时间不连续压力序列的傅立叶分析方法

提出了一种用于对不连续压力采样序列的傅立叶分析方法.此方法将周期函数展开成傅立叶级数,但在数值积分时取函数周期内有采样值的区间作为积分域,然后求解线性方程组得到傅立叶级数的系数值.为了检验本方法的有效性,利用此方法对解析函数进行了拟合,当一个周期内的取样时间大于1/2周期时,利用此方法能够得到满意的结果.利用实验方法研究了波浪作用下截断圆柱表面的压力分布.在波浪作用下静水面附近的测点在露出水面时没有压力值.利用所提出的傅立叶分析方法对略低于静水面位置的实测压力进行了分析,拟合结果与实测结果吻合很好,说明此方法在处理物理模型实验中间断采样得到的数据是有效的.利用数值方法对波浪压力进行了计算,并将一阶和二阶波压力的数值结果与实测值进行了比较.     

Standing wave pressures on walls

The pressure variations exerted on a vertical wall in a constant water depth are computed from the calculation of a short-crested wave system using the Fourier series approximation method. The numerical results have been compared with experimental results from literature. The comparison with the linear solution of the present theory gives a good estimate for the variation of dynamic pressures. The double peak formation in the experimental results for pressure curves at still water level and at the bottom for the steeper waves was not observed for the linear case. In the case of surface elevation, deviations with the third order perturbation results are observed for higher waves. In addition, deviations are also observed within the elevation results for higher waves.     

Effect of a base structure on the wave forces and pressures on a vertical cylinder

The influence of a square base placed at the bottom of a vertical cylinder on the wave induced forces and pressures on the cylinder is reported in this paper. In order to carry out this study, initially, the two dynamic variables on the cylinder in the absence of the base was studied so as to make sure the quality of measurements is satisfactory. The experimental results are compared with MacCamy and Fuchs' theory and the agreement found good.     

Hydrodynamic coefficients for inclined cylinders

The wave induced dynamic pressures around a circular cylinder of diameter 0.2 m due to regular waves were measured in a wave flume in a water depth of 1 m and in a wave basin in a water depth of 3 m. The experimental investigations were carried out with the cylinder inclined along and against the direction of wave propagation. The least-squares technique was employed to evaluate the coefficients of drag (C_D) and inertia (C_M) from the sectional force time histories obtained by integrating the measured circumferential pressure distribution. The variation of drag and inertia coefficients are presented as a function of Keulegan-Carpenter number (KC) for different inclinations of the cylinder. The comparison between the measured and the theoretical force derived from the evaluated hydrodynamic coefficients is found to be good.     

多个淹没水平圆柱诱发高阶谐波特性的数值与试验研究

基于势流理论采用时域高阶边界元方法建立了模拟非线性波浪与淹没水平双、三圆柱作用的数值水槽模型,其中采用混合欧拉-拉格朗日方法更新自由水面,四阶Runga-Kutta方法进行时间步进。利用两点法分离得到潜体下游高阶自由波,进而研究潜体间距、布置形式等对高倍频自由波的影响。同时在物理水槽内开展多潜体高阶谐波物理模型试验,并将试验结果与数值结果进行对比,吻合较好。研究发现:淹没双圆柱下游高阶谐波幅值随潜体间距呈现周期性振荡变化,其振荡的重现距离约为波长一半。而淹没三圆柱下游的高阶谐波随第一个间距呈周期性振荡变化,随第二个间距的增大而减小。     

Wave runup on a concentric twin perforated circular cylinder

The regular wave interaction with a twin concentric porous circular cylinder system consisting of an inner impermeable cylinder and an outer perforated cylinder was studied through physical model and numerical model studies. The experiments were carried out on the twin concentric cylinder model in a wave flume to study the wave runup and rundown at the leading and trailing edges of the perforated cylinder. It was found that the maximum wave runup on the perforated cylinder is almost same as the incident wave height. The experimental results were used to develop the predictive formulae for the wave runup and rundown on the perforated cylinder, which can be easily used for design applications. The wave runup profiles around the perforated cylinder for different values of ka and porosities were studied numerically using Green's Identity Method. The results of the numerical study are presented and compared with the experimental measurements.     

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。     

波浪与多孔介质结构相互作用SPH模拟

应用经CSPM法和黎曼解修正后的光滑粒子流体动力学(SPH)方法,建立了主动吸收无反射数值波浪水槽,研究波浪作用下多孔介质结构的水动力特性。流体运动控制方程采用N-S方程,多孔渗水结构内流体的运动控制方程考虑渗流力的影响。数值计算结果给出了水槽内不同位置测点的波面历时曲线和越浪量随时间变化曲线,并同试验结果和Philip Liu的数值计算结果进行了比较。并对一个波浪周期内斜坡堤多孔介质结构内外的速度场和压力分布进行了讨论分析。计算分析表明,数值计算波面较Philip Liu的计算结果与试验结果吻合更好。说明应用SPH方法建立的二维数学模型能够较好地模拟破碎波在多孔渗水斜坡上的爬坡和越浪。     

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.     

Pressures and forces on inclined cylinders due to regular waves

The variation of the dynamic pressures around a circular cylinder due to regular waves is studied in a wave basin of constant water depth of 3 m. The measuring segment consisted of 12 pressure transducers placed at an elevation of 0.8 m below the still water level. The tests were conducted with the cylinder axis inclined with respect to the vertical plane along and against wave direction. The results on the variation of dimensionless pressures with the non-dimensional input wave parameters are reported for different angles of orientation of the cylinder. The sectional normal force obtained by integrating the pressures is also presented as a function of wave steepness and the effect of angle of orientation of the cylinder is also reported.     

Breaking wave loads at vertical seawalls and breakwaters

This paper presents recent advances in knowledge on wave loads, based on experimental work carried out in the CIEM/LIM large flume at Barcelona within the framework of the VOWS (Violent Overtopping by Waves at Seawalls) project. Both quasi-static and impact wave forces from the new data set have been compared with predictions by empirical and analytical methods. The scatter in impact forces has been found to be large over the whole range of measurements, with no existing method giving especially good predictions. Based on general considerations, a simple and intuitive set of prediction formulae has been introduced for quasi-static and impact forces, and overturning moments, giving good agreement with the new measurements. New prediction formulae have been compared with previous measurements from physical model tests at small and large scale, giving satisfactory results over a relatively wide range of test conditions. The time variation of wave impacts is discussed, together with pressure distribution up the wall, which shows that within experimental limitations the measured pressures are within existing limits of previous study.     

Higher Harmonics Induced by Waves Propagating over A Submerged Obstacle in the Presence of Uniform Current

To investigate higher harmonics induced by a submerged obstacle in the presence of uniform current, a 2D fully nonlinear numerical wave flume（NWF） is developed by use of a time-domain higher-order boundary element method（HOBEM） based on potential flow theory. A four-point method is developed to decompose higher bound and free harmonic waves propagating upstream and downstream around the obstacle. The model predictions are in good agreement with the experimental data for free harmonics induced by a submerged horizontal cylinder in the absence of currents. This serves as a benchmark to reveal the current effects on higher harmonic waves. The peak value of non-dimensional second free harmonic amplitude is shifted upstream for the opposing current relative to that for zero current with the variation of current-free incident wave amplitude, and it is vice versa for the following current. The second-order analysis shows a resonant behavior which is related to the ratio of the cylinder diameter to the second bound mode wavelength over the cylinder. The second-order resonant position slightly downshifted for the opposing current and upshifted for the following current.     

Numerical simulation of nonlinear wave radiation by a moving vertical cylinder

In this paper the fully nonlinear potential model based on a finite element method is used to investigate the nonlinear wave motion around a moving circular cylinder. The results for the cylinder in transient motion are compared with the experimental data and a much better agreement than the linear theory is found. Further simulation for a circular cylinder in sinusoidal motion is made. It is found that when the ratio of the cylinder diameter D to the wavelength L is relatively small at a fixed motion amplitude the nonlinear components of the runup on the cylinder surface at the second- and third-harmonic frequencies become more important and this is confirmed by the experimental data. Results for the hydrodynamic force are also provided for a cylinder oscillating in a channel. It is noticed that when the frequency of the cylinder motion in a channel is between the first and the second natural frequencies of the symmetric mode, the time history has components not only at the frequency of the cylinder motion but also at the first natural frequency. The latter remains significant over the period that the simulation is made. This has important implications to model testing. If measurement is to be made at such a frequency it may take long time for the motion to become periodic at the frequency of the cylinder motion.     

Prototype measurements and small-scale model tests of wave overtopping at shallow rubble-mound breakwaters: the Ostia-Rome yacht harbour case

The paper presents the comparison between the results of small-scale model tests and prototype measurements of wave overtopping at a rubble-mound breakwater. The specific structure investigated is the west breakwater of the yacht harbour of Rome at Ostia (Italy) and is characterized by a gentle seaward slope (1/4) and by a long, shallow foreshore. The laboratory tests firstly aimed at carefully reproducing two measured storms in which overtopping occurred and was measured. The tests have been carried out in two independent laboratories, in a wave flume and in a wave basin, hence using a two-dimensional (2-D) and a three-dimensional (3-D) setup. In the 2-D laboratory tests no overtopping occurred during the storm reproductions; in the 3-D case discharges five to ten times smaller than those observed in prototype have been measured. This indicates the existence of model and scale effects. These effects have been discussed on the basis of the results of several parametric tests, which have been carried out in both laboratories, in addition to the storm reproductions, varying wave and water level characteristics. Final comparison of all the performed tests with 86 prototype measurements still suggests the existence of scale and model effects that induce strong underestimation of overtopping discharge at small scale. The scale reproduction of wave breaking on the foreshore, together with the 3-D features of the prototype conditions and the absence of wind stress in the laboratory measurements, have been individuated as the main sources of scale and model effects. The paper also provides a comparison between the data and a largely used formula for wave overtopping discharges in the presence of structures similar to the one at hand. The suitable value of a roughness factor that appears in that formula is investigated and good agreement is found with other recent researches on rubble-mound breakwaters.     

透水cosine-type同心圆柱波浪绕射研究

在势能流及微小振幅波理论假设下,采用复合边界元素法(CBEM)数值解析规则波通过单根外壁透水cosine-type型同心圆柱结构物绕射。将cosine-type外壁不透水条件改为透水外,并在内部设有一半径为b的不透水内圆柱共同组成同心圆柱,为了验证CBEM数值模式正确性与可行性,将其退化成圆柱,均得到合理结果。数值计算条件包含波浪正向入射凸端、透水参数及绕射参数,探讨波浪通过单根cosine-type同心圆柱体四周水面波动变化情况,并与双重圆筒同心圆柱作比较。计算结果显示结构物外壁采用透水型式,可以大幅降低cosine-type同心圆柱体四周整个波浪绕射场的水面波动。     

Video DCIV measurements of mass and momentum fluxes and kinetic energies in laboratory waves breaking over a bar

The experimental investigation of water waves breaking over a barred beach in a glass walled flume is presented. The time series of the water levels along the flume were measured using wave gauges and video imaging of the water surface, providing estimates of the mean wave-heights and water levels at various positions along the flume. The instantaneous velocity fields were measured using digital correlation image velocimetry for positions beyond the initial breaking point. The mass (/velocity) and momentum fluxes, and kinetic energies were computed from the velocity flow fields by means of phase ensemble averaging and then time averaging of relevant quantities derived from the instantaneous velocity fields. These parameters reached a maximum value some distance shorewards of the break point on the bar. The relative density of the fluid in the crest of the wave, estimated using the forward and reverse velocity fluxes, was found to be in the range from 0.4 to 0.8. Preliminary analysis of the momentum fluxes and mean water levels indicates a decreasing dynamic pressure shorewards of a peak that occurs shortly after wave breaking.     

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.     

The vibration of a large ring-stiffened prolate dome under external water pressure

The paper presents a theoretical and an experimental investigation into the free vibration of a large ring-stiffened prolate dome in air and under external water pressure.The theoretical investigation was via the finite element method where a solid fluid mesh with an isoparametric cross-section was used to model the water surrounding the dome, and a truncated conical shell and ring stiffener were used to model the structure. Good agreement was found between theory and experiment. Both the theory and the experiment found that as the external water pressure was increased the resonant frequencies decreased.     

基于光滑质点流体动力学方法数值波浪水槽研究

基于光滑质点流体动力学(smoothed particle hydrodynamics,简称SPH)方法建立二维数值波浪水槽,利用推波板造波生成孤立波和不规则波,模拟结果跟实验值及解析解做了对比分析,结果令人满意.SPH数值水槽中生成的波浪具有明显的非线性,波浪能量沿程有所衰减,与物理水槽结果吻合良好.