Wave-height distributions and nonlinear effects

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.     

北部湾沿岸海区设计波浪的确定

本文基于北部湾沿岸海区多年的实测资料，于不同海区主浪向和次主浪向分别取年极值波高为样本资料．采用Ｐ－Ⅲ型和短期测波资料频率分析方法，分别估算了各海区不同重现期的设计波高，并依据式（１）计算出相应的平均周期。尽管样本资料和估算方法不变，但每次估算的结果互不相同，其差异甚至很大．利用Ｋｏｌｍｏｇｏｒｏｆｆ等适合度方法检验所得的结果，能够准确地判断出沿岸各海区不同重现期的最佳设计波浪。     

Multidirectional wave transformation around detached breakwaters

The performance of the new wave diffraction feature of the shallow-water spectral model SWAN, particularly its ability to predict the multidirectional wave transformation around shore-parallel emerged breakwaters is examined using laboratory and field data. Comparison between model predictions and field measurements of directional spectra was used to identify the importance of various wave transformation processes in the evolution of the directional wave field. First, the model was evaluated against laboratory measurements of diffracted multidirectional waves around a breakwater shoulder. Excellent agreement between the model predictions and measurements was found for broad frequency and directional spectra. The performance of the model worsened with decreasing frequency and directional spread. Next, the performance of the model with regard to diffraction–refraction was assessed for directional wave spectra around detached breakwaters. Seven different field cases were considered: three wind–sea spectra with broad frequency and directional distributions, each coming from a different direction; two swell–sea bimodal spectra; and two swell spectra with narrow frequency and directional distributions. The new diffraction functionality in SWAN improved the prediction of wave heights around shore-parallel breakwaters. Processes such as beach reflection and wave transmission through breakwaters seem to have a significant role on transformation of swell waves behind the breakwaters. Bottom friction and wave–current interactions were less important, while the difference in frequency and directional distribution might be associated with seiching.     

A note on wave energy dissipation over steep beaches

This paper revisits the derivation of the parametric surf zone model proposed by Baldock et al. [Baldock, T. E., Holmes, P., Bunker, S. & Van Weert, P. 1998 Cross-shore hydrodynamics within an unsaturated surf zone. Coast. Eng. 34, 173–196.]. We show that a consistent use of the proposed Rayleigh distribution for surf zone wave heights results in modification of the expressions for the bulk dissipation rate and enhanced dissipation levels on steep beaches and over-saturated surf zone conditions. As a consequence, the modification proposed herein renders the model robust even on steep beaches where it could otherwise develop a shoreline singularity.     

Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone

The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.     

Determination of wave energy dissipation factor and numerical simulation of wave height in the surf zone

Based on the time-dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation. The wave height of regular and irregular waves is numerically simulated by use of the parabolic mild slope equation considering the energy dissipation due to wave breaking. Comparison of numerical results with experimental data shows that the expression for the energy dissipation factor is reasonable. The effects of the wave breaking coefficient on the breaking point and the distribution of wave height after breaking are discussed through the study of a specific experimental topography.     

Optimisation of wave energy extraction with the Archimedes Wave Swing

This paper addresses the Archimedes Wave Swing (an offshore wave energy converter, which produces electricity from sea waves). It compares the performances of latching control (a discrete, highly non-linear, intrinsically sub-optimum control strategy), of reactive control, of phase and amplitude control (two optimum control strategies that involve non-causal transfer functions, which have to be implemented with approximations, thus rending the control sub-optimum), and of feedback linearisation control (a non-linear control strategy). From extensive simulations it is concluded that the latter performs clearly better irrespective of the sea state, and leads to a significant increase of absorbed wave power.     

Considerations of the discontinuous deformation analysis on wave propagation problems

In rock engineering, the damage criteria of the rock mass under dynamic loads are generally governed by the threshold values of wave amplitudes, such as the peak particle velocity and the peak particle acceleration. Therefore, the prediction of wave attenuation across fractured rock mass is important on assessing the stability and damage of rock mass under dynamic loads. This paper aims to investigate the applications of the discontinuous deformation analysis (DDA) for modeling wave propagation problems in rock mass. Parametric studies are carried out to obtain an insight into the influencing factors on the accuracy of wave propagations, in terms of the block size, the boundary condition and the incident wave frequency. The reflected and transmitted waves from the interface between two materials are also numerically simulated. To study the tensile failure induced by the reflected wave, the spalling phenomena are modeled under various loading frequencies. The numerical results show that the DDA is capable of modeling the wave propagation in jointed rock mass with a good accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

Digital spatial cracking behaviors of fine-grained sandstone with precracks under uniaxial compression

X-ray computed tomography (CT) imaging and digital image correlation techniques are applied to study spatial cracking behaviors of sandstone under uniaxial compression, in which the angle between precracks is 45°, 90°, and 135° and the crack depth is 7.5 mm and 10 mm, respectively. Layered anisotropy damages and spatial cracking evolution are quantitatively analyzed by the defined digital layered anisotropy index and digital damage ratio, respectively. Three cases with different array of precracks evidence the depth effects of precracks on spatial crack propagation. Results show that the failure process of samples is first controlled by the coalescence of surface cracks in 2D space and then the samples are failed by the propagation of coalesced cracks (shear cracks with different shapes). The crack types for samples with precrack depth of 7.5 mm are all shear cracks for Cases 1‑3. Nevertheless, the crack types for samples with precrack depth of 10 mm are, respectively, the half X-shape crack for Case 1, X-shape crack for Case 2, and double shell crack for Case 3. The precrack has a significant promotion effect on the failure process when the angle between the two precracks is β = 90°, and the precrack has little to no effect on the failure process when the angle between the two precracks is β = 135°. As the depth of precrack increases to 10 mm, the crack types are changed in this study. The peak strength of sample subjected to uniaxial compression decreases with increasing depth of precracks, implying the decrease of the rock strength by the discontinuity.     

岩石I型裂纹定向扩展规律试验研究

为精准获得岩石I型裂纹扩展演化全过程,采用一种简易裂纹定向扩展装置开展了不同岩性试样裂纹扩展试验研究,借助声发射及数字散斑技术对裂纹扩展全过程进行了监测,建立了裂纹定向扩展力学模型,分析了裂纹扩展过程中声发射及变形场的演化规律,提出了评价岩石I型裂纹扩展难易程度的能量指标CE,探讨了I型裂纹定向起裂扩展机制。结果表明：该简易裂纹定向扩展装置能够有效实现I型裂纹沿预定方向稳定扩展,其起裂角均小于10º,同时通过简化力学模型计算得到白砂岩、灰砂岩的裂纹扩展峰值强度与巴西劈裂抗拉强度相比偏差分别为22.76%、7.53%;根据变形场演化规律,可将裂纹扩展分为微裂隙发育（散斑变形场分区不明显）、主控裂纹孕育（散斑变形场出现分区现象）和主控裂纹扩展3个阶段;声发射演化过程可分为平静期、缓增期、急增期和降低期4个阶段,由于灰砂岩相较于白砂岩质地更致密、更坚硬,导致其声发射平静期长,而后3个阶段持续时间短;将载荷−位移曲线峰前与峰后的面积之比定义为评价岩石I型裂纹扩展难易程度的能量指标CE,计算得到灰砂岩、白砂岩的CE分别为13～16、1～2,表明CE可有效评价岩石I型裂纹扩展难易程度;岩石I型裂纹起裂扩展机制可概况为：在加载峰值前裂隙尖端受最大拉应力作用,存储的弹性能快速增加、耗散能缓慢增加,但在加载峰值后裂隙尖端存储弹性能超过其储能极限迅速释放,此时输入能大部分转化为耗散能促进主控裂纹快速扩展。后续将对裂纹定向扩展试验装置进一步优化改进,以期为裂纹扩展机制、岩石破坏前兆信息、裂纹止裂原理等研究提供一种新方法,同时为工程现场煤岩层定向爆破、压裂、止裂等相关技术优化提供理论指导。