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1.
It is well established that the modulational instability enhances the probability of occurrence for extreme events in long crested wave fields. Recent studies, however, have shown that the coexistence of directional wave components can reduce the effects related to the modulational instability. Here, numerical simulations of the Euler equations are used to investigate whether the modulational instability may produce significant deviations from second-order statistical properties of surface gravity waves when short crestness (i.e., directionality) is accounted for. The case of a broad-banded directional wave field (i.e. wind sea) is investigated. The analysis is concentrated on the wave crest and trough distribution. For completeness a comparison with a unidirectional wave field is presented also. Results will show that the distributions based on second-order theory provide a good estimate for the simulated crest and trough height also at low probability levels. 相似文献
2.
As a fully developed (Airy) wave propagates from deep into shallow water, its crest becomes more peaked while the trough flattens out. The median crest diameter MCD, defined as the distance between the wave flanks under the crest at a level halfway between the crest and trough, therefore decreases relative to the similarly defined median trough diameter MTD, which remains constant up to the breaking point. The MCD is directly related to other wave characteristics, which enables water particle velocities to be calculated for any water depth without having to recur to more complex, higher-order Stokes, cnoidal or Fenton theories. Over a nearly horizontal bottom, most fully developed wave characteristics can be expressed as functions of the wave period Tw. It is shown that the horizontal particle velocity at the bottom under the breaker crest is at least 9 times faster than under the breaker trough, which explains why sediment is transported landward under fair weather conditions. The proposed equations also shed new light on the formation of spilling, plunging and surging/collapsing breakers. 相似文献
3.
Statistics of nonlinear wave crests and groups 总被引：1，自引：0，他引：1
Groups of large nonlinear waves with sharper higher crests can pose hazards to ships, induce harbor resonance and cause wave-overtopping of fixed and floating structures. Past interest in wave groups has mostly been focused on the statistics and modeling of linear wave groups. Studies on nonlinear wave groups are surprisingly few, and address deep water waves only. Here, statistics of nonlinear wave crests and wave-crest groups in deep and transitional water depths are considered, using an appropriate second-order representation for crest heights and the continuous wave-envelope approach. In particular, theoretical expressions describing the statistics of nonlinear wave crests and their groups are posed in the form of a simple second-order transformation of well-known results on linear waves. Predictions from the transformation so posed compare well with nonlinear wave data gathered in the North Sea, and demonstrate that nonlinearities do affect the statistics of large wave crests and their groups significantly. 相似文献
4.
M.Aziz Tayfun 《Ocean Engineering》1984,11(3):245-264
The effect of nonlinearities, such as wave-breaking and vertical asymmetry associated with sea waves, on the distribution of wave amplitudes is explored. Semiclosed theoretical expressions are derived to describe the distributions of breaking-limited crest and trough amplitudes for Stokes-type nonlinear sea waves. These are compared with the conventional Rayleigh distribution appropriate to linear wave amplitudes. The construction of nonlinear wave envelopes with the fast Fourier transform technique is described. The technique can be utilized to enlarge the data base in empirical analyses of field records which typically contain limited information on amplitude characteristics. The theoretical distributions and the proposed data enlargement technique are demonstrated with the analysis of a nonlinear wave record. 相似文献
5.
Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves 总被引：2，自引：0，他引：2
This is the first of three papers on the modelling of various types of surf zone phenomena. In this first paper, part I, the model is presented and its basic features are studied for the case of regular waves. The model is based on two-dimensional equations of the Boussinesq type and it features improved linear dispersion characteristics, possibility of wave breaking, and a moving boundary at the shoreline. The moving shoreline is treated numerically by replacing the solid beach by a permeable beach characterized by an extremely small porosity. Run-up of nonbreaking waves is verified against the analytical solution for nonlinear shallow water waves. The inclusion of wave breaking is based on the surface roller concept for spilling breakers using a geometrical determination of the instantaneous roller thickness at each point and modelling the effect of wave breaking by an additional convective momentum term. This is a function of the local wave celerity, which is determined interactively. The model is applied to cross-shore motions of regular waves including various types of breaking on plane sloping beaches and over submerged bars. Model results comprise time series of surface elevations and the spatial variation of phase-averaged quantities such as the wave height, the crest and trough elevations, the mean water level, and the depth-averaged undertow. Comparisons with physical experiments are presented. The phaseaveraged balance of the individual terms in the momentum and energy equation is determined by time-integration and quantities such as the cross-sectional roller area, the radiation stress, the energy flux and the energy dissipation are studied and discussed with reference to conventional phase-averaged wave models. The companion papers present cross-shore motions of breaking irregular waves, swash oscillations and surf beats (part II) and nearshore circulations induced by breaking of unidirectional and multidirectional waves (part III). 相似文献
6.
A Navier-Stokes solver in OpenFOAM® is combined with the Volume of Fluid (VOF) surface capturing method to investigate the wave interaction with depth-varying currents in intermediate and shallow waters. A special attention is paid to the separate effect of vertical current shear on near resonant triad wave interactions. It was found that in the presence of following vertical current shear, the wave exhibits a sharper crest and flatter trough, and the opposite is true in the presence of opposing vertical current shear. Our model results indicate that the wave steepness at which the current shear starts to affect the crest elevation is greater in deeper water than in shallower water. We found that adding vertical current shear to the uniform current further enhances the relative harmonic wave energy and the extent of triad interaction in the following current while weakens them in the opposing current. As a result, following and opposing current shear may cause wave to break at a lower and higher sea state respectively. Due to the increased wave nonlinearity in the presence of a following current shear, a linear superposition of the individual wave and current velocities is no longer adequate to represent the total horizontal velocity close to the free surface. 相似文献
7.
1 IntroductionIn coastal areas a ubiquitous phenomenon is theformation of ripples in the seabed. It is now widelyaccepted that the flow and sediment transport overseabed are vital in relation to erosion, surface wavedissipation and pollution dispersion et… 相似文献
8.
基于Boussinesq水波模型的聚焦波模拟 总被引：1，自引：1，他引：0
基于最高导数为3阶的单层Boussinesq方程,建立了聚焦波的时域波浪计算模型。数值模型求解采用了预报?校正的有限差分法。对于时间差分格式,预报和校正分别采用3阶Adams-Bashforth格式和4阶Adams-Moulton格式。首先,针对不同水深条件下水槽中传播的强非线性波进行模拟,并将数值结果与流函数的数值解析解进行了比较,结果表明无论是波面位移、波面处的水平速度和垂向速度均与解析解符合较好,最大波峰面的速度分布伴随水深的增加与解析解吻合程度变差,非线性速度分布的适用范围与线性解析解适应范围kh<3.5基本一致。其次,对深水聚焦波演化进行了模拟研究,研究中聚焦波的生成采用在边界点累加不同频率线性规则波的方法。应用聚焦波物理模型实验结果验证模型,计算聚焦位置处的波面位移和沿水深的速度分布与实验结果的对比表明,波面位移吻合程度较好,垂向的水平速度分布基本吻合。最后,保持中心频率(周期)不变,数值模拟了周期范围变化下最大聚焦波峰面以及波峰面水平速度的变化趋势,结果表明波峰面值和波峰面水平速度随着周期范围缩小而增大。 相似文献
9.
Ｎｏｎｌｉｎｅａｒｅｆｆｅｃｔｏｎｉｎｅｒｔｉａｃｏｍｐｏｎｅｎｔｏｆｗａｖｅｆｏｒｃｅｓｏｎａｃｙｌｉｎｄｅｒ￥ＬｉＹａｎｂａｏａｎｄＳｏｎｇＲｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＨｙｄｒａｕｌｉｃＥｎｇｉｎｅｅｒｉｎｇ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉ... 相似文献
10.
Field measurement of waves and wave pressure in a given harbour were carried out in the years 1973 and 1977 and then the statistical analysis was made. Based on this analysis and the linear wave theory some problems concerning the total pressure spectrum and the total pressure crest value and trough value are discussed, and the method of calculating these quantities is given. 相似文献
11.
为了解极端波浪非线性特征,明确波群在演化过程中的水动力学特性,针对一系列高斯波群进行了深水物理试验分析。试验结果显示,增加波陡或波群宽度,均可使波面偏度Sk发生明显变化,尤其当波浪发生破碎后,在破碎区域内,波面偏度变化范围剧烈增大,说明该偏度极大值可能作为判断破碎的一个指标。波陡和波群宽度对波面不对称度影响程度不同:当波陡或波群宽度增加后,波峰不对称度所受影响最大,波峰前端波谷不对称度次之,波峰后端波谷不对称度所受影响最小,但仍不可忽略。在波浪演化过程中,幅值谱出现不同程度频带下移,波浪破碎后,会出现永久频带下移;当调制不稳定发生时,随着调制不稳定指数增加,频带下移量呈现快速增长趋势。 相似文献
12.
13.
Statistical analysis of nonlinear random waves is important in coastal and ocean engineering. One approach for modeling nonlinear waves is second-order random wave theory, which involves sum- and difference-frequency interactions between wave components. The probability distribution of the non-Gaussian surface elevation can be solved using a technique developed by Kac and Siegert [21]. The wave field can be significantly modified by wave diffraction due to a structure, and the nonlinear diffracted wave elevation can be of interest in certain applications, such as the airgap prediction for an offshore structure. This paper investigates the wave statistics due to second-order diffraction, motivated by the scarcity of prior research. The crossing rate approach is used to evaluate the extreme wave elevation over a specified duration. The application is a bottom-supported cylindrical structure, for which semi-analytical solutions for the second-order transfer functions are available. A new efficient statistical method is developed to allow the distribution of the diffracted wave elevation to be obtained exactly, accounting for the statistical dependency between the linear, sum-frequency and difference-frequency components. Moreover, refinements are proposed to improve the efficiency for computing the free surface integral. The case study yields insights into the problem. In particular, the second-order nonlinearity is found to significantly amplify the extreme wave elevation, especially in the upstream region; conversely, the extreme elevation at an oblique location downstream is attenuated due to sheltering effects. The statistical dependency between the linear and sum-frequency components is also shown to be important for the extreme wave statistics. 相似文献
14.
Wave-height distributions and nonlinear effects 总被引：2，自引：0，他引：2
Theoretical distributions proposed for describing the crest-to-trough heights of linear waves are reviewed briefly. To explore the effects of nonlinearities, these are generalized to second-order waves, utilizing quasi-deterministic results on the expected shape of large waves. The efficacy of Gram–Charlier models in describing the effects of third-order nonlinearities on the distributions of wave heights, crests and troughs are examined in detail. All models and a fifth-order Stokes–Rayleigh type model recently proposed are compared with linear and nonlinear waves simulated from the JONSWAP spectrum representative of long-crested extreme seas, and also with oceanic data gathered in the North Sea. Uncertainties arising from the variability of probability estimates derived from sample populations of limited size are considered. Ultimately, the comparisons show that nonlinearities do not have any discernable effect on the crest-to-trough heights of oceanic waves. Most of the linear models considered yield similar and reasonable predictions of the observed data trends. Gram–Charlier type distributions seem neither effective nor particularly useful in describing the statistics of large wave heights or crests under oceanic conditions. However, they do surprisingly well in predicting unusually large wave heights and crests observed in some 2D wave-flume experiments and 3D numerical simulations of long-crested narrow-band random waves. 相似文献
15.
This article concerns the calculation of nonlinear crest distribution for shallow water Stokes waves. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic analysis method. This is a new approach to the calculation of wave crest distribution, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The accuracy and efficiency of this new approach for calculating the wave crest distribution are validated by comparing the results predicted using it with those predicted by using the Monte Carlo simulation (MCS) method, by using a previous Transformed Rayleigh method, by using some existing wave crest distribution formulas, and by using the measured surface elevation data at the Poseidon platform in the Japan Sea. 相似文献
16.
I. I. Didenkulova E. N. Pelinovsky O. I. Didenkulov 《Izvestiya Atmospheric and Oceanic Physics》2014,50(5):532-538
We study the run-up of long solitary waves of different polarities on a beach in the case of composite bottom topography: a plane sloping beach transforms into a region of constant depth. We confirm that nonlinear wave deformation of positive polarity (wave crest) resulting in an increase in the wave steepness leads to a significant increase in the run-up height. It is shown that nonlinear effects are most strongly pronounced for the run-up of a wave with negative polarity (wave trough). In the latter case, the run-up height of such waves increases with their steepness and can exceed the amplitude of the incident wave. 相似文献
17.
Analysis of freak wave measurements in the Sea of Japan 总被引：3，自引：0，他引：3
This paper presents an analysis of a set of available freak wave measurements gathered from several periods of continuous wave recordings made in the Sea of Japan during 1986–1990 by the Ship Research Institute of Japan. The analysis provides an ideal opportunity to catch a glimpse of the statistics of freak waves in the ocean. The results show that a well-defined freak wave may occur in the developed wind–wave condition: S(f)∝f−4, with single-peak directional spectra. The crest and trough amplitude distributions of the observed sea waves including freak waves are different from the Rayleigh distribution, although the wave height distribution tends to agree with the Rayleigh distribution. Freak waves can be readily identified from the wavelet spectrum where a strong energy density occurs in the spectrum, and is instantly surged and seemingly carried over to the high-frequency components at the instant the freak wave occurs. 相似文献
18.
The accuracy of several asymptotic series expansions for wave speed and particle velocity under the crest of a solitary wave (on a fluid at rest) up to maximum height is investigated. The very accurate numerical results of Williams (1985) are the measure for our comparisons. The results are based on a scaling of calculated properties of long periodic waves to the case of solitary waves.For wave speeds the classical Boussinesq–Rayleigh expression gives good agreement up to a relative wave height of, say, 0.3. An asymptotic fourth-order expression based on Fenton (1990) can be used up to a relative wave height of 0.7, whereas the corresponding fifth-order expression is slightly less accurate.The Eulerian particle velocity profile under the wave crest is examined using a cnoidal wave expression from Fenton (1990) in the limit of the solitary wave. For low waves a `consistent' (i.e. properly truncated) fifth-order expression and an `inconsistent' ditto both coincide with Williams' results. Beginning at medium high waves, the consistent expression surprisingly exhibits oscillations in the velocity profile, and the oscillations become stronger as the wave gets higher. The inconsistent expression, however, yields the same shape as Williams' profile, but is displaced parallel to this, resulting in slightly larger velocities. For high waves also the inconsistent expression begins to differ in shape from Williams' profile, and asymptotic theory fails. Only for low waves `lowest order theory' gives acceptable results. We show analytically that for the highest wave the particle velocity profile has a horizontal tangent at the water surface; this is corroborated by Williams' numerical results.We also study the particle velocity at the wave crest as a function of wave height. It is shown that the variation has a vertical tangent for the highest wave. Two fifth-order asymptotic series for this velocity, based on the wave speed through the Bernoulli equation, show very good agreement with Williams up to a relative wave height of about 0.6.It is finally shown that it is possible to produce very accurate rational-function approximations to Williams' results for the wave speed as well as for the particle velocity at the wave crest. 相似文献
19.
A. Toffoli M. Onorato E. Bitner-Gregersen A.R. Osborne A.V. Babanin 《Ocean Engineering》2008,35(3-4):367-379
When the wave spectrum is sufficiently narrow-banded and the wave steepness is sufficiently high, the modulational instability can take place and waves can be higher than expected from second-order wave theory. In order to investigate these effects on the statistical distribution of long-crested, deep water waves, direct numerical simulations of the Euler equations have been performed. Results show that, for a typical design spectral shape, both the upper and lower tails of the probability density function for the surface elevation significantly deviate from the commonly used second-order wave theory. In this respect, the crest elevation is observed to increase up to 18% at low probability levels. It would furthermore be expected that wave troughs become shallower due to nonlinear effects. Nonetheless, the numerical simulations show that the trough depressions tend to be deeper than in second-order theory. 相似文献