Establishment of Numerical Wave Flume Based on the Second-Order Wave-Maker Theory

With growing computational power, the first-order wave-maker theory has become well established and is widely used for numerical wave flumes. However, existing numerical models based on the first-order wave-maker theory lose accuracy as nonlinear effects become prominent. Because spurious harmonic waves and primary waves have different propagation velocities, waves simulated by using the first-order wave-maker theory have an unstable wave profile. In this paper, a numerical wave flume with a piston-type wave-maker based on the second-order wave-maker theory has been established. Dynamic mesh technique was developed. The boundary treatment for irregular wave simulation was specially dealt with. Comparisons of the free-surface elevations using the first-order and second-order wave-maker theory prove that second-order wave-maker theory can generate stable wave profiles in both the spatial and time domains. Harmonic analysis and spectral analysis were used to prove the superiority of the second-order wave-maker theory from other two aspects. To simulate irregular waves, the numerical flume was improved to solve the problem of the water depth variation due to low-frequency motion of the wave board. In summary, the new numerical flume using the second-order wave-maker theory can guarantee the accuracy of waves by adding an extra motion of the wave board. The boundary treatment method can provide a reference for the improvement of nonlinear numerical flume.     

Efficient computation method for two-dimensional nonlinear waves

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Numerical simulations using momentum source wave-maker applied to RANS equation model

For Navier-Stokes equation model using the VOF scheme, Lin and Liu (Lin, P. and Liu, P.L.-F. (1999). Internal wave-maker for Navier-Stokes equations models. J. Waterw. Port Coast. Ocean Eng., 125 (4), 207–215.) developed an internal wave-maker method for which a mass source function of the continuity equation was used to generate target wave trains. Using this internal wave-maker method, various numerical experiments have been conducted without any problems due to waves reflected by a wave-maker. In this study, an internal wave-maker method using a momentum source function was proposed. Various numerical simulations in two and three dimensions were performed using the momentum source wave-maker applied to the RANS equation model in a CFD code, FLUENT. To verify their applicability in 2 dimensions, the computational results obtained using the momentum source wave-maker in a channel of constant depth were compared with the results obtained by using the mass source wave-maker and with the analytical solutions. And the results of the present numerical simulations of hydraulic experiments, which represent nonlinear waves on a submerged shoal and breaking waves on a plane beach, were compared with measurements. The comparisons showed good agreements between them. To see their applicability into 3-dimensional cases, the present results in a basin of constant depth were compared with the analytical solutions, and they agreed well with each other. In addition, vertical variation of longshore current was presented by using the 3-dimensional simulation results.     

基于格子Boltzmann方法的斜坡堤越浪数值模拟研究

准确确定越浪量对于斜坡堤设计有重要意义。利用格子Boltzmann方法(LBM),并采用主动吸收式速度入口造波、出流边界消波、VOF方法追踪自由表面以及静态Smagorinsky模型模拟紊流运动,建立二维数值波浪水槽,对光滑斜坡堤上规则波与不规则波越浪进行数值模拟。模拟结果与试验值及其他数值模型结果比较表明,二维LBM数值波浪水槽具有模拟斜坡堤越浪的能力,但对于破碎较为剧烈的越浪过程模拟,该模型还存在一定的不足,未来可从提高自由表面模型精度等方面进一步改善其性能。     

Design wave method for the extreme horizontal slow-drift motion of moored floating platforms

The present study introduces a design wave method for estimating the extreme horizontal slow-drift motion of moored floating offshore platforms under extreme conditions. Here, the design wave refers to an irregular incident wave of short duration that induces the extreme response of the desired return period. The present method is composed of the following four steps: linearization of the dynamic system, probabilistic analysis of the second-order Volterra series, generation of the irregular design waves, and the fully-coupled nonlinear simulations. For generating the design waves, two different conditioning methods are presented and compared: the conditioning of the extreme response amplitude and the conditioning of the most likely extreme response profile. The procedure was applied to a deep-water semi-submersible, and the results appeared to be promising compared to the full-length nonlinear simulations.     

An Irregular Wave Maker of Active Absorption with VOF Method

A numerical irregular wave flume with active absorption of re-reflected waves is simulated by use of volume of fluid （VOF） method. An active ＇absorbing wave-maker based on linear wave theory is set on the left boundary of the wave flume. The progressive waves and the absorbing waves are generated simultaneously at the active wave generating-absorbing boundary. The absorbing waves are generated to eliminate the waves coming back to the generating boundary due to reflection from the outflow boundary and the structures. SIRW method proposed by Frigaard and Brorsen （1995） is used to separate the incident waves and reflected waves. The digital filters are designed based on the surface elevation signals of the two wave gauges. The corrected velocity of the wave-maker paddle is the output from the digital filter in real time. The numerical results of regular and irregular waves by the active absorbing-generating boundary are compared with the numerical results by the ordinary generating boundary to verify the performance of the active absorbing-generator boundary. The differences between the initial incident waves and the estimated incident waves are analyzed.     

Separation of Waves by Interpolation Method

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The experimental study on infra-gravity wave

A series of experiments were conducted in a super-wave flume (300 m×5 m×5.2 m) to examine the low-frequency motion induced by waves with different incident steepness, sloping gradients and normalized frequency (sideband space). Two kinds of waves including initial uniform wave train and modulated wave train (one carrier with a pair of sidebands) are utilized for incident wave conditions. From the experimental results, it is found that for a given slope gradient the infra-gravity wave component decreases as wave nonlinearity increases and frequency downshift is a predominant factor. Furthermore, the magnitude of low-frequency component decreases with slope gradients for a given initial wave condition. In addition, the maximum value of low-frequency motion is found to be close to the normalized frequency, δ=1.0.     

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.     

Effect of wave nonlinearity on fatigue damage and extreme responses of a semi-submersible floating wind turbine

Floating wind turbine has been the highlight in offshore wind industry lately. There has been great effort on developing highly sophisticated numerical model to better understand its hydrodynamic behaviour. A engineering-practical method to study the nonlinear wave effects on floating wind turbine has been recently developed. Based on the method established, the focus of this paper is to quantify the wave nonlinearity effect due to nonlinear wave kinematics by comparing the structural responses of floating wind turbine when exposed to irregular linear Airy wave and fully nonlinear wave. Critical responses and fatigue damage are studied in operational conditions and short-term extreme values are predicted in extreme conditions respectively. In the operational condition, wind effects are dominating the mean value and standard deviation of most responses except floater heave motion. The fatigue damage at the tower base is dominated by wind effects. The fatigue damage for the mooring line is more influenced by wind effects for conditions with small wave and wave effects for conditions with large wave. The wave nonlinearity effect becomes significant for surge and mooring line tension for large waves while floater heave, pitch motion, tower base bending moment and pontoon axial force are less sensitive to the nonlinear wave effect. In the extreme condition, linear wave theory underestimates wave elevation, floater surge motion and mooring line tension compared with fully nonlinear wave theory while quite close results are predicted for other responses.     

Efficient Generation of Freak Waves in Laboratory

In the present study,Kriebel's method is improved to generate freak waves in laboratory.The improved method superposes a random wave train with two transient wave trains to simulate freak wave events in a wave tank.The freak waves are more nonlinear than what generated with Kriebel's method of the same energy.It can also generate freak waves to satisfy all the qualifications of the adopted definition with less energy than Kriebel's and can hardly influence the significant wave height.     

Analysis of hydrodynamic behaviors of gravity net cage in irregular waves

Based on the lumped-mass method and rigid-body kinematics theory, a mathematical model of a gravity cage system attacked by irregular waves is developed to simulate the hydrodynamic response of cage system, including the maximum tension of mooring lines and the motion of float collar. The normalized response amplitudes (response amplitude operators) are calculated for the cage motion response in heave and surge, and the mooring line tension response, in regular waves. In addition, a statistical approach is taken to determine the motion and tension transfer functions in irregular waves. In order to validate the numerical model of a gravity cage attacked by irregular waves, numerical predictions have been compared with the experimental observations in the time and frequency domain. The effect of wave incident angle on the float collar motion, mooring line tension and net volume reduction of the gravity cage system in irregular waves is also investigated. The results show that at high frequencies, the cage system has no significant heave motion. It tends to contour itself to longer waves. The variation amplitude of mooring line forces decreases as the wave frequency increases. With the increasing of wave incident angle, the horizontal displacement of the float collar increases.     

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.     

数值波浪水槽中完全非线性浅水波仿真特性研究

应用基于势流理论的时域高阶边界元方法,建立一个完全非线性的三维数值波浪水槽,通过实时模拟推板造波运动的方式产生波浪。通过混合欧拉-拉格朗日方法和四阶Runge-Kutta方法更新自由水面和造波板的瞬时位置。利用所建模型分别模拟了有限水深波和浅水波,与试验结果、相关文献结果和浅水理论结果吻合较好,且波浪能够稳定传播。系统地讨论造波板的运动圆频率、振幅和水深等对波浪传播和波浪特性的影响,并对波浪的非线性特性进行分析,研究发现造波板运动频率、运动振幅以及水深均将对波浪形态和波浪非线性产生显著影响。结果为真实水槽造波机的运动控制以及波浪生成试验提供了依据,便于实验室设置更合理的参数来准确模拟不同条件下的波浪。     

Modeling of propagation and transformation of transient nonlinear waves on a current

A novel theoretical approach is applied to predict the propagation and transformation of transient nonlinear waves on a current. The problem was solved by applying an eigenfunction expansion method and the derived semi-analytical solution was employed to study the transformation of wave profile and the evolution of wave spectrum arising from the nonlinear interactions of wave components in a wave train which may lead to the formation of very large waves. The results show that the propagation of wave trains is significantly affected by a current. A relatively small current may substantially affect wave train components and the wave train shape. This is observed for both opposing and following current. The results demonstrate that the application of the nonlinear model has a substantial effect on the shape of a wave spectrum. A train of originally linear and very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short distance from an initial position. The discrepancies between the wave trains predicted by applying the linear and nonlinear models increase with the increasing wavelength and become significant in shallow water even for waves with low steepness. Laboratory experiments were conducted in a wave flume to verify theoretical results. The free-surface elevations recorded by a system of wave gauges are compared with the results provided by the nonlinear model. Additional verification was achieved by applying a Fourier analysis and comparing wave amplitude spectra obtained from theoretical results with experimental data. A reasonable agreement between theoretical results and experimental data is observed for both amplitudes and phases. The model predicts fairly well multi-peak spectra, including wave spectra with significant nonlinear wave components.     

随机波浪下泰勒离散系数的时域解

利用Wolk提出的粒子追踪方程,通过等分频率法划分不规则波谱,利用MATLAB做粒子运动模拟计算,得到无因次化泰勒离散系数K/D随时间t变化的曲线;通过与Huang等得到的P-M谱的泰勒离散系数K/D计算结果比较证明了本计算方法的可靠性。采用该方法研究了不规则波条件下,波序列(同一谱型不同波面序列)和谱型(谱峰周期、有效波高、谱峰升高因子)对波浪离散系数的影响;计算结果表明:同一谱型不同波序列对泰勒纵向离散系数稳定值和稳定时间无影响;不规则波谱峰周期越大,纵向离散系数K/D越小,稳定时间越短;有效波高越大,纵向离散系数K/D越大,稳定时间越长;谱峰升高因子越大,泰勒离散系数K/D越大,稳定时间越长;与规则波相比,不规则波的泰勒离散系数K/D的值略小10%~30%。     

Estimation of Design Wave Height for the Waters around the Korean Peninsula

Long term wave climate of both extreme wave and operational wave height is essential for planning and designing coastal structures. Since the field wave data for the waters around Korean peninsula is not enough to provide reliable wave statistics, the wave climate information has been generated by means of long-term wave hindcasting using available meteorological data. Basic data base of hindcasted wave parameters such as significant wave height, peak period and direction has been established continuously for the period of 25 years starting from 1979 and for major 106 typhoons for the past 53 years since 1951 for each grid point of the North East Asia Regional Seas with grid size of 18 km. Wind field reanalyzed by European Center for Midrange Weather Forecasts (ECMWF) was used for the simulation of waves for the extratropical storms, while wind field calculated by typhoon wind model with typhoon parameters carefully analyzed using most of the available data was used for the simulation of typhoon waves. Design wave heights for the return period of 10, 20, 30, 50 and 100 years for 16 directions at each grid point have been estimated by means of extreme wave analysis using the wave simulation data. As in conventional methodsi of design criteria estimation, it is assumed that the climate is stationary and the statistics and extreme analysis using the long-term hindcasting data are used in the statistical prediction for the future. The method of extreme statistical analysis in handling the extreme events like typhoon Maemi in 2003 was evaluated for more stable results of design wave height estimation for the return periods of 30–50 years for the cost effective construction of coastal structures.     

Comparison of experimental irregular water wave elevation and kinematic data with new hybrid wave model predictions

Surface water wave elevations and kinematics from four unidirectional irregular wave trains, with a Pierson and Moskowitz or JONSWAP random wave spectrum, were measured in the laboratory using resistance wave probes and a laser Doppler anemometer. The wave elevation data, velocity time series, extreme (largest) wave horizontal velocity profiles and extreme wave acceleration fields are compared with the predictions of a new wave kinematics model, named the hybrid wave model. Irregular waves are commonly viewed as the summation of many linear wave components of different frequencies, but more accurate predictions of downstream surface elevations (wave evolution) and wave kinematics are attained by considering the non-linear interactions among wave components. The hybrid wave model incorporates these non-linear wave component interactions, and its wave evolution predictions and kinematics estimates are compared with laboratory measurements in this study. Linear random wave theory, Wheeler stretching and linear extrapolation wave kinematic prediction techniques are also compared. Comparisons between measurements and hybrid wave model estimates demonstrate its improved capability to predict velocity and acceleration fields and wave evolution in two-dimensional irregular waves.     

波浪谱形对不规则波数值模拟的影响

通过数值模拟分析了波浪谱形对不规则波浪数值模拟结果的影响.采用不同参数的JONSWAP谱模拟入射波要素,基于抛物型缓坡方程模拟不规则波浪的传播,分析了波浪谱形状对波浪数值模拟结果的影响.结果表明,采用抛物型缓坡方程模拟不规则波浪时,入射波浪谱形对模拟结果影响不明显;但由于模型中非线性项的影响,采用不规则波模拟的波高分布和采用规则波模拟的结果略有差别.     

A Calculation Method for Incidence and Reflection of Irregular Waves Along Seawalls

Some researches have been made in this aspect.In the method by Walton Jr.(1992),incidentwaves are supposed to be the overlapping result of M component waves with different frequencies whichmay take different directions,the direction of incident waves should be available in advance,but in fact thedirection of incident waves is not available.In our study,incident waves are supposed to be composed ofM overlapping component waves with different frequencies,and different frequencies have different direc-tions.Based on the irregular wave reflection theory,the calculation formulas of wave direction,complexamplitude of incident waves,and complex amplitude of reflected waves in surface which are composed ofcomponent waves are derived by means of discrete Fourier transform.Then,the frequency spectra of inci-dent waves and reflected waves and the reflection coefficient of waves with corresponding frequencies areobtained.Verification of the method and the calculation results from in-situ measured data indicate thatt