波群的波向线散开因子方程

本文将既适用于平面笛卡尔直角坐标系又适用于球面坐标系的基本式同文献[16]中的波向线方程结合,导出波群的波向线散开因子方程。由此方程解出的散开因子是波群组成波的波要素的函数。据此因子连同浅水系数和摩擦系数就可求得波群的波动强度或波高沿波向线的变化。在一定条件下,所导得的方程便分别化为形同于相应坐标系中单频率波的。 所讨论的波群的折射是唯一地由水深变浅所致的。 根据线性势论,得到由波数、波向和频率都彼此稍异的两系正弦波迭加而成的简单波群,海洋中的波群虽较这复杂得多,但两者本质上是相同的。故所提方程可作为计算浅水域中波群的折射系数的模式。     

波群的波向线散开因子方程

本文将既适用于平面筒卡尔直角坐标系又适用于球面坐标系的基本式同文献(16)中的波向线方程结合，导出波群的波向线散开因子方程。由此方程解出的散开因子是波群组成波的波要素的函数。据此因子连同浅水系数和摩擦系数就可求得波群的波动强度或波高沿波向线的变化。在一定条件下，所导得的方程便分别化为形同于相应坐标系中单频率波的。所讨论的波群的折射是唯一地由水深变浅所致的。根据线性势论，得到由波数、波向和频率都彼此稍异的两系正弦波迭加而成的简单波群，海洋中的波群虽较这复杂得多，但两者本质上是相同的。故所提方程可作为计算浅水域中波群的折射系数的模式。     

计算波群折射的方法及其应用

根据汪炳祥１９８提出的普遍几何群速概念和波群波向线及其波向线散开因子方程，提出一种计算和绘制波群折射的数值方法。为使本方法较具普遍性，将旋转坐标系引入控制方程并予以变形与简化。数值计算采用Ｒｕｎｇｅ－Ｋｕｔｔａ法。将上述方法应用于胶州湾湾口附近海域的波群折射计算并绘制其折射图。将计算结果分别与依几何群速建立的波群折射和单频率波折射结果比较，可明显地看出基本方法的结果优于后两者。     

波群内单个波的波陡分布与波破碎

对波群内单个波的波陡分布和波破碎进行了实验研究。研究结果是,波群中波动的最大振幅出现在波群前部而不是出现在波群中央,这种不对称性导致波群前部单个波出现大波陡的概率大于后部单个波出现大波陡的概率;进一步的波破碎统计发现波群前部单个波破碎的频率是后部单个波破碎频率的4倍。因此认为,波群结构的不对称性能够导致单个波发生破碎的...     

波群结构和波群中的波破碎

本文将小波分析用于波群结构和波群中波破碎的研究。实验结果表明,波群中波动的振幅不是关于波群中央对称的,而是波群前部波动的振幅较大。这种不对称性导致波群前部单个波的波陡较大,后部单个波的波陡较小,当谱宽度增大时波群前部与后部单个波的平均波陡之差增大。波群前部波陡较大导致波群前部的波动最容易发生破碎,而不是波群中央的波动最容易发生破碎,波群中波动最可能发生破碎的位置距波群中央的长度为波群长度的1/6。     

深水随机波列中畸形波统计特征的研究

本文基于Longuet-Higgins随机波浪模型和JONSWAP谱,进行了大量深水随机波的模拟,获取了畸形波发生概率稳定的随机波列,并对随机波列中的畸形波进行了分析。结果表明,畸形波发生的概率小于基于Rayleigh分布预测结果,且随谱宽的减小而增大。在固定时间段内,畸形波发生的频次服从泊松分布,时间间隔服从指数分布,且随着谱宽的增大,畸形波的发生频次减小,相邻畸形波的发生时间间隔增加。通过小波变换方法分离随机波中的波群,研究了出现畸形波的波群特征,发现一个波群中最多会出现4个畸形波,但是在发生畸形波的波群中,单个畸形波的概率最大。随着谱宽减小,一个波群中包含多个畸形波的概率增加。另外,出现畸形波的波群时间长度服从广义极值分布,随着谱宽减小,畸形波波群的时间跨度增加。     

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。     

风浪波群中波高分布研究

在实验室风浪槽中观测风浪,发现波群连长是影响波群中波高分布的重要因素,随着波群连长增大,波群中波高分布信息熵增大。当以平均波高无因次化,连长较大时波群中波高累积概率明显大于连长较小时情形。波群中波高分布受谱宽度影响。当谱宽度增大,波群中波高累积概率降低。谱宽度和波群连长对波群中波高累积概率的影响相当。引进体现波群特性的1个无因次化波高参量研究波群中波高累积概率。     

海浪波群的谱特征分析

海浪的波谱特征分析对认识海浪有重要的意义，因为海浪谱反映了海浪的结构成分。这对海工建筑、海洋运输、船舶制造、海浪预报和海浪模拟等均有重要的实用意义。 波群是伴随海浪经常出现的一种自然现象，且经常伴随大浪的出现而出现。实践证明，波群具有极大的破坏力，其破坏性远比单个波大得多，它是海浪破坏海工建筑物的重要因子，许多防波堤的破坏并非是由单个波的作用，而是由相继出现的几个大波(波群)作用的结果。早先，人们对波群这种习见的现象研究甚少。自1974年葡萄牙锡尼斯港深水防波堤的破坏之后，对波群的研究才日益受到重视。 对波群的研究目前多采用包络方法、马尔科夫链方法和波能过程线法。波群研究的主要内容是波群的统计特征(如波群链长统计)；另外，波群的模拟也是重要的研究内容之一。目前用包络方法研究波群比较普遍，且有不少研究成果。徐德伦等(2001)综述了这方面的研究进展及结果，文圣常等(1984)也进行了详尽的讨论。 以往的研究大都是研究波群的统计特征，如合田良实(1976)、 Ewing(1973)、Rye(1974)。而针对地域性的波浪，我国学者也只是以包络方法为基础讨论了不同地域海浪波群的统计特征(常德馥，1987；葛明达，1986；范顺庭，1998)。就波群本身的结构特征而言，即波群的波谱分析特征以往的研究涉及尚少。作者拟借助于谱分析方法，对带有典型波群的实测的海浪记录来分析海浪波群的波谱结构，进而借此对海浪波群的结构特征进行深入探讨。     

破碎波群间隔统计分布

基于一系列实验室风浪破碎实验,讨论破碎波群间隔的统计分布。实验时风速分别设定在6～9 m/s间几个不同的风速水平,破碎波群间隔定义为两个相继发生破碎的波群中破碎首发时刻之间的时间间隔,破碎依据波面信号和实验者同步记录的破碎标记信号判别,分布拟合检验采用Kolmogorov-Smirnov检验。数据分析结果表明:1)所有实验信号的破碎波群间隔都服从Gamma分布;2)低风速情形的破碎波群间隔大多服从指数分布——Gamma分布的一种特殊情形;3)相同实验条件下的破碎波群间隔具有相同的分布。这意味着破碎波群的发生可以视为一种更新过程。     

Large-scale experiments on beach profile evolution and surf and swash zone sediment transport induced by long waves,wave groups and random waves

New large-scale laboratory data are presented on the influence of long waves, bichromatic wave groups and random waves on sediment transport in the surf and swash zones. Physical model testing was performed in the large-scale CIEM wave flume at UPC, Barcelona, as part of the SUSCO (swash zone response under grouping storm conditions) experiment in the Hydralab III program (Vicinanza et al., 2010). Fourteen different wave conditions were used, encompassing monochromatic waves, bichromatic wave groups and random waves. The experiments were designed specifically to compare variations in beach profile evolution between monochromatic waves and unsteady waves with the same mean energy flux. Each test commenced with approximately the same initial profile. The monochromatic conditions were perturbed with free long waves, and then subsequently substituted with bichromatic wave groups with different bandwidth and with random waves with varying groupiness. Beach profile measurements were made at half-hourly and hourly intervals, from which net cross-shore transport rates were calculated for the different wave conditions. Pairs of experiments with slightly different bandwidth or wave grouping show very similar net cross-shore sediment transport patterns, giving high confidence to the data set. Consistent with recent small-scale experiments, the data clearly show that in comparison to monochromatic conditions the bichromatic wave groups reduce onshore transport during accretive conditions and increase offshore transport during erosive conditions. The random waves have a similar influence to the bichromatic wave groups, promoting offshore transport, in comparison to the monochromatic conditions. The data also indicate that the free long waves promote onshore transport, but the conclusions are more tentative as a result of a few errors in the test schedule and modifications to the setup which reduced testing time. The experiments suggest that the inclusion of long wave and wave group sediment transport is important for improved near-shore morphological modeling of cross-shore beach profile evolution, and they provide a very comprehensive and controlled series of tests for evaluating numerical models. It is suggested that the large change in the beach response between monochromatic conditions and wave group conditions is a result of the increased significant and maximum wave heights in the wave groups, as much as the presence of the forced and free long waves induced by the groupiness. The equilibrium state model concept can provide a heuristic explanation of the influence of the wave groups on the bulk beach profile response if their effective relative fall velocity is larger than that of monochromatic waves with the same incident energy flux.     

Effect of higher-order bottom variation terms on the refraction of water waves in the extended mild-slope equations

This study investigates how the refraction of water waves is affected by the higher-order bottom effect terms proportional to the square of bottom slope and to the bottom curvature in the extended mild-slope equations. Numerical analyses are performed on two cases of waves propagating over a circular shoal and over a circular hollow. Numerical results are analyzed using the eikonal equation derived from the wave equations and the wave ray tracing technique. It is found that the higher-order bottom effect terms change the wavelength and, in turn, change the refraction of waves over a variable depth. In the case of waves over a circular shoal, the higher-order bottom effects increase the wavelength along the rim of shoal more than near the center of shoal, and intensify the degree of wave refraction. However, the discontinuity of higher-order bottom effects along the rim of shoal disperses the foci of wave rays. As a result, the amplification of wave energy behind the shoal is reduced. Conversely, in the case of waves over a circular hollow, the higher-order bottom effects decrease the wavelength near the center of the hollow in comparison with the case of neglecting higher-order bottom effects. Consequently, the degree of wave refraction is decreased, and the spreading of wave energy behind the hollow is reduced.     

Sediment transport and beach morphodynamics induced by free long waves,bound long waves and wave groups

New laboratory data are presented on the influence of free long waves, bound long waves and wave groups on sediment transport in the surf and swash zones. As a result of the very significant difficulties in isolating and identifying the morphodynamic influences of long waves and wave groups in field conditions, a laboratory study was designed specifically to enable measurements of sediment transport that resolve these influences. The evolution of model sand beaches, each with the same initial plane slope, was measured for a range of wave conditions, firstly using monochromatic short waves. Subsequently, the monochromatic conditions were perturbed with free long waves and then substituted with bichromatic wave groups with the same mean energy flux. The beach profile changes and net cross-shore transport rates were extracted and compared for the different wave conditions, with and without long waves and wave groups. The experiments include a range of wave conditions, e.g. high-energy, moderate-energy, low-energy waves, which induce both spilling and plunging breakers and different turbulent intensities, and the beaches evolve to form classical accretive, erosive, and intermediate beach states. The data clearly demonstrate that free long waves influence surf zone morphodynamics and promote increased onshore sediment transport during accretive conditions and decreased offshore transport under erosive conditions. In contrast, wave groups, which can generate both forced and free long waves, generally reduce onshore transport during accretive conditions and increase offshore transport under erosive conditions. The influence of the free long waves and wave groups is consistent with the concept of the relative fall velocity, H/w_sT, as a dominant parameter controlling net beach erosion or accretion. Free long waves tend to reduce H/w_sT, promoting accretion, while wave groups tend to increase the effective H/w_sT, promoting erosion.     

Intermittency of wind wave group breaking

Knowledge on intermittency of wave breaking is so far limited to a few summary statistics, while the probability distribution of time interval between breaking events can provide a full view of intermittency. Based on a series of experiments on wind wave breaking, such probability distributions are investigated. Breaking waves within a wave group were taken as a single breaking event according to recent studies. Interval between successive wave groups with breaker is the focus of this paper. For intervals in our experiments with different fetch and wind conditions, their distributions are all skewed and weighted on small intervals. Results of Kolmogorov-Smirnov tests on time series of these intervals indicate that they all follow gamma distribution, and some are even exponential type. Average breaking-group-interval decreases with friction velocity and significant steepness until the wind is strong enough;most of them are more than 10 times the dominant wave period. Group breaking probability proposed by Babanin recently and the average number of breaking waves in wave groups are also discussed, and they are seemingly more reasonable and sensitive than traditional breaking probability defined in terms of single wave.     

ON THE JOINT DISTRIBUTION OF THE PERIODS AND HEIGHTS OF SEA WAVES

Based on the ray theory of waves and the linear model of sea waves, a joint distribution of periods and heights is derived. The theoretical expression has the same merits as those of Lon-guet-Higgins', but the wave height distribution is still Rayleigh's.     

Groupiness of Sea Waves and Their Characteristic Parameters

Three methods for studying wave groups and their main parameters for describing wave groupiness are reviewed in this paper. Then they are analyzed and compared combined with field data from both aspects of group height and group length. A method and two parameters that can describe wave groupiness are suggested. The groupiness parameters of sea waves at three field stations are given. The effects of groupiness on both distributions of the wave height and the phase of component waves are investigated. The effects of datum length on the calculated value of grouping parameters are also discussed.     

Simulation and prediction of swash oscillations on a steep beach

This paper presents numerical simulations and analytical predictions of key aspects of swash oscillations on a steep beach. Simulations of the shoreline displacement based on bore run-up theory are found to give excellent agreement with recent experimental data for regular waves, wave groups and random waves. The theory is used to derive parameters that predict the onset of swash saturation and the spectral characteristics of the saturated shoreline motion. These parameters are again in good agreement with the measured laboratory data and are also consistent with previous experimental data. Simulation of irregular wave run-up using a series of overlapping monochromatic swash events is found to reproduce typical features of swash oscillations and can accurately describe both the low and high frequency spectral characteristics of the swash zone. In particular, the low frequency components of the run-up can be modelled directly using a sequence of incident short wave bores, with no direct long wave input to the numerical simulations. This suggests that wave groupiness must be accounted for when modelling shoreline oscillations.