Probabilistic Models for the Probability of Wave Breaking and Whitecap Coverage Based on Kinematic Breaking Criterion

More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact moders the models either for the probability of wave breaking B or for the whitecap coverage W based on these criteria difficult to apply. In this paper and the one which follows we seek to develop models for the prediction of both B and W based on the kinematical criterion. First, several joint probabihstic distribution functions (PDFs) of wave characteristics are derived, based on which the breaking properties B and W are estimated. The estimation is made on the assumption that a wave breaks ff the horizontal velocity of water particles at its crest exceeds the local wave celerity, and whitecapping occurs in regions of fluid where water particles travel faster than the waves. The consequent B and W depend on wave spectral moments of orders 0 to 4.Then the JONSWAP spectrum is used to represent the fetch-limited sea waves in deep water, so as to relate the probahility of wave breaking and the whitecap coverage with wind parameters. To this end, the time-averaging technique proposed by Glazman (1986) is applied to the estimation of the spectral moments involved, and furthermore, the theoretical models are compared with available observations collected from published literature. From the comparison, the averaging time scale is determined. The final models show that the probability of wave breaking as well as the whitecap coverage depends on the dimensionless fetch. The agreement between these models and the database is reasonable.     

A Whitecap Coverage Model Based on the Surface Slope For Criterion of Wave Breaking

Using the limit surface slope as a criterion of wave breaking,a simple model for estimatingthe spatial fraction of breaking surface of sea at an instant,which is regarded as the whitecap coverge inthis paper,is analytically derived from the probability density of surface slope based on Gaussianstatistics.The resulting fraction is found depending on the fourth moment of wave spectum,m_4,as well asthe critical threshold of surface slope.By expressing the fourth moment in terms of the Neumannspectrum,a formula linking the fraction and wind speed for fully developed sea states is obtianed.Anotherformula relating the fraction to both wind speed and fetch(or duration)is achieved by expressing m_4 interms of the Krylov spectrum and applying the empirical relationships used in the SMB ocean wave pre-dicting technique.A comparison between these results and the field data of whitecap coverage collected byMonahan and O＇Muircheartuigh shows an encouraging agreement.     

一种白浪覆盖率与风要素关系模式

采用Ｇｌａｚｍ ａｎ 提出的“微尺度平均”的方法,在合理选择平均尺度的基础上计算了ＪＯＮＳＷＡＰ谱的四阶矩,并将此结果与Ｓｎｙｄｅｒ提出的白浪覆盖率模式结合,从而建立起依赖于风速和风区两者的半经验、半理论的白浪覆盖率与风要素关系模式。此模式给出的结果与Ｍｏｎａｈａｎ 等汇集的海洋白浪覆盖率测量数据总体符合良好。     

基于白冠覆盖率的飞沫生成函数参数化

海浪破碎使得海面产生飞沫水滴,由于飞沫水滴的存在改变着大气和海洋之间的能量传输。飞沫生产函数一般认为是水滴初始半径和风速的函数,但海浪时刻存在于海-气界面,仅仅考虑海面风的作用,而忽略海浪的影响是不够完善的。白冠覆盖率是海浪破碎的重要特征参数,有研究者发现白冠覆盖率与海面风速和海浪均存在相关性。本文尝试从白冠覆盖率出发,构建飞沫水滴的生成函数参数化方案,将描述不同飞沫水滴半径的飞沫生成函数基于白冠覆盖率参数有机整合,然后结合白冠覆盖率和海浪状态的关系,利用实验室观测数据,分析不同海浪状态条件下海浪对飞沫生成函数的影响。研究结果表明,新的考虑波浪效应的飞沫生成函数可以合理地描述不同海浪状态条件下飞沫水滴的生成过程。     

破碎波群的显著特征指标

群发性是风浪破碎的显著特征,最近的研究表明风浪破碎研究应该基于波群而不是单个波。本文探讨破碎波群区别于非破碎波群的显著特征指标。依据一系列风浪破碎实验数据,采用多种判据与实验现场目测的破碎标记信号相结合的原则划分破碎波群与非破碎波群,考查波群特征量、单个波几何特征量、局地破碎判据指标、波包络几何特征量以及波群能量结构特征量等5大类28个指标在破碎波群与非破碎波群上的分布差异。结果表明:波陡、峰前波陡、瞬时波面斜率、运动学判据指标和动力学判据指标等在破碎非破碎波群上的分布几乎没有交叠;后两者尤为理想,分布明显分离,是破碎波群区别于非破碎波群的显著指标;而其它各指标在破碎波群非破碎波群上的分布都有不同程度的交叠,不能单独依据它们区分破碎波群与非破碎波群。     

基于卫星数据改进计算白冠覆盖率的模型

本文基于白冠覆盖率的历史研究,总结了计算白冠覆盖率的参数化方案和海浪破碎统计模型,并分析比较其优缺点。通过结合基于卫星数据的参数化公式,利用最优拟合的方法,得到不同限制条件下模型中的系数C_en和n。通过分析考虑海浪破碎条件,确定了适用于一般海浪状况的系数值。通过比较白冠覆盖率的卫星数据和原始模型的模拟结果,可知改进后模型的结果更合理,同时与历史研究结论相符。文中还分析了从1998年到2008年十年平均的全球白冠覆盖率的季节性分布特征。在中高纬度海域,全年白冠覆盖率的值最大,而在低纬度和赤道海域,白冠覆盖率小于0.5%,全球白冠覆盖率的平均值大约为1% ~3%。北半球中高纬度海域的白冠覆盖率的季节性变化显著大于南半球。     

海洋环境因素对白冠覆盖率的影响及其数值估算

波浪破碎是一个强非线性过程,破碎时产生的大量气泡在海面上表现为白冠,白冠覆盖率是刻画波浪破碎一个重要参数。研究表明,白冠覆盖率与海上风速、海浪状态和大气稳定度等多种海洋环境因素有关。综合前人的观测数据,本文给出了更为可靠的依赖风速的白冠覆盖率公式,发现海水温度越高,白冠覆盖率越大。提出了以波浪破碎耗散函数为参数的白冠覆盖率公式,同时发现波龄小于某个临界值时,白冠覆盖率随波龄增大,波龄大于临界值时,白冠覆盖率保持不变,该临界值随风速增大而减小。     

Approach to Calculating Methods of Wave Breaking Depth and Height

- Engineers in coastal engineering have been paying much attention to the research subject on wave breaking. In this paper, previous research results on the calculating methods of wave breaking depth and height are enumerated, the laws of wave transformation before and after wave breaking are investigated, an adequate supposition is made, and the effect of beach slope, bed friction and breaking turbulence on wave breaking is considered. By applying the theory of wave energy dissipation rate and combining with proper formulas of solitary waves, a new calculating formula of wave breaking depth and height on the movable bed is derived and examined with the data from experimental pools of different sizes, and it is proved to be of practicability.     

Determining the Onset and Strength of Unforced Wave Breaking in A Numerical Wave Tank

A numerical wave tank is used to investigate the onset and strength of unforced wave breaking, and the waves have three types of initial spectra: constant amplitude spectrum, constant steepness spectrum and Pierson-Moscowitz spectrum. Numerical tests are performed to validate the model results. Then, the onset of wave breaking is discussed with geometric, kinematic, and dynamic breaking criteria. The strength of wave breaking, which is always characterized by the fractional energy loss and breaking strength coefficient, is studied for different spectra. The results show how the energy growth rate is better than the initial wave steepness on estimating the fractional energy losses as well as breaking strength coefficient.     

Comparisons of Computational and Experimental Results of Solitary Wave Breaking

- In this paper, the solitary wave deformation along a gentle slope and the impact pressure, on the wall are investigated experimentally and the results are compared with numerical results obtained based on the volume of fluid (VOF) method. The topography used in the experiment consists of three segments. The left segment is a 1:4 slope, the middle segment 1 :SO slope and the right segment a horizontal bed. Both the wave heights and breaking points obtained from numerical simulation and experiments are in good agreement. Numerical results give reasonable pressure distributions of breaking waves on the wall.     

Effects of Wave Breaking on Freak Wave Generation in Ramdom Wave Train

The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index, AI=Hmax/Hs, being used to characterize the freak waves, and the changes of the coefficient due to wave breaking. The results show that the occurence in deep water is larger than that in shallow water.     

Physical Investigation of Directional Wave Focusing and Breaking Waves in Wave Basin

An experimental scheme for the generation of directional focusing waves in a wave basin is established in this paper. The effects of the directional range, frequency width and center frequency on the wave focusing are studied. The distrihution of maximum amplitude and the evolution of time series and spectra during wave packet propagation and the variation of water surface parameters are extensively investigated. The results reveal that the characteristics of focusing waves are significantly influenced hy wave directionality and that that breaking criteria for directional waves are distinctly different from those for unidirectional waves.     

Effects of Wave Breaking on Freak Wave Generation in Random Wave Train

The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index,AI=Hmax/Hs,being used to characterize the freak waves,and the changes of the coefficient due to wave breaking. The results show that the occurrence probability of freak wave events in non-breaking waves is much larger than that in breaking waves and such occurrence in deep water is larger than that in ...     

Wave Transformation and Breaking in Diagonal Opposing Current

- When waves propagate into diagonal opposing current from non-current area, not only the wave parameters but also the direction of wave propagation will change, that is, wave refraction will occur. The authors have calculated the changes of wave parameters, including wave refraction, by Linear Wave Theory, and have also done systematic study on wave transformation and breaking in opposing current by means of experimental analysis and theoretical calculation. In order to know the effect of wave refraction, computation is done in this paper about wave transformation and breaking on gentle slopes in diagonal opposing current.     

A Boussinesq Equation-Based Model for Nearshore Wave Breaking

Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally‘ s analytical solution to the wave-height decay instead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data.     

Breaking of Solitary Waves on Uniform Slopes

The propagation,shoaling and breaking of solitary waves on mild slopes are simulated byboundary element method.In this paper,the criterion of breaking solitary waves on mild slopes is discussed.The criterion is that the ratio of horizontal velocity of water particles on the wave crest to wave celerity equalsone.However,the case that the ratio of horizontal velocity of water particles on the wave crest to wave ce-lerity is below one but the front face of wave profile becomes vertical is also considered as a breaking criteri-on.According to the above criteria,the breaking index for slopes 1:10 to 1:25 is studied.The result is com-pared to other researchers'.The deformation of solitary waves on slopes is discussed and the distribution offluid velocities at breaking is shown.     

Numerical Prediction of Regular Wave Breaking on Very Gentle Slopes

Regular wave deformation and breaking on very gende slopes is calculated by Mixed-Eulerian-Lagrangian procedure. The velocity potentials and their normal derivatives on the boundary are calculated through the mixed 0-1 boundary element method. The wave elevation and the potentials of time-stepping integration are detertnined by the 2nd-order Taylor expansion at the nodes of free surface boundary elements. During calculation the x-coordinates of the free surface element nodes are supposed to remain unchanged, i.e. the partial derivatives of wave elevation and potentials with respect to x are considered as zero. The numerical results of asymmetric parameters of breaking waves are verified by experimental study. It is shown that when the wave asymmetry is weak, the maximum horizontal velocity of water particales occurs at the wave peak and, the average ratio of this maximum velocity to wave celerity is 0.96. However, when the wave asymmetry is strong, the maximum horizontal velocity of water particles occu     

Dynamic Response Behaviors of Upright Breakwaters Under Breaking Wave Impact

- The dynamic response behaviors of upright breakwaters under broken wave impact are analysed based on the mass-damper-spring dynamic system model. The effects of the mass, damping, stiffness, natural period, and impulse duration (or oscillation period) on the translation, rotation, sliding force, overturning moment, and corresponding dynamic amplifying factors are studied. It is concluded that the ampli-ying factors only depend on the ratio of the system natural period to impulse duration (or oscillation period) under a certain damping ratio. Moreover, the equivalent static approach to breakwater design is also discussed.     

Vibrating-Rocking Motion of Caisson Breakwater Under Breaking Wave Impact

The possible motions of a caisson breakwater under dynamic load excitation include vibrating, vibrating-sliding and vibrating-rocking motions. The models of vibrating motion and vibrating-sliding motion have been proposed in an early paper. In this paper, a model of vibrating-rocking motion of caisson breakwaters under breaking wave impact is presented, which can be used to simulate the histories of vibrating-rocking motion of caisson breakwaters. The effect of rocking motion on the displacement, rotation, sliding force and overturning moment of breakwaters is investigated. In case the overturning moment exceeds the stability moment of a caisson, the caisson may only rock. The caisson overturns only in case the rocking angle exceeds the critical angle. It is shown that the sliding force and overturning moment of breakwaters can be reduced effectively due to the rocking motion. It is proposed that some rocking motion should be allowed in breakwater design.