Linear irregular wave generation in a numerical wave tank

In the design of any floating or fixed marine structure, it is vital to test models in order to understand the fluid/structure interaction involved. A relatively inexpensive method, compared to physical model testing, of achieving this is to numerically model the structure and the wave conditions in a numerical wave tank. In this paper, a methodology for accurately replicating measured ocean waves in a numerical model at full scale is detailed. A Fourier analysis of the measured record allows the wave to be defined as a summation of linear waves and, therefore, Airy's linear wave theory may be used to input the wave elevation and associated water particle velocities. Furthermore, a structure is introduced into the model to display the ability of the model to accurately predict wave–structure interaction. A case study of three individual measured waves, which are recorded at the Atlantic marine energy test site, off the west coast of Ireland, is also presented. The accuracy of the model to replicate the measured waves and perform wave–structure interaction is found to be very high. Additionally, the absolute water particle velocity profile below the wave from the numerical model is compared to a filtered analytical approximation of the measured wave at a number of time-steps and is in very good agreement.     

Longshore sorting on a beach under wave action

Sorting of sediment on a beach under wave action takes several forms. Stratified layers of finer and coarser sediment, which depend on wave climate, grain size and beach slope are formed. This complex problem can be simplified by defining the cross-shore and longshore sorting according to the angle between the breaking wave and the coast. In the present study, longshore distribution of sediment as well as corresponding beach profiles was measured in a wave basin. Three-dimensional hydraulic model experiments were performed with regular waves. Eighteen sets of experiments performed in longshore sorting mechanism using two different sand beds. The sorting of the bed material and the formation of armour coats along the beach were defined by grain size distributions and dimensionless parameters for sandy beaches.The rate of sediment transport with grain size sorting was measured in a wave basin. A method introduced sorting process was presented in this study. The sediment rate based on sorting mechanism was also discussed with known methods. It has been found that the non-uniformity of the grain size and hence sorting of the beaches play a very important role in the sand transport due to wave motion in a similar way to the case of steady flow in alluvial channels.     

Using video imagery to reconstruct the 3D intertidal terrain along a beach with multiple cusps

A high-frequency, high-resolution shore-based video monitoring system(VMS) was installed on a macrotidal(tidal amplitude >4 m) beach with multiple cusps along the Quanzhou coast, China. Herein, we propose a video imagery-based method that is coupled with waterline and water level observations to reconstruct the terrain of the intertidal zone over one tidal cycle. Furthermore, the beach cusp system(BCS) was precisely processed and embedded into the digital elevation model(DEM) to more effectiv...     

Measured and modeled wave overtopping on a natural beach

The rate of wave overtopping of a barrier beach is measured and modeled. Unique rate of wave overtopping field data are obtained from the measure of the Carmel River, California, lagoon filling during a time when the lagoon is closed-off with no river inflow. Volume changes are based on measured lagoon height changes applied to a measured hypsometric curve. Wave heights and periods are obtained from directional wave spectra data in 15 m fronting the beach. Beach morphology was measured by GPS walking surveys. Three empirical overtopping models by Van der Meer and Janssen (1995), Hedges and Reis (1998) and Pullen et al. (2007) with differing parameterizations on wave height, period and beach slope and calibrated using extensive laboratory data obtained over plane, impermeable beaches are applied in a quasi-2D manner and compared with the field observations. Three overtopping events are considered when morphology data were available less than 2 weeks prior to the event. The models are tuned to fit the data using a reduction factor to account for beach permeability, berm characteristics, non-normal wave incidence and surface roughness influence. In addition, the run-up model by Stockdon et al. (2006) based on field data is examined and found to underestimate run-up as the calculated values were too small to predict any of the observed overtopping. The three overtopping models performed similarly well with values of 0.72–0.87 for the two narrow-banded wave cases, with an average reduction factor of 0.78. The European model (Pullen et. al., 2007) performed best overall and in particular for the case of the broad-banded, double peaked wave spectrum.     

Determining the onset and strength of unforced wave breaking in a numerical wave tank

A numerical wave tank is used to investigate the onset and strength of unforced wave breaking, and the waves have three types of initial spectra： constant amplitude spectrum, constant steepness spectrum and Pierson-Moscowitz spectrum. Numerical tests are performed to validate the model results. Then, the onset of wave breaking is discussed with geometric, kinematic, and dynamic breaking criteria. The strength of wave breaking, which is always characterized by the fractional energy loss and breaking strength coefficient, is studied for different spectra. The results show how the energy growth rate is better than the initial wave steepness on estimating the fractional energy losses as well as breaking strength coefficient.     

一个二维数值波浪水槽的改进

对Drimer,Agnon及Segre研发的数值波浪水槽(简称DAS),首先通过修正DAS中某些积分计算的错误,建立了第一个修正模型(MDAS1),使得模型更加准确稳定。其次,将DAS模型自由表面线性元近似替换为更为合理准确的三阶元近似,建立了第二个修正模型(MDAS2),使得模型计算的波面更合理可靠。平底水槽中波群的生成及传播算例表明:与DAS结果相比,MDAS1对波面没有显著影响,而采用三阶元的MDAS2对波面有显著影响。与Hansen和Svendsen的实测资料相比较证实了两个修正模型的有效性。     

Extreme value statistics for wave run-up on a natural beach

Statistics of wave run-up maxima have been calculated for 149 35-minutes data runs from a natural beach. During the experiment incident wave height varied from 0.4 to 4.0 m, incident wave period from 6 to 16 s, and beach face slope from 0.07 to 0.20. Four extreme statistics were calculated; the maximum run-up height during each run, the 2% exceedence level of shoreline elevation, the 2% exceedence height for individual run-up peaks, and the 2% exceedence level for swash height as determined by the zero-upcrossing method. These statistics were best parameterized when normalized by the incident significant wave height and plotted against the Iribarren number, ξ = β/(H/L₀)^1/2. The swash data (with set-up removed) showed less scatter than total run-up (with set-up included). For Iribarren number greater than 1.5 the run-up was dominated by the incident frequencies, for lower Iribarren number longer period motions dominated the swash. A reasonable value of wave steepness for a fully developed storm sea is 0.025 so that a storm Iribarren number can be estimated as 6.3 times the beach slope. Using this and an offshore design wave height, the included graphs may provide guidance in determining a design run-up height.     

波浪作用下级配泥沙海滩滩面变化试验研究

砂质海滩的泥沙具有一定的级配,在波浪作用下,滩面泥沙粒径将发生分选,引起海滩质量变化。在水槽中用不同波高和周期的波浪分别对不同级配的沙滩进行作用,探究滩面在波浪外动力作用下的变化规律。结果表明：全级配沙滩在相同波高波浪作用下形成的沙坝型海滩滩型中,破波点向海的区域表层泥沙分选会随波浪周期增大变差;相同周期(T=1.68s)波浪作用下,全级配沙滩在大波高(H=13.2cm)和小波高(H=6.7cm)的波浪作用下分别形成沙坝型和滩肩型海滩,滩面泥沙分选变好;原始沙滩级配与滩面泥沙变化密切相关,同种波浪动力作用下,中细、粗中沙滩沙坝表层泥沙迎波面粗于背波面,粗细沙滩粗颗粒集中在沙坝和滩顶之间。     

Experimental and numerical investigation of viscous effects on solitary wave propagation in a wave tank

Two-dimensional depth-averaged Boussinesq-type equations were presented with the consideration of slowly varying bathymetry and effects of bottom viscous boundary layer. These Boussinesq-type equations were written in terms of the horizontal velocity components evaluated at an arbitrary elevation in the water depth and the free surface displacement. The leading order effects of the bottom boundary layer were represented by a convolution integral in the depth-integrated continuity equation. To test the validity of the theory, a set of laboratory experiments was performed to measure the viscous damping and shoaling of a solitary wave propagating in a wave tank. The time histories of the free surface profiles were measured at several locations along the centerline of the flume. To compare these laboratory data with theoretical results, the two-dimensional Boussinesq-type equations were integrated across the wave tank, resulting in a set of one-dimensional equations, while the side-wall boundary layers were properly considered. The agreement between the experimental data and numerical results was very good. The bottom shear stress formula was also given and its impact on the sediment transport rate was discussed.     

A two-point method for estimating wave reflection over a sloping beach

This work presents a frequency-domain method for estimating incident and reflected waves when normally incident waves’ propagating over a sloping beach in a wave flume is considered. Linear wave shoaling is applied to determine changes of the wave amplitude and phase due to variations of the bathymetry. The wave reflection coefficient is estimated using wave heights measured at two fixed wave gauges with a distance. The present model demonstrates a high capacity of estimating reflection and shoaling coefficients from synthetic wave-amplitude data. Sensitivity tests for the present model due to measurement errors of wave amplitudes and distance of two probes can more accurately predict the reflection coefficients. The measurement error of wave amplitude affects more significantly than measurement error of distance of two probes on calculating reflection coefficient of waves over a sloping bed.     

Mean drift forces on arrays of axisymmetric structures in a wave tank

An approximate method is presented for calculating drift forces on arrays of vertically axisymmetric bodies in a wave tank. It is assumed that the wave scattering properties of an isolated element and of the array in the open sea are known. The procedure described allows the open-sea results to be post-processed to give good estimates of drift forces when a structural array is placed in a wave tank. For the particular case of an array of vertical circular cylinders extending throughout the depth, the method is compared with accurate results from the full linear problem for scattering by the array both when the array is in the tank and when it is in the open sea. The results show how the mean forces on the array when in the tank may differ considerably from those experienced in the open sea.     

数值水槽内的阻尼消波和波浪变形计算

采用时域内对波面运动位置追踪的边界元方法,建立了一种非线性波浪变形计算的三维数值模式,并借助Spongelayer阻尼消波和Sommerfeld放射条件相匹配的处理方式,开发了一条三维非线性波的数值造波水槽,进而对水槽内的Stokes波进行了波浪变形计算。     

An evaluation of wave propagation simulations over a barred beach with a Boussinesq-type model

The FUNWAVE model is used for simulating simulation of monochromatic and irregular wave propagation in a channel with a bar-trough profile. FUNWAVE is based upon the extended Boussinesq equations. The study aims to analyze the model's performance when simulating shoaling, wave breaking and nonlinear interactions that are present in nearshore wave propagation. For that, high-order time domain statistics (root mean-square wave height, skewness, asymmetry and the kurtosis) of the model simulations and of the observations were compared along the whole channel. Also, a frequency domain analysis including standard spectral analysis and the bispectrum was carried out in selected points of the flume. The evaluation included the role of the wave breaking internal model parameters. The main conclusion is that, in general, the one-dimensional version of FUNWAVE simulates quite well the nonlinear transformation of a wave over a bottom with a bar-tough profile, for both regular and irregular wave conditions. The model reproduces the transformation of the wave shape, specially the increasing sharper wave crests and flatter troughs and also the lack of vertical symmetry with crests pitching forward, as it propagates along the domain. However, some differences persist after wave breaking, mainly due to the nature of the wave-breaking module. In this module, the energy dissipation is induced by the increase of viscosity, a rather simple mechanism, without the modification of the wave shape. Also, the energy dissipation develops in a smooth way which is appropriated for spilling breaking waves, but not for plunging breaking waves where the dissipation starts more abruptly.     

Wave tank and bench-top control testing of a wave energy converter

An increasing number of experiments are being conducted to study the design and performance of wave energy converters. Often in these tests, a real-time realization of prospective control algorithms is applied in order to assess and optimize energy absorption as well as other factors. This paper details the design and execution of an experiment for evaluating the capability of a model-scale WEC to execute basic control algorithms. Model-scale hardware, system, and experimental design are considered, with a focus on providing an experimental setup capable of meeting the dynamic requirements of a control system. To more efficiently execute such tests, a dry bench testing method is proposed and utilized to allow for controller tuning and to give an initial assessment of controller performance; this is followed by wave tank testing. The trends from the dry bench test and wave tank test results show good agreement with theory and confirm the ability of a relatively simple feedback controller to substantially improve energy absorption. Additionally, the dry bench testing approach is shown to be an effective and efficient means of designing and testing both controllers and actuator systems for wave energy converters.     

Linear and nonlinear irregular waves and forces in a numerical wave tank

A time-domain higher-order boundary element scheme was utilized to simulate the linear and nonlinear irregular waves and diffractions due to a structure. Upon the second-order irregular waves with four Airy wave components being fed through the inflow boundary, the fully nonlinear boundary problem was solved in a time-marching scheme. The open boundary was modeled by combining an absorbing beach and the stretching technique. The proposed numerical scheme was verified by simulating the linear regular and irregular waves. The scheme was further applied to compute the linear and nonlinear irregular wave diffraction forces acting on a vertical truncated circular cylinder. The nonlinear results were also verified by checking the accuracy of the nonlinear simulation.     

Mean drift forces on an articulated column oscillating in a wave tank

An analytical solution is presented for calculating the regular wave induced respones of an articulated column in a wave tank. Extension of the procedure leads to calculation of second order mean drift forces and moments. Hydrodynamic interaction between a cylindrical column and the parallel walls of the tank is shown theoretically to be highly significant and experimental data are presented to corroborate this finding.     

Statistical simulation of wave climate and extreme beach erosion

Recent developments in extreme values modelling have been used to develop a framework for determining the coastal erosion hazard on sandy coastlines. This framework quantitatively reproduced the extreme beach erosion volumes obtained from field measurements at Narrabeen Beach, Australia. This encouraging finding was achieved using Kriebel and Dean's [Kriebel, D.L. and Dean, R.G., 1993. Convolution method for time-dependent beach profile response. Journal of Waterway, Port, Coastal and Ocean Engineering, 119(2): 204–226.] simple beach erosion and accretion model. The method includes allowances for joint probability between all basic erosion variates including; wave height, period and direction, event duration, tidal anomalies and event spacing. A new formulation for the dependency between wave height and period has been developed. It includes the physical wave steepness limitation. Event grouping, where significantly more erosion can occur from two closely spaced storms is handled by temporally simulating the synthetic wave climate and the resulting beach erosion and accretion.     

Field experiment on secondary wave generation on a barred beach and the consequent evolution of energy dissipation on the beach face

A field experiment, conducted on a sandy, barred beach situated on the southern part of the French Atlantic coastline, allowed us to investigate the formation of secondary waves when a moderate (significant wave height of about 0.8 m in 3.7-m water depth), long (11–14 s) narrowband swell propagated over an intertidal ridge and runnel system, in both breaking and nonbreaking conditions. Field evidence using higher spectral analysis is given for the sum interactions between pairs of waves at the primary spectral peak and the consequent energy transfer to nearly harmonic wave components. Although wave breaking appears to weaken the strength of nonlinear couplings, the generation of high-frequency energy is hardly affected by wave breaking. The phenomenon of harmonic decoupling, which takes place behind the bar, cannot be completely ascribed to the increase in water depth and the so-called deshoaling effect. Indeed, the variation in the values of the maximum bicoherence was very moderate when no breaking occurred. Finally, the doubling in the number of wave crests and the consequent decrease in the significant wave period delay the energy dissipation on the beach face.     

三维完全非线性波浪水槽的数值模拟

用有限元求解拉普拉斯方程,建立了三维完全非线性数值波浪水槽.跟踪流体自由表面的方法为满足完全非线性自由表面条件的半拉格朗日法,对离散单元采用20节点的六面体二次等参数单元.并把数值计算结果与水面初始升高产生箱体内流体运动解析解和二阶斯托克斯波理论解进行了对比,结果表明该模型是稳定的、守恒的,能精确模拟非线性波浪的产生和传播.