Wave-Current Forces on Small Square Cylinders (Part I)

-Based on the extended Morison Equation and model tests, the in-line forces on small square cylinders caused by waves (regular and irregular) and currents are analyzed in detail in this paper. The hydrodynamic coefficient CD and Cu related to KC number and the effect of direction of wave incidence are also given, which can be used in engineering practice.     

Wave-Current Forces on Slender Circular Cylinders

- A series model tests of wave forces by both regular and irregular waves combined with currents on single piles and bipiles in tandem and parallel arrays have been carried out. Based on Morison Equation, linear wave theory and linear wave spectrum theory as well, the characteristics of inline, lift and resultant forces on cylinders have been analyzed respectively. The drag, inertia and lift coefficients CD, CM and CL f皉 single piles related to KC number and the grouping effect coefficients of inline, lift and resultant forces on bipiles in tandem and parallel arrays related to KC number are given in this paper.     

Wave Action on Structures of Combined Cylinders

1.Introduction Owingtoitssignificanteffectofreductionofwaveloadsandwaverun up,theperforatedwallon anarrayofcylindricalstructureshasreceivedconsiderableattentioninrecentyears.Manyresearches havebeencarriedoutinthisfield.Anexactsolutionforthediffractionoflinearwaterwaveswithan arrayofimpermeablecylinderswasfirstgivenbySpringandMonkmeyer(1974)usinganeigenfunction expansionapproach.Subsequently,LintonandEvans(1990)madeamajorsimplificationtothetheo ry,whichallowedthenear fieldquantitiessuchasload…     

Wave-Current Forces on Vertical Cylinders in Side-by-Side Arrangement for Irregular Waves Combined With Opposing Current

- The wave-current forces on vertical piles in side-by-side arrangement induced by irregular waves with opposing current are investigated experimentally in this paper. The characteristics in both time and frequency domain of in-line, lift and resultant forces are analyzed. The grouping effect coefficients of inline, lift and resultant forces on piles related to KC number and relative spacing parameters are given. These results are compared with those in the case of irregular waves combined with following currents. It is found that the results in these two cases are quite different. The range of KC number tested is 10- 60, the range of Reynolds number is (0.55-3.43) ×104.     

A Finite Element Solution of Wave Forces on Submerged Horizontal Circular Cylinders

In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two-dimensional Navier-Stokes equations is solved numerically with a finite element method. In order to track the moving non-linear wave surface boundary, the Navier-Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three-step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data.Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder.The effects of the KC number and the cylinder depth on the wave forces are studied.     

Analysis of Interaction of Plane Waves with Multiple Circular Cylinders

The interaction of water waves with multiple circular cylinders is analysed briefly in this paper.The formula obtained by Linton and Evans is improved to introduce a relation of phase between cylinders.The condition for the existence of the solution has been proved.The numerical results are compared with ana-lytic solutions(Linton and Evans),numerical solutions and experimental data(Isaacson),and good agree-ment has been found.     

大尺度圆柱墩群周围的波流场的数值模拟

本文对波流共同作用下大尺度圆柱墩群周围的波流场进行了数值研究。利用波浪弥散关系的迭代计算求得波向与流向的夹角以及波浪的相对频率。流场通过求解浅水环流方程得到,波浪场通过求解含流的缓坡方程得到,通过二者的迭代计算得到大尺度圆柱墩群周围的波流场的耦合解。用有限元法建立了数值模型,并将本文的计算数据与试验数据以及其他学者计算数据进行了比较,结果较为合理。     

Wave Uplift Forces on the Bottom of a Circular Cylinder

The analysis of the data of model tests of two large deep wharves and monographic experimental studies show that two aspects are to be improved so as to predict the wave uplift forces on the bottom of a circular cylinder. The first aspect is the uplift pressure distribution on the bottom, and the second is the correct determination of the phase for maximum horizontal wave forces. The second problem has been solved. Synthesizing the results of theoretical analysis and experiments, we suggest a diagram for the determination of the phase when the maximum horizontal wave force appears. On the basis-ef the diagram the simultaneous wave uplift forces can be obtained for the structural stability analysis.     

圆柱形沉浮式深海养殖网箱的受力分析

应用一系列力学关系，研究了深海圆柱形沉浮式养殖网箱所承受的波浪力情况。导出深海沉浮式养殖网箱的运动方程，并给出数值计算。在网箱波浪力的研究中采用绕射理论和Morison方程，讨论了在波高、波长及周期变化下水动力的变化趋势，得出网箱所受到的水平波浪力远大于竖直波浪力，波高的变化对波浪力的影响最大的结论，为深海网箱的设计校核提供1种参考方法。     

Hydrodynamic Forces on Inclined Cylinder due to Waves with Crossing Current

Based on Morison's Equation and linear wave theory, hydrodynamic forces acting on inclined cylinders due to waves and crossing current at an angle of a, are analyzed. A method for calculating exciting forces is proposed. Experimental results show that the proposed method in this paper is feasible and can be used in engineering practice.     

Shoaling Surface Gravity Waves Cause a Force and a Torque on the Bottom

Freely propagating surface gravity waves are observed to slow down and to stop at a beach when the bottom has a relatively gentle upward slope toward the shore and the frequency range of the waves covers the most energetic wind waves (sea and swell). Essentially no wave reflection can be seen and the measured reflected energy is very small compared to that transmitted shoreward. One consequence of this is that the flux of the wave’s linear momentum decreases in the direction of wave propagation, which is equivalent to a time rate of change of the momentum. It takes a force to cause the time rate of change of the momentum. Therefore, the bottom exerts a force on the waves in order to decrease the momentum flux. By Newton’s third law (action equals reaction) the waves then impart an equal but opposite force to the bottom. In shallow (but finite) water depths the wave force per unit bottom area is calculated, for normal angle of incidence to the beach, to be directly proportional to the square of the wave amplitude and to the bottom slope and inversely proportional to the mean depth; it is independent of the wave frequency. Constants of proportionality are: 1/4, the fluid density and the acceleration of gravity. Swell attenuation near coasts and some characteristics of sand movement in the near-shore region are not inconsistent with the algebraic structure of the wave force formula. Since the force has a depth variation which is significantly faster than that of the dimensions of the particle orbits in the vertical direction, the bottom induces a torque on the fluid particles that decreases the angular momentum flux of the waves. By an extension of Newton’s third law, the waves also exert an equal but opposite torque on the bottom. And because the bottom force on the waves exists over a horizontal distance, it does work on the waves and decreases their energy flux. Thus, theoretically, the fluxes of energy, angular and linear momentum are not conserved for shoaling surface gravity waves. Mass flux, associated with the Stokes drift, is assumed to be conserved, and the wave frequency is constant for a steady medium.     

Wave Forces Acting on Vertical Walls

Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical model, and satisfactory agreements are obtained. The variation of wave forces with incident angles and the shape of simultaneous pressure distribution are investigated, and the comparisons between numerical results and Goda＇ s predictions are also carried out. It is concluded that the maximum wave forces acting on the unit length of vertical wall is often induced by the obliquely incident waves instead of normally incident waves, while Goda＇ s formula may be inapplicable for oblique wave incidence. The shape of simultaneous pressure distribution is not significantly influenced by incident angles, and it can be favorably predicted by Goda＇ s formula. When regular wave heights are taken as the same as irregular wave height H1%, the irregular wave forces Ph. 1% are slightly larger than regular wave forces in most cases.     

关于小直径垂直桩柱结构的波浪力研究

本文归纳了应用Morison方程中涉及的研究成果。分别从阻力系数和惯性力系数。规则波与不规则波，二阶力和线性化，桩群受力等方面进行了论述。对目前该领域的研究给出了系统的介绍。     

New Formulas of Earth Pressure on Large Successive Cylinders

The retaining wall made of large successive cylinders is a kind of structure which draws muchattention in coastal engineering of China.The earth pressure on the arched back of large successive cylin-ders is different from that on the plane back of a general wall.On the basis of equilibrium of forces on thestrip element taken from the soil between two cylinders,the differential equation is established and theanalytic solution to the equation is obtained.The formulas of earth pressure on large successive cylindersare given in this paper.The distribution of earth pressure around the circle given by the present formulas isdifferent from that given by the formulas commonly used at present,but it is identical with that measuredin the model test.     

Fully Nonlinear Simulations of Wave Resonance by An Array of Cylinders in Vertical Motions

The finite element method (FEM) is employed to analyze the resonant oscillations of the liquid confined within multiple or an array of floating bodies with fully nonlinear boundary conditions on the free surface and the body surface in two dimensions. The velocity potentials at each time step are obtained through the FEM with 8-node quadratic shape functions. The finite element linear system is solved by the conjugate gradient (CG) method with a symmetric successive overelaxlation (SSOR) preconditioner. The waves at the open boundary are absorbed by the combination of the damping zone method and the Sommerfeld-Orlanski equation. Numerical examples are given by an array of floating wedge- shaped cylinders and rectangular cylinders. Results are provided for heave motions including wave elevations, profiles and hydrodynamic forces. Comparisons are made in several cases with the results obtained from the second order solution in the time domain. It is found that the wave amplitude in the middle region of the array is larger than those in other places, and the hydrodynamic force on a cylinder increases with the cylinder closing to the middle of the array.     

基于浪流耦合模型的台风浪数值模拟

基于CCMP风场资料,采用无结构网格、浪-流双向实时耦合模型FVCOM-SWAVE,模拟强热带风暴"米雷"在中国近海区域产生的海浪场,将耦合模型模拟的有效波高和平均周期与实测浮标资料进行比对,发现模拟结果的各类误差总体较小,说明耦合模型能够较好地模拟考虑浪流相互作用下中国近海台风浪过程。对比考虑潮汐引起的水位变化与不考虑水位变化情况下对耦合模型模拟结果的影响,发现在近岸区域考虑潮水位情况下的有效波高和平均周期模拟结果周期性特征明显,说明潮汐对耦合模型在近岸处有效波高的模拟影响显著。     

Experimental Study on Ocean Internal Wave Force on Vertical Cylinders in Different Depths

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.     

Wave Forces on Submerged Semi-Circular Breakwater and Similar Structures

—The results of design and experiment of a submerged semi-circular breakwater at the Yangtzeestuary show that the submerged structure will be unsafe when the general empirical wave force formulafor semi-circular breakwater is used in design.Therefore,a new calculation method for the wave forces act-ing on a submerged semi-circular structure is given in this paper,in which the wave force acting on the in-side circumference of semi-circular arch is included,and the phase modification coefficient in the generalempirical formula is adjusted as well.The new wave force calculation method has been verified by the re-sults of seven related physical model tests and adopted in the design of the south esturary jetty of the firststage project of Deep Channel Improvement Project of the Yangtze River Estuary,the total jetty length be-ing 17.5km.     

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.     

弹性双柱在规则波作用下振动响应

通过速度势的特征展开方法,建立垂直圆柱对波浪绕射的解析解,得到作用在柱体上的波浪力计算表达式,通过谐波增量平衡法(IHB法),计算研究弹性双柱相对位置对双柱振动响应的影响。设计了弹性双柱体模型试验,数值结果与模型试验结果较吻合,为海洋工程结构振动设计提供一种解决方法。