The Nonlinear Wave Force on a Circular Cylinder in Shallow Water

Based on the 1st order cnoidal wave theory, the nonlinear wave diffraction around a circular cylinder in shallow water is studied in this paper. The equation of the wave surface around the cylinder is formulated and by using this formula the wave surface elevation on the cylinder surface can be obtained. In this paper, the formula for calculating the cnoidal wave force on a circular cylinder is also derived. For the wave conditions which are often encountered in practical engineering designs, the ratios of the nonlinear wave forces to the linear wave forces are calculated, and the results are plotted in this paper for design purposes. In order to verify the theoretical results, model tests are conducted. After comparing the test results with the theoretical ones, it is concluded that, in shallow water, for the case of T g / d~(1/2) > 8-10 and H / d > 0.3, the cnoidal wave theory should be used to calculate the wave action on a cylindrical pier.     

直立式防波堤兼码头水工结构设计与试验研究

基于青岛崂山前海直立式防波堤兼码头工程的设计,通过规范计算值与断面物理模型试验数据的对比分析,合理确定断面尺度、堤顶高程和越浪量等重要设计参数。特别是通过多组试验的数据分析,对挡浪墙的外形尺度和护底宽度进行优化,采用通过增大护底块体重量的方式有效地减小护底长度,充分运用试验手段对于设计规范的护底相关规定做出了有益的探索和补充,为深水直立式防波堤的设计改进提供了借鉴。     

Numerical simulation of solitary wave scattering by a circular cylinder array

The interaction of a solitary wave with an array of surface-piercing vertical circular cylinders is investigated numerically. The wave motion is modeled by a set of generalized Boussinesq equations. The governing equations are discretized using a finite element method. The numerical model is validated against the experimental data of solitary wave reflection from a vertical wall and solitary wave scattering by a vertical circular cylinder respectively. The predicted wave surface elevation and the wave forces on the cylinder agree well with the experimental data. The numerical model is then employed to study solitary wave scattering by arrays of two circular cylinders and four circular cylinders respectively. The effect of wave direction on the wave forces and the wave runup on the cylinders is quantified.     

孤立波与带窄缝双箱相互作用模拟研究

针对孤立波与带窄缝双箱的作用问题,应用时域高阶边界元方法建立了二维数值水槽。其中,自由水面满足完全非线性运动学和动力学边界条件,对瞬时自由表面流体质点采用混合欧拉-拉格朗日法追踪,采用四阶龙格库塔法对下一时刻的自由水面的速度势和波面升高进行更新。采用加速度势法求解物体湿表面的瞬时波浪力。采用推板方法生成孤立波。通过模拟孤立波在直墙上的爬高以及施加在直墙上的波浪力,并与已发表的实验和数值结果对比,验证本数值模型的准确性。通过数值模拟计算研究了窄缝宽度、方箱尺寸对波浪在箱体迎浪侧爬高,窄缝内波面升高,箱体背浪侧透射波高及箱体受波浪荷载的影响。同时研究了有一定时间间隔的双孤立波与带窄缝双箱系统作用问题。     

波浪在Jarlan型开孔潜堤上的运动

The wave motion over a submerged Jarlan-type breakwater consisting of a perforated front wall and a solid rear wall was investigated analytically and experimentally. An analytical solution was developed using matched eigenfunction expansions. The analytical solution was confirmed by previously known solutions for single and double submerged solid vertical plates, a multidomain boundary element method solution, and experimental data. The calculated results by the analytical solution showed that compared with double submerged vertical plates, the submerged Jarlan-type perforated breakwater had better wave-absorbing performance and lower wave forces. For engineering designs, the optimum values of the front wall porosity, relative submerged depth of the breakwater, and relative chamber width between front and rear walls were 0.1–0.2, 0.1–0.2, and 0.3–0.4, respectively. Interchanging the perforated front wall and solid rear wall may have no effect on the transmission coefficient. However, the present breakwater with a seaside perforated wall had a lower reflection coefficient.     

三维二阶水波绕射问题的有限元时域计算

本文用有限元法配合时步处理来求解三维非线性水波的绕射问题,自由表面条件和物面条件都满足到二阶,采用人工阻尼区来吸收反射波,流场内的速度势通过求解有限元方程得到。对垂直圆柱体的绕射问题进行了计算,得到了自由表面波高时间历程和圆柱所受到的波浪力,计算结果和有关文献的理论计算结果进行了比较。     

斜向不规则波对直墙作用的实验研究

通过长峰不规则波和方向波谱对直墙作用的实验研究 ,分别给出了每延米斜向不规则波波浪力与正向力之比 ,方向波谱波浪力与斜向长峰不规则波波浪力之间的关系 ,通过与规则波实验结果的比较给出了斜向规则波与不规则波波浪力之间的相对关系 ;并对斜向不规则波的反射系数与正向波时的变化作出了分析     

Calculation of Wave Pressure and Pressure Spectrum for Perforate-Pipe Breakwater

Standing waves are formed due to the reflection when waves meet vertical wall,thereforestrong structures are needed to keep the wall stability under the serious wave attack.For the improvementof the working condition and increase of the stability of the wall,the lower reflecting breakwaters have at-tracted close attention Reports mostly from Japanese researchers are often concerned with the wall ofcaisson equipped with open windows.In this paper a kind of hollow-pipe perforated breakwater is exam-ined which waves may partially perforate into the harbour basin.The wave in front of the wall can onlyform partial standing wave and wave force is reduced obviously.And the theoretical calculation of waveforce and analysis of wave force spectrum are all derived.Comparison between the results from theoreticalcalculation and hydraulic modeling shows reasonable agreement.     

The force of oblique incident wave on the breakwater with a partially perforated wall

1 IntroductionRecently breakwaters with perforated front wallshave been widely used. The use of perforated break-waters mainly has two advantages. Firstly, wave forcesacting on the whole structure can be divided into twoparts on two different walls with a phase difference.To select the distance between the two plates suitably,the total wave force on the whole structure can bemaintained at a low level. Secondly, waves will dissi-pate when they transmit over a porous medium. Thus,the reflection…     

部分反射直墙前二维物体的绕射和辐射问题

基于映像理论将部分反射直墙前物体的散射问题,等效于开敞水域中原物体的散射和关于直墙映像体散射的线性叠加进行求解。采用高阶边界元方法建立了部分反射直墙前二维任意形状物体波浪绕射和辐射问题的数值分析模型,通过与已发表的海底方箱和淹没圆柱结果的对比验证了数值模型的准确性。应用该模型研究了直墙反射系数幅值及相位、方箱与墙间距离等参数对水面方箱上波浪激振力、附加质量和辐射阻尼的影响。结果表明：直墙反射系数幅值越大,波浪激振力、附加质量和辐射阻尼的波动越大,附加质量在一些频率下出现负值;相位角的变化会改变波浪激振力、附加质量和辐射阻尼曲线的偏移,在低频区对升沉附加质量有显著影响;方箱距离直墙越远,方箱上的波浪激振力、附加质量和辐射阻尼随波数振荡的频率越快,峰值频率向低频侧移动。     

A SPH numerical wave basin for modeling wave-structure interactions

Based on a parallel SPH-LES model, a three dimensional numerical wave basin is developed to study wave interaction with coastal structures. The OpenMP programming technology combined with an existing MPI program contained in the parallel version of SPHysics code has been implemented to enable the simulation of hundred millions of particles running on a computer cluster. As part of the numerical basin development work an active absorbing wave maker and a sponge layer are introduced. The dynamic boundary conditions are also corrected to reduce the spurious effects. Wave generation and propagation in the numerical wave basin is first tested and confirmed with analytical results. Then, the model is applied to simulate wave interactions with a vertical breakwater and a vertical cylinder in order to further assess the capability of the numerical wave basin. The predicted free surface elevation near the vertical breakwater is compared with the experimental data while the horizontal forces and overturning moments acting on the vertical cylinder are verified with the analytical results. In all these cases the model results show excellent agreement with the validation data.     

Nonlinear wave loads on a vertical cylinder

Nonlinear contributions due to elevation of the free surface, the dynamic head, and the second-order velocity potential on the wave loads are presented in closed-form expressions. Such nonlinearities resulting from large-amplitude ocean waves are associated with the irrotational flow interacting with a fixed bottom-mounted vertical cylinder piercing the surface. These are expressed in the form of dynamic, waterline and quadratic forces all of which depend on the square of the wave amplitude. The appropriate modifications are made to both the classical Morison equation and the well-known linear diffraction theory of MacCamy and Fuchs for accounting the second-order effects.A limited comparative study is performed to verify the present theoretical derivations. In general, satisfactory agreements have been obtained with the test results from various laboratory studies by different researchers. However, under certain environmental conditions, some discrepancies still exist with the measured results.     

张力腿平台内孤立波作用特性数值模拟

依据三类内孤立波理论KdV、eK dV和MCC的适用性条件,采用Navier-Stokes方程为流场控制方程,以内孤立波诱导上下层深度平均水平速度作为入口边界条件,建立了两层流体中内孤立波对张力腿平台强非线性作用的数值模拟方法。结果表明,数值模拟所得内孤立波波形及其振幅与相应理论和实验结果一致,并且在内孤立波作用下张力腿平台水平力、垂向力及力矩数值模拟结果与实验结果吻合。研究同时表明,张力腿平台内孤立波载荷由波浪压差力、粘性压差力和摩擦力构成,其中摩擦力很小,可以忽略;水平力的主要成分为波浪压差力和粘性压差力,粘性压差力与波浪压差力相比较小却不可忽略,流体粘性的影响较小;垂向力中粘性压差力很小,流体粘性影响可以忽略。     

Spectral Analysis of Nonlinear Drag Forces

The spectral properties of nonlinear drag forces of random waves on vertical circular cylinders are analyzed in this paper by means of nonlinear spectral analysis. The analysis provides basic parameters for estimation of the characteristic drag forces. Numerical computation is also performed for the investigation of the effects of nonlinearity of the drag forces.The results indicate that the wave drag forces calculated by linear wave theory are larger than those calculated by the third order Stokes wave theory for given waves. The difference between them increases with wave height. The wave drag forces calculated by use of hnear approximation are about 5% smaller than their actual values when measured in the peak values of spectral densities. This will result in a safety problem for the design of offshore structures. Therefore, the nonlinear effect of wave drag forces should be taken into comidemtion in design and application of important offshore structures.     

Hydraulic Design Method of Wave Dissipating Structure with Partially Perforated Front Wall

Based on the matching conditions of different fluid regions, the eigenfunction expansion method is used to develop a theoretical formula for wave reflection in front of the perforated structure with a partially slit front wall. The accuracy of the solution is verified by comparing the numerical results with experimental data. In addition, a new hydraulic design method is developed by derivation of the theoretical formula with respect to the porosity of the slit wall, and the results of this design method is drafted for harbour engineers to use.     

Numerical investigation on the dynamics of a vertical wall defenced by an offshore breakwater

The numerical and experimental investigations on the performance of an offshore-submerged breakwater in reducing the wave forces and wave run-up on vertical wall are presented. A two-dimensional finite-element model is employed to study the hydrodynamic performance of the submerged breakwater under the action of regular and random waves. The numerical prediction has been supported with experimental measurements. The wave forces and wave run-up on the vertical wall were measured for different breakwater configurations. The applicability of linear theoretical model in the prediction of wave forces on the wall by a submerged breakwater has been discussed.     

Experimental Study of Sand Bed Configurations in Front of a Vertical Wall Under Wave Action

—When a 2-D progressive wave train normally or obliquely approaches a vertical wall and thenis normally or obliquely reflected from it,the combination of the approaching and reflected waves may re-sult in a standing wave or a short-crested wave in front of the wall.This paper presents the experimentalobservations of sand bed configurations under the action of these water waves in front of the wall.The ge-ometry of sand ripples under these water waves in front of the vertical wall is presented as a function offlow parameters,such as the water particle semi-excursion and the mobility number.     

The irregular broken wave forces on vertical wall

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Numerical modeling of wave runup and forces on an idealized beachfront house

In this paper, a numerical wave model based on the incompressible Reynolds-averaged Navier–Stokes (RANS) and k–ε equations is used to estimate the impact of a solitary wave on an idealized beachfront house located at different elevations on a plane beach. The locations of the free surface are reconstructed by volume of fluid (VOF) method. The model is satisfactorily tested against the experimental data of wave runup, and the analytical solution of wave forces on vertical walls. The time histories of wave profiles, forces, and overturning moments on the idealized house are demonstrated and analyzed. The variations of wave forces and overturning moments with the elevation of the idealized beachfront house are also investigated.     

基于粘性流模型的筒型基础防波堤波浪力数值分析

筒型基础防波堤是一种新型港口海岸工程结构,其基础上部是由连续排列的圆筒构成的直立防浪墙.采用粘性流数值模型,研究连续圆筒防波堤上波浪力竖向分布、水平(沿圆筒环向)分布和波浪力合力特性,并对粘性流数值模型计算的平面直墙波浪力与海港水文规范方法计算结果;粘性流数值模型计算的连续圆筒墙面波浪力与平面直墙波浪力;无限长连续圆筒墙面波浪力与有限长连续圆筒墙面波浪力进行比较分析.针对所选工程算例,建议按<海港水文规范>中平面直墙波浪力计算方法确定连续圆筒防波堤上的波浪力时,波峰时考虑0.90左右的折减系数,波谷时考虑0.95左右的折减系数.