave height H is derived from a Euler equation subject to some necessary and rational constraints. 2) The parameters in the function are expressed in terms of the mth moment of H. 3) This PDF is convenient to theoretical and practical applications as it is simple and its four parameters are easy to be determined from observed extreme data. An example is given for estimating the TRPW in 50 and 100 years by the present approach and by some currently used methods using observed data at two hydrographic stations.The comparison of the estimated results shows that the present approach is quite similar to the Pearson-Ⅲ and Gumbel methods.     

REPRESENTATION OF STATISTICAL PROPERTIES OF WAVE GROUPS FOR SEA PROCESSES WITH DOUBLE-PEAKED SPECTRA

A method using group-induced second-order long waves(GSLW) to represent statistical properties of wave groups with double-peaked spectra is put forward in this paper on the basis of the GSLW theory. The GSLW is regarded as a weighted linear superimposition of the second-order long Wave induced by the low peak frequency section and that induced by the high peak frequency section. There is a parabolic relationship between the GSLW and the wave envelope. Then the probability density function and the distribution function of the GSLW amplitude are derived. Thus the formulas for the average time duration and the mean length of runs can be derived. Good agreement between theoretical results and measured values was achieved. as verified with the measured double-peaked spectra in different regions.     

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.     

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 COMBINED REFRACTION-DIFFRACTION-DISSIPATION MODEL OF WAVE PROPAGATION

A numerical model based on the mild-slope equation of water wave propagation over complicated bathymetry,taking into account the combined effects of refraction,diffraction and dissipation due to wavebreaking is presented.Wave breaking is simulated by modifying the wave height probability density func-tion and the wave energy dissipation mechanism is parameterized according to that of the hydraulic jumpformulation.Solutions of the wave height,phase function,and the wave direction at every grid point areobtained by finite difference approximation of the governing equations,using Gauss-Seidel Iterative Method(GSIM)row by row.Its computational convenience allows it to be applied to large coast regions tostudy the wave transformation problem.Several case studies have been made and the results compare verywell with the experiment data and other model solutions.The capability and utility of the model forreal coast areas are illustrated by application to a shallow bay of northeast Australia.     

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 .     

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…     

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.     

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 .     

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.     

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…     

基于光滑粒子流体动力学算法的海浪建模仿真研究

针对传统海浪建模方法中存在海洋表面真实感差、计算复杂的问题,本文进行了基于光滑粒子流体动力学算法（SPH）与移动立方体算法（MC）相结合的海浪建模仿真研究。通过基于空间网格的粒子分配,建立了粒子群单向列表存储结构,在海浪粒子物理量计算时,实现了其光滑核半径内粒子群的快速检索,并基于拉格朗日流体控制方程,进行了海浪粒子受力分析及状态计算;在模拟海浪与环境障碍物碰撞时,将碰撞问题简化为粒子在一定时间段内所经过的路径与障碍物表面三角面片是否相交来进行判定,并假设粒子为理想刚体,采用改进的欧拉方法实现了粒子新位置的动态计算;为增强海浪流体模拟的真实感,在移动立方体节点密度动态计算基础上,依据确定的海浪表面密度阈值,耦合MC算法进行了海浪表面的动态提取,从而实现了海浪三维表面建模与动态演变仿真。通过模拟验证了该算法的时效性与可行性,可为海洋环境信息三维可视化提供一定的参考。     

Extracting the subsonic anti-symmetric lamb wave from a submerged thin spherical shell backscattering through iterative time reversal

The extraction of the weakly excited anti-symmetric Lamb wave from a submerged thin spherical shell backscattering is very difficult if the carrier frequency of the incident short tone burst is not at its frequency of greatest enhancement. Based on a single channel iterative time reversal technique, a method for isolating the subsonic anti-symmetric Lamb wave is proposed in this paper. The approach does not depend on the form function of a thin shell and any other priori knowledge, and it is also robust in the presence of some stochastic noise. Both theoretical and numerical results show that the subsonic anti-symmetric Lamb wave can be identified, even when the carrier frequency of the incident short tone burst is away from the frequency of greatest enhancement. The phenomenon may also be observed even in the case that the subsonic anti-symmetric Lamb wave is submerged in the noise, other than the case with the Signal to Noise Ratio being less than 10 dB, when the amplitude of the noise is comparable with the specular wave. In this paper, each iteration process contains a traditional transmission and time reversal transmission steps. The two steps can automatically compensate the time delay of the subsonic anti-symmetric Lamb wave relative to the specular wave and within-mode dispersion in the forward wave propagation.     

非活动论与地球脉动式演化学说的再崛起──纪念张伯声院士逝世二周年

以强调岩石圈作大规模水平移动为特色的活动论在兴旺了２０余年之后，由于首先在大陆上，继之在海洋上碰上了麻烦；在研究地球演化的过程中，又在古地磁学与古气候学上遇到了不解之谜；地球的分层结构及其各种物理、化学参数对于经典的乃至修正了的板块学说的支持都显得软弱无力。人们不得不回过头来冷静思考其反对者们的意见。其实，持否定态度的学者一直没有停止过他们的研究，尤其脉动论者。如今，脉动学说有了新的发展，其中“地球多级驻波式脉动理论模型”的提出，使活动论的各种麻烦都成了它的根据。尽管以再崛起的脉动论为代表的非活动论尚未形成一股强大的科学势力，但其前景是不可低估的。     

雷州半岛夏季闪电特征分析

根据雷州半岛夏季雷暴的气候特征,利用布设在雷州半岛徐闻、遂溪两点的LD型闪电定位系统对雷州半岛的闪电进行观测,对雷州半岛7月份的逐日闪电总次数、正闪比、幅值均值、幅值分布、闪电波前陡度、闪电累积概率分布等观测值进行分析,得出了雷州半岛夏季闪电活动的部分规律。分析表明:雷州半岛夏季最大闪电电流峰值为-153 kA;负闪明显多于正闪,占闪电总数的71.71%;电流峰值都主要集中在10 kA～40 kA;闪电波前上升陡度相对集中在1μs～20μs,占观测总闪击的91.5%,3μs～10μs达到峰值。分析所得结论对本地区防雷减灾工作有一定的实际指导意义。