Exact solution and approximate solution of irregular wave radiation stress for non-breaking wave

Wave radiation stress is the main driving force of wave-induced near-shore currents. It is directly related to the hydrodynamic characteristics of near-shore current whether the calculation of wave radiation stress is accurate or not. Irregular waves are more capable of reacting wave motion in the ocean compared to regular waves.Therefore, the calculation of the radiation stress under irregular waves will be more able to reflect the wave driving force in the actual near-shore current. Exact solution and approximate solution of the irregular wave radiation stress are derived in this paper and the two kinds of calculation methods are compared. On the basis of this, the experimental results are used to further verify the calculation of wave energy in the approximate calculation method. The results show that the approximate calculation method of irregular wave radiation stress has a good accuracy under the condition of narrow-band spectrum, which can save a lot of computing time, and thus improve the efficiency of calculation. However, the exact calculation method can more accurately reflect the fluctuation of radiation stress at each moment and each location.     

强非线性规则波在防波堤上爬高公式研究

为了研究波浪非线性对爬高的影响,解决防波堤等工程设计的实际问题,通过对数学模型试验、物理模型试验、规范公式得到的防波堤波浪爬高对比分析,分析了非线性主要影响参数厄塞尔数、相对水深和波陡对波浪爬高的影响规律,指出规范公式计算时存在的缺陷,并对其计算公式、适用范围进行修正、拟合,得到了强非线性规则波浪爬高的计算方法,可适用于斜坡堤断面的波浪爬高计算,与物理模型试验和数学模型试验结果对比表明,新的波浪爬高计算公式具有较好的计算精度,研究结果可为防波堤等实际工程设计提供重要参考。     

Experimental Research on Wave Transmission over Submerged Rubble Mound Breakwaters

This paper discusses some previous, and presents some new experimental results on wave transmission over submerged breakwaters. The objective of this study is to evaluate wave transmission coefficient and develop a two-dimensional （2D） model as an improvement to the existing wave transmission coefficient models. Factors which affect wave transmission over stbmerged breakwaters are discussed through a series of laboratory experiments. Basic recommendations for evaluation and design of submerged rubble-monud breakwaters are presented. From the test results, a calculation formula of wave transmission coefficient is proposed.     

波浪的非线性显式弥散关系

波浪的非线性弥散关系在应用于求解波浪的变形问题时很不方便，需要与含非线性效应的缓坡方程一起进行迭代运算，往往导致数值计算的计算量太大，计算过于复杂。采用显式形式表达非线性弥散关系，可以克服上述缺点，大为简化波浪变形数值计算的计算量。本文通过将现有的非线性弥散关系进行分析比较，给出了一个更为一般的非线性弥散关系及其显式表达式，经比较可知，该显式弥散关系与相对应非线性弥散关系吻合的很好。本文最后用该显式结合含弱非线性效应的缓坡方程，对复式浅滩地形上的波浪折射绕射进行了计算。结果表明，考虑弱非线性可以得出与实验数据更为相符的结果，而采用显式弥散关系可以有效提高计算效率,在波浪的非线性计算中不失为一种切实有效的方法。     

基于高阶边界元的三维数值波浪港池--波浪破碎的模拟

在势流理论的框架内,采用高阶边界元方法和混合欧拉-拉格朗日法,实现了对三维波浪破碎过程的数值模拟.数值模型使用可调节时间步长的基于二阶显式泰勒展开的混合欧拉-拉格郎日时间步进来求解自由表面的演化过程.在所使用的边界元方法中,采用16节点三次滑移四边形单元来表示,这种单元在单元内具有高阶的精度同时在单元之间具有良好的连续性.给出了孤立波的传播和周期性非线性波浪沿缓坡传播的计算结果,表明数值模型具有良好的稳定性.     

Numerical Model of Internal Solitary Wave Evolution on Impermeable Variable Seabed in A Stratified Two-Layer Fluid System

1.IntroductionIn mathematics and physics,a soliton is a self-reinforcing solitary wave caused by nonlinear ef-fectsinthe medium.Solitons are found in many physical phenomena(Chou and Shih,1996;Chouand Quyang,1999;Chouet al.,2003;Chenet al.,2004;Wang,2004;…     

Experimental Research on Wave Transmission over Submerged Rubble-Mound Breakwaters

This paper discusses some previous, and presents some new experimental results on wave transmission oversubmerged breakwaters. The objective of this study is to evaluate wave transmission coefficient and develop two-dimensional (2D) model as an improvement to the existing wave transmission coefficient models. Factors which affect wave transmission over submerged breakwaters are discussed through series of laboratory experiments. Basic recommendations for evaluation and design of submerged rubble-monud breakwaters are presented.From the test results, calculation formula of wave transmission coefficient is proposed.     

Fixed-frequency Stokes wave expansion

The study describes a new fixed-frequency Stokes wave theory that differs from previous Stokes wave theories that fix the wave number. The present wave expansion analytically reveals that the wavelength increases with wave height and exceeds than the wavelength obtained by linear wave theory. A method proposed to comparably transform the wave celerity of Fenton's [Fenton, J.D., 1985. A fifth-order Stokes theory for steady waves. Journal of Waterway, Port, Coastal and Ocean Engineering 111, 216–234.] wave theory to the present one. A direct calculation of the wavelength is introduced for practical solutions, avoiding the need to solve a nonlinear equation using an iterative numerical method.     

Predictions on Irregular Wave run-up and Overtopping

A series of hydraulic model tests are carried out to investigate random wave run-up and overtopping on smooth, impermeable single slope and composite slope. Based on analysis of the influences of wave steepness, structure slope, incident wave angle, width of the berm and water depth on the berm and the wave run-up, empirical formulas for wave run-up on dike are proposed. Moreover, empirical formula on estimating the wave run-up on composite slope with multiple berms is presented for practical application of complex dike cross-section. The present study shows that the influence factors for wave overtopping are almost the same as those for wave run-up and the trend of the wave overtopping variation with main influence parameters is also similar to that for wave run-up. The trend of the wave overtopping discharge variations can be well described by two main factors, i.e. the wave run-up and the crest freeboard of the structure. A new prediction method for wave overtopping discharge is proposed for random waves. The proposed prediction formulas are applied to case study of over forty cases and the results show that the prediction methods are good enough for practical design purposes.     

基于高阶边界元的三维数值波浪港池

初步建立了一个基于高阶边界元的三维数值波浪港池,港池具有造波和消波功能。采用高阶边界元16节点四边形单元和基于二阶显式泰勒展开的混合欧拉-拉格朗日时间步进求解带自由表面的完全非线性势流方程。模型中对于影响数值精度的问题作了细致的处理。数值计算结果表明本港池可以用来模拟非线性波浪的传播,具有很高的数值精度和稳定性。     

Analytical determination of nearshore wave height variation due to refraction shoaling and friction

Explicit wave formulae derived from the dispersion relation for linear waves are used to find an analytical solution to the problem of wave height variation on a simple topography; i.e. topographies with incrementally constant slope and straight parallel contours. The solution accounts for shoaling, refraction and frictional dissipation and will be sufficiently accurate for practical purposes considering the simplifying assumptions that are necessary for treatment of this problem by any method. The solution is simple enough to be handled on a personal calculator and has the advantage over numerical solutions that it can be solved for other parameters, for example to give friction factors from observed wave height data. The last chapter contains updated formulae for wave friction factors over movable beds.     

Boundary element modeling of multidirectional random waves in a harbor with partially reflecting boundaries

A numerical model is presented for the prediction of the wave field due to the diffraction of directional random waves in a harbor of arbitrary shape with partially reflecting boundaries. The water depth is assumed uniform and the method is based upon the superposition of diffraction solutions for monochromatic waves obtained by a two-dimensional boundary integral equation approach. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The present numerical model has been validated through comparisons with previous experimental data and theoretical results for both regular and random wave diffraction by offshore breakwaters and in harbors. Good agreement was obtained in all cases. Based on these comparisons it is concluded that the present numerical model is an accurate and efficient tool to predict the wave field inside a harbor or around a breakwater in many practical applications.     

海湾内台风波浪的分析

海湾内台风波浪的计算合理与否，直接影响互海洋工程所需的设计波浪参数的精确度及施工和使用期间的安全及合理造价。本文通过对广东省两个不同海湾内不同位置台风波浪计算实例的剖析，说明在特定地理条件下，波能变化的复杂性，并分析了具体的地理位置，不同的湾风台风波浪具有的不同变化特征。     

一种计算有限水深波能功率的新方法

海洋波浪能平均功率的准确计算是波浪能开发和利用的基础。实践中,波浪能转换装置一般安装在有限水深区域。对于随机波,只有当详尽的波浪谱已知的时候,有限水深区的波能功率才能被准确计算出来。由于种种原因,实践中波浪的实测数据大多以散点图或有义波高和统计波周期的形式给出,而波浪谱信息有时则很难获得。基于这种情况,传统上人们利用无限水深条件下的相关公式来估算有限水深区域的波能功率,但这种做法会造成较大的误差。本研究显示,对于50 m水深的理论波谱JONSWAP谱来说该误差高达14.6%。为了提高波能功率计算的准确性,本文提出了一种基于能量频率的一阶和二阶近似算法,可以在未知波浪谱的情况下较为准确地计算不同水深时的波能功率。针对两种理论波浪谱的计算结果表明,本方法在计算有限带宽内的波能功率时计算误差低于2.8%。     

波浪增减水的实用数学模型及其数值模拟

提出了一种模拟近岸区波浪增减水的实用数学模型.首先采用考虑波能损失的抛物型缓坡方程数值模拟波浪破碎引起的波浪复振幅变化,接着根据计算得到的波浪复振幅,采用一种新的辐射应力公式计算辐射应力分量,然后采用深度平均方程计算波浪破碎产生的增减水.采用该模型对规则波和不规则波破碎引起的增减水进行了数值模拟,数值模拟结果与实验结果吻合良好,表明该模型可有效模拟近岸区由于波浪破碎引起的增减水.     

珊瑚礁地形上破碎波高试验研究

破碎波高是珊瑚礁地形上波浪演化的重要参数之一,对工程安全和海岸变形具有重要影响。通过二维波浪水槽,对珊瑚礁地形上破碎波高进行试验研究,分析破碎波高随波陡、礁坪水深以及礁前斜坡坡度的变化。研究表明,相对破碎波高随相对礁坪水深的增大而增大,随入射波陡的增大而减小,但礁前斜坡坡度对相对破碎波高的影响并不明显。通过引入相对礁坪水深,将经典的破碎波高计算公式拓展至珊瑚礁地形上破碎波高的计算。该公式计算值与前人的试验值进行对比验证,吻合较好。研究成果可为工程实践和数值模拟提供参考与借鉴。     

Numerical Simulation of Wave Height and Wave Set-Up in Nearshore Regions

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, and then a practical method for the simulation of wave height and wave set-up in nearshore regions is presented. The variation of the complex wave amplitude is numerically simulated by use of the parabolic mild slope equation including the effect of wave energy dissipation due to wave breaking. The components of wave radiation stress are calculated subsequently by new expressions for them according to the obtained complex wave amplitude, and then the depth-averaged equation is applied to the calculation of wave set-up due to wave breaking. Numerical results are in good agreement with experimental data, showing that the expression for the energy dissipation factor is reasonable and that the new method is effective for the simulation of wave set-up due to wave breaking in nearshore regions.     

Full wave solution for hydrodynamic behaviors of pile breakwater

Rayleigh expansion is used to study the water-wave interaction with a row of pile breakwater in finite water depth. Evanescent waves, the wave energy dissipated on the fluid resistance and the thickness of the breakwater are totally included in the model. The formulae of wave reflection and transmission coefficients are obtained. The accuracy of the present model is verified by a comparison with existing results. It is found that the predicted wave reflection and transmission coefficients for the zero order are all highly consistent with the experimental data (Hagiwara, 1984; Isaacson et al., 1998) and plane wave solutions (Zhu, 2011). The losses of the wave energy for the fluid passing through slits play an important role, which removes the phenomena of enhanced wave transmission.     

Analytical and Experimental Studies on Hydrodynamic Performance of Semi-Immersed Jarlan-Type Perforated Breakwaters

The present study proposes a new semi-immersed Jarlan-type perforated breakwater including a perforated front wall, a solid rear wall, and a horizontal perforated plate connecting the lower tips of the two walls. An analytical solution is developed to estimate the hydrodynamic performance of the new breakwater. The analytical solution is confirmed by solutions for special cases, an independently developed multi-domain boundary element method solution and experimental data. Numerical examples based on the analytical solution indicate that compared with previous semi-immersed breakwaters, the new breakwater may have better wave-absorbing performance and smaller wave forces. Some useful results are presented for practical designs of semi-immersed Jarlan-type perforated breakwaters.     

Large Eddy Simulation for Wave Breaking in the Surf Zone

In this paper, (he large eddy simulation method is used combined with the marker and cell method to study the wave propagation or shoaling and breaking process. As wave propagates into shallow water, the shoaling leads lo the increase of wave height, and then at a certain position, the wave will be breaking. The breaking wave is a powerful agent for generating turbulence, which plays an important role in most of the fluid dynamic processes throughout the surf zone, such as transformation of wave energy, generation of near-shore current and diffusion of materials. So a proper numerical model for describing the turbulence effect is needed. In this paper, a revised Smagorinsky subgrid-scale mode! is used to describe the turbulence effect. The present study reveals that the coefficient of the Smagorinsky model for wave propagation or breaking simulation may be taken as a varying function of the water depth and distance away from the wave breaking point. The large eddy simulation model presented in this pape