Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram–Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram–Charlier series, and found our distribution gives a more reasonable fit to the data.     

埕岛油田海域波—底相互作用

基于1976，1993年埕岛油田海域测深资料，应用HISWA浅水海浪数值计算模式，研究风暴浪入侵该海域导致的波-底相互作用后果。数值计算结果表明，海区固定点海底冲刷导致波场强化；波参数增量与冲刷深度有关；海底水质点轨道流速峰值，底摩擦耗散峰值及临界波高值相对水深分布均表明，该海域深水区海底冲刷将减弱，浅水区海底冲刷将加强。     

Probability distribution of random wave–current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave–wave and wave–current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan–Pierson–Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied.     

未破碎变浅随机海浪的波面高度概率分布

利用青岛海洋大学物理海洋实验室现代化的大型水槽,设计进行了多种海浪强度下,由深水传入近岸不同坡度水底上的变浅随机海浪的实验.依据实验资料分析结果表明,对变浅非正态海浪过程而言,其波面高度分布取Gram-Charlier级数前3项,所得结果与实验分布符合良好.该分布中σ、λ₃、λ₄3个参量是测点水深和波浪强度的函数,并获得了与无因次参量Hs/d之间的经验关系,为预测变浅随机海浪的波面高度分布提供了可能.     

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second-order random wave solutions of water wave equations in tinite water depth, statistical distributions of the depth-integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all detemained by the water depth and the wavenumber spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.     

A Study on the Spectral Form of Nearshore Water Waves

- The spectral form of wind waves is investigated based on the ocean wave data observed at three nearshore stations of Taiwan. In this study, the generalized forms of Pierson-Moskowitz spectrum and JONSWAP spectrum are used to describe the local wave spectrum by selecting suitable spectral form parameters. It is shown that, at a specific site, the similarity of wave spectral form exists. Thus it is possible to use a representative spectral form for a given nearshore region to describe the wave spectrum at this nearshore. On the other hand, the effects of relative water depth on spectral form are examined. The feasibility of two spectral models in finite water depth is evaluated by using the same field wave data.     

Wash Waves Generated by High Speed Displacement Ships

It is difficult to compute far-field waves in a relative large area by using one wave generation model when a large calculation domain is needed because of large dimensions of the waterway and long distance of the required computing points. Variation of waterway bathymetry and nonlinearity in the far field cannot be included in a ship fixed process either. A coupled method combining a wave generation model and wave propagation model is then used in this paper to simulate the wash waves generated by the passing ship. A NURBS-based higher order panel method is adopted as the stationary wave generation model; a wave spectrum method and Boussinesq-type equation wave model are used as the wave propagation model for the constant water depth condition and variable water depth condition, respectively. The waves calculated by the NURBS-based higher order panel method in the near field are used as the input for the wave spectrum method and the Boussinesq-type equation wave model to obtain the far-field waves. With this approach it is possible to simulate the ship wash waves including the effects of water depth and waterway bathymetry. Parts of the calculated results are validated experimentally, and the agreement is demonstrated. The effects of ship wash waves on the moored ship are discussed by using a diffraction theory method. The results indicate that the prediction of the ship induced waves by coupling models is feasible.     

The impact of sea level rise and climate change on inshore wave climate: A case study for East Anglia (UK)

In coastal areas, offshore wave propagation towards the shore is influenced by water depth variations, due to sea bed bathymetry, tides and surges. Considering implications of climate change both on atmospheric forcing and sea level rise, a simple methodology involving numerical modelling is implemented to compute inshore waves from 1960 to 2099. Simulations take into account five scenarios of linear sea level rise and one climatic scenario for storm surges and offshore waves. The methodology is applied to the East Anglia coast (UK). Extreme event analysis is performed to estimate climate change implication on inshore waves and the occurrence of extreme events. It is shown, for this coastal region, that wave statistics are sensitive to the trend in sea level rise, and that the climate change scenario leads to a significant increase of extreme wave heights in the northern part of the domain. For nearshore points, the increase of the mean sea level alters not only extreme wave heights but also the frequency of occurrence of extreme wave conditions.     

Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins’s linear model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper.     

渤海波浪和潮汐风暴潮相互作用对波浪影响的数值研究

基于依赖波浪成长状态波令的表面风应力，提出了一个波浪和风暴潮潮汐运动相互作用的联合数值模式，实现了第三代波浪模式和三维风暴潮潮汐模式联合作用的数值研究，并结合渤海典型天气个例的研究，给出了渤海波浪和风暴潮潮汐相互作用对波浪影响的机制和大小量级的定量估计。研究表明，对不同天气过程，波浪和风暴潮潮汐相互作用对波浪影响的性质和大小不同；对强寒潮过程，对波浪影响主要由风暴潮所支配波高调制可达1m，在黄河口区一般达0．5m；对弱天气过程，对波浪影响主要由潮所控制，波高调制约在0．2m，联合作用模式给出的结果与实测更吻合。     

Probability distribution of random wave forces in weakly nonlinear random waves

Based on the second-order random wave theory, the joint statistical distribution of the horizontal velocity and acceleration is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random wave forces are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. It is found that the distribution of wave forces depends solely on the frequency spectrum of sea waves associated with the first order approximation and the second order wave–wave interaction.     

An experimental study on the parameterization of reshaped seaward profile of berm breakwaters

Berm breakwaters are rubble mound structures in which the seaward slope of the initial profile may be reshaped to become more stable under severe wave attack. The stones in the seaward slope move from the initial slope to an equilibrium profile. A 2D experimental study has been carried out in a wave flume at a hydraulic laboratory of Tarbiat Modares University to study the effects of sea state and structural parameters on the reshaped profile parameters of such breakwaters. A series of 287 tests have been performed to cover the effect of various sea state conditions such as wave height, wave period, number of waves and water depth at the toe of the structure, and structural parameters such as berm width, berm elevation above still water level and armor stone size. All the tests have been done employing irregular waves with a JONSWAP spectrum. In this paper, first the reshaped profiles are schematized, and then the key parameters of the reshaped seaward profiles such as step height, step length and depth of intersection point of initial and reshaped profile are investigated, using results of this experimental work. Eventually, formulae that include some sea state and structural parameters are derived for estimation of the reshaped profile parameters. To assess the validity of the proposed formulae, comparisons are made between the estimated parameters of reshaped profiles by these formulae and earlier formulae given by other researchers. The comparisons show that the estimation procedure foretells reshaping parameters well and with less scatter according to the present data and also other experimental results within the range of parameters tested.     

The retrieval of the nonlinear random waves from the non-Gaussian characteristics of the sea surface elevation distribution

In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.     

Numerical simulation of non-gaussian process of wind waves

In this paper further mathematical analysis on "correlation transfer technique" by Polge el al. is carried out, the tenable conditions and the extent of suitability for the said method are proved as well. In consideration of the influence of skewness of the sea surface elevation on spectral shape, a "quasi-correlation transfer techique" is developed by the modification of the simulated target spectrum. Meanwhile, the numerical simulation of the non-Gaussian process of wind waves is carried out in view of the two conditions of the surface elevation probability distribution and the spectrum. By using its simulated results, the influence of skewness of the sea surface elevation on two parameters in the distribution of wave heights (which had been fitted by using the Weibull distribution) is analysed. The "quasi- correlation tranfer technique" is verified and compared with the selection wave data observed in the Jiaozhou Bay in the period of 1980 to 1981. Results make clear (hat, as far as the statistical d     

基于波形不对称性的波浪破碎指标

为了探寻波浪破碎与波形不对称性的关系,通过对1/200缓坡上波浪破碎实验研究结果的进一步分析,运用最小二乘法,拟合了波形不对称性参数与相对水深的关系,以及用波形不对称性参数表示的波浪破碎指标表达式。所得规则波的结果与Kjeldsen的深水波结果相同,而不规则波的结果比规则波的小。研究还表明,这一破碎指标与相对水深有关系,随着水深变浅,指标值增大。     

马蹄波波形特征和对圆柱作用实验研究

为了研究真实海洋表面马蹄波特性以及对建筑物的作用,通过物理模型实验研究了马蹄波的波形特征参数以及马蹄波对圆柱体的作用。实验中通过对浪高仪采集的波面升高时间历程曲线进行分析得出了不同水深情况下马蹄波的垂向几何特征,并通过快速傅里叶变换得出了马蹄波波幅谱的特征,研究了马蹄波各组成波波幅沿空间的变化从而得出了圆柱存在对马蹄波演化的影响,同时给出马蹄波绕射形成的波面分布和不同频率谐波在圆柱周围的分布,讨论了马蹄波不同于Stokes波对圆柱作用的特征。结果表明,马蹄波波形受水深影响较大,水深越浅,马蹄波的波面形状越接近椭圆余弦波。圆柱体的存在干扰了马蹄波不稳定的增长,使其在接近圆柱时呈下降趋势,导致不稳定幅值最大值的位置提前并且出现在偏离圆柱迎浪点的侧表面,从而使圆柱受到侧向力的作用。     

A new formula for the sea state and structural parameters influencing the stability of homogeneous reshaping berm breakwaters

The berm recession of a reshaping berm breakwater has a very important role for the stability of this kind of structure. Based on a 2D experimental modeling method in a wave flume, the recession of the berm due to sea state and structural parameters has been studied. Irregular waves with a JONSWAP spectrum were used. A total of 215 tests have been performed to cover the impact of sea state conditions such as wave height, wave period, storm duration and water depth at the toe of the structure, and structural parameters such as berm elevation from still water level, berm width and stone diameter on berm recession. In this paper, first a new dimensionless parameter is introduced to evaluate the combined effect of wave height and wave period on berm recession using results of the experimental work. Then, a formula that includes some sea state and structural parameters is derived using the new dimensionless parameter for estimating the berm recession. A comparison is made between the estimated berm recessions by this new formula and formulae given by other researchers to show the preference of using the new dimensionless parameter. The comparison shows that the recession estimated by the new formula has not only a better correlation with the present experimental data, but also has an improved correlation with other experimental results within the range of parameters tested. Outside the range of parameters tested the Lykke Andersen (2006) formula performed best.     

Prediction of Seaward Slope Recession in Berm Breakwaters Using M5' Machine Learning Approach

In the design process of berm breakwaters, their front slope recession has an inevitable rule in large number of model tests, and this parameter being studied. This research draws its data from Moghim's and Shekari's experiment results. These experiments consist of two different 2D model tests in two wave flumes, in which the berm recession to different sea state and structural parameters have been studied. Irregular waves with a JONSWAP spectrum were used in both test series. A total of 412 test results were used to cover the impact of sea state conditions such as wave height, wave period, storm duration and water depth at the toe of the structure, and structural parameters such as berm elevation from still water level, berm width and stone diameter on berm recession parameters. In this paper, a new set of equations for berm recession is derived using the M5' model tree as a machine learning approach. A comparison is made between the estimations by the new formula and the formulae recently given by other researchers to show the preference of new M5' approach.     

马蹄波波形几何参数的试验研究

为了研究真实海洋表面马蹄波的波形特征,通过物理模型试验研究了马蹄波的波形特征参数。研究中通过引入满足共振条件的扰动波成功在试验室内产生了马蹄波,测量和分析了马蹄波的波面升高和水平弧形波峰的几何特征,定义了新的垂向几何参数和水平几何特征参数,给出了不同水深情况下的这些参数的结果,得出了水深对马蹄波几何形态的影响。理论分析了马蹄波的横向结果,并与试验测量结果和弧形处理结果进行了对比。结果表明,马蹄波波形受水深影响较大;水深越浅,马蹄波的波面形状越接近椭圆余弦波,横向波长也越大。