Wave motion over a submerged breakwater with an upper horizontal porous plate and a lower horizontal solid plate

This study examines the hydrodynamic performance of a modified two-layer horizontal-plate breakwater. The breakwater consists of an upper submerged horizontal porous plate and a lower submerged horizontal solid plate. By means of the matched eigenfunction expansion method, a linear analytical solution is developed for the interaction of water waves with the structure. Then the reflection coefficient, the transmission coefficient, the energy-loss coefficient and the wave forces acting on the plates are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a single submerged horizontal solid plate and a single submerged horizontal porous plate. Numerical results show that with a suitable geometrical porosity of the upper plate, the uplift wave forces on both plates can be controlled at a low level. Numerical results also show that the transmission coefficient will be always small if the dimensionless plate length (plate length versus incident wavelength) exceeds a certain moderate value. This is rather significant for practical engineering, as the incident wavelength varies over a wide range in practice. Moreover, it is found that the hydrodynamic performance of the present structure may be further enhanced if the lower plate is also perforated.     

透空式水平板波浪总上托力试验研究

通过系列模型试验,对透空水平板下波浪总上托力进行了研究,结果表明：平板下最大总上托力并不与最大冲击压强同步发生。为此,依据试验结果对波浪总上托力产生机理和影响因素进行详细分析,提出透空水平板波浪最大总上托力的计算公式,试验结果表明,该公式与实验值有着较好的一致性。     

Experimental study on the performance of twin plate breakwater

The wave transmission characteristics and wave induced pressures on twin plate breakwater are investigated experimentally in regular and random waves.A total of twenty pressure transducers are fixed on four surfaces of twin plate to measure the wave induced dynamic pressures.The spatial distribution of dynamic wave pressure is given along the surface of the twin plate.The uplift wave force obtained by integrating the hydrodynamic pressure along the structure is presented.Discussed are the influence of different incident wave parameters including the relative plate width B /L,relative wave height /i H a and relative submergence depth s /a on the non-dimensional dynamic wave pressures and total wave forces.From the investigation,it is found that the optimum transmission coefficient,t K occurs around B /L 0.41 ~ 0.43,and the twin plate breakwater is more effective in different water depths.The maximum of pressure ratio decreases from 1.8 to 1.1 when the relative submergence depth of top plate is increased from 0.8to +0.8.     

Vertical uplift resistance of close-spaced shallow rectangular group anchor plates embedded in sand

Abstract

This study describes an analytical solution for determining the ultimate vertical uplift resistance of a group of two and multiple number of close-spaced shallow rectangular anchor plates embedded horizontally in sand. The analysis was performed by using an upper bound theorem of limit analysis with the employment of the kinematically admissible three-dimensional (3D) rigid wedge collapse mechanisms. Results are obtained in terms of dimensionless uplift factors F_γ and F_q due to the components of soil self-weight and surcharge pressure acting on the ground surface for a wide range of parameters. It was found that the magnitude of uplift factors decreases substantially with a decrease in the clear spacing between the anchors, soil friction angle, and embedment ratio, and an increase in the aspect ratio of anchors. Further, it was noticed that when the clear spacing between the anchors is greater than or equal to the certain critical value, the interaction effect of anchors vanishes and the magnitude of uplift factors associated with a group of anchors becomes equal to that of single isolated anchors. The present solutions are found to compare reasonably well with those theoretical, numerical, and experimental results available in the literature.     

Uplift Pressure of Waves on A Horizontal Plate

1 .IntroductionOwingtotheneedfordevelopingoffshoreresources,moreandmorehollow trussedstructuresareconstructed ,suchasalongshorequays ,islandquays,artificialislands ,bollards ,maritimeplatforms ,etc .Thelargeentitypartofthosemaritimestructuresusuallyconsistsofahorizontalplateabovethestillwaterlevel,anditusuallysuffersfromwaveattacksandthuscaneasilybedestroyed .Toavoidsuchakindofaccidents ,themostimportantistoaccuratelyevaluatetheupliftpressuresofwavesontheplateundervariouswaveconditionsandbound…     

Wave interaction with twin plate wave barrier

The wave transmission and reflection characteristics and wave induced pressures on single surface plate and twin plate barriers were investigated experimentally for a wide range of wave heights and periods in regular and random waves. Seven different spacing between the plates were tested. It is found in general, hydrodynamically the twin plate is better than the single surface plate to reduce the wave transmission and increase the wave reflection. It is found that the transmission coefficient of twin plate reduced from 0.8 to 0.3 when the relative plate width is increased from 0.18 to 0.84. Transmission coefficient of twin plate barrier shows oscillating behavior, when relative plate width is increased due to blocking and pumping effect. The reflection coefficient increased from 0.25 to 0.65, when the relative width of the plate is increased from 0.18 to 0.84. The increase in spacing between the plates was also found to increase the reflection coefficient. The transmission coefficient, K_t for 98% probability of non-exceedence was found to be minimum and is about 0.60 when the relative spacing between the plate is about 0.12, compared to K_t=0.76 for single surface plate. The reflection coefficient for 98% probability of non-exceedence was found to exceed 0.66 for single surface plate, whereas it is 0.73 for twin plate with relative spacing of about 0.40. From the investigation with wide range of input parameters, it is found that the twin plate barrier needs to be designed for highest 98% pressure ratio of 2.0, which is equal to the static pressure induced by the design incident wave height.     

孤立波与升沉水平板相互作用数值模拟研究

合理的刚度和潜深设计可以使升沉水平板获得优异的消浪性能。基于考虑流体黏性的二维不可压缩Navier-Stokes方程,以高阶紧致插值CIP(constrained interpolation profile)方法求解方程对流项,采用VOF(volume of fluid)方法重构自由液面,构建二维数值波浪水槽。采用试验数据验证模型后,研究孤立波与升沉水平板相互作用,分析相对刚度K*、相对潜深d/h、相对波高H/h对于升沉板的消浪性能和运动响应的影响,揭示升沉板对孤立波的消浪机理。研究表明:在孤立波通过时,升沉板会经历一个先上升后下降的运动,随后非线性自由振动,板下方水体近似均匀流动,且水流的垂向流动与板的垂荡方向一致;升沉板主要通过不对称涡旋脱落、浅水变形、波浪反射与辐射波转化等方式消耗孤立波能量;一定条件下,采用最优相对刚度K*=4.0和最优相对潜深d/h=0.52可以取得良好的消浪效果,此时透射系数最小,同时升沉板的运动响应在合理的范围内。     

The motions of a ship in swallow water

A general formulation is given of the hydrodynamic forces on a ship, oscillating about a state of rest in 6df in response to excitation by a harmonic wave in shallow water. A method is described to obtain a numerical approximation of the velocity potential, describing the flow around the moving ship by means of a distribution of discrete three-dimensional sources.With this method it is possible to take the influence of a quay into account.Calculated values of wave excited forces, hydrodynamic coefficients and motions of a 200,000 tdw tanker in shallow water are presented and compared with experimental results.     

Hydrodynamics identities and wave-drift force of a porous body

In the present study, hydrodynamic interactions between water waves and porous bodies are investigated. Various hydrodynamic identities, such as the Haskind relation, Bessho-Newman relation etc., are systematically re-examined. Some of these identities, such as the symmetry of added mass and damping and the Haskind-Hanaoka relation, are still valid for porous bodies even without modification to the identities. However, when energy dissipation due to porosity is involved, appropriate supplementation is required to properly consider porous effects. In addition, the calculation of wave drift forces acting on a porous body is formulated either by pressure integration or using momentum conservation as basis. We conclude that porosity dissipation makes a more substantial contribution to wave drift forces than does conventional dissipation created by scattered and radiated waves.     

Vertical uplift capacity of a group of shallow circular plate anchors in sand

ABSTRACT

The uplift capacity of a group of circular plate anchors buried horizontally in sand along a line has been determined. The uplift capacity of an interfering anchor is presented in terms of nondimensional uplift factors, F_γi and F_qi, due to components of soil unit weight and surcharge pressure acting on the ground surface, respectively. Theoretical solutions have been developed by applying the upper bound theorem of limit analysis based on a simple rigid wedge collapse mechanism. In the case of two and infinite number of anchors, closed-form solutions have been developed for computing the factor F_qi, whereas the factor F_γi is determined using a semianalytical approach. As expected, the interference of the anchors leads to a continuous reduction in the uplift resistance with a decrease in the spacing between the anchors, and the uplift resistance decreases with the increasing number of anchors at a given spacing. The results compare reasonably well with the available theoretical and experimental data from the literature.     

Hydrodynamic Coefficients and Wave Excitation Forces for A Ship near A Quay

In this paper,the effects of a quay or a solid jetty on hydrodynamic coefficients and vertical wave excitation forces on a ship woth or without forward speed are discussed.A modified simple Green function technique is used to calculate the 2D coefficients while the strip theory is used to calculate the 3D coefficients. Wave excitation forces are also calculated with the strip theory. Numerical results are provided for hydrodynamic coefficients and vertical wave excitation forces on a 200000 DWT tanker ship. It is found that the quay has a considerable effect on the hydrodynamic coefficients and wave excitation forces for a ship.     

Wave motion over a breakwater system of a horizontal plate and a vertical porous wall

A two-dimensional analytical solution is presented to study the reflection and transmission of linear water waves propagating past a submerged horizontal plate and through a vertical porous wall. The velocity potential in each fluid domain is formulated using three sets of orthogonal eigenfunctions and the unknown coefficients are determined from the matching conditions. Wave elevations and hydrodynamic forces acting on the porous wall are computed. Reflection and transmission coefficients are presented to examine the performance of the breakwater system. The present analytical solutions are found in fairly good agreement with the available laboratory data. The results indicate that the plate length, the porous-effect, the gap between plate and porous wall, and the submerged depth of the plate all show a significant influence on the reflected and transmitted wave fields. It is also interesting to note that the submerged plate plays an important role in reducing the transmitted wave height, especially for long incident waves.     

Wave set-up on coral reefs. 1. Set-up and wave-generated flow on an idealised two dimensional horizontal reef

Wave set-up may be significant in determining water levels on coral reefs particularly in microtidal environments and hence is an important factor for the design of reef-top structures and for the stability of reef-top islands. Laboratory experiments have been made on a two dimensional model of an idealised horizontal reef under two different conditions corresponding to a fringing reef (or closed lagoon) situation and a platform reef (or open lagoon) situation. Both wave set-up on the reef-top and the wave-generated flow across the reef were measured and related to wave and tide level conditions.All other factors being the same, wave set-up is greatest at low tide levels whereas wave-generated flow is greater at higher tide levels. The magnitude of the set-up on a platform reef with a wave-generated flow is less than on a fringing reef without any net flow by an amount equal to the velocity head of the flow across the reef. Dimensionless parameters and q/√gH_o³ are found to be functions of relative submergence parameters h_r/H_o or . For values of ( ) H_o > 1 waves break on the reef-top and radiation stress theory can be used to calculate set-up. For ( )H_o < 0.7 waves break on the reef-face and set-up is determined by broadcrested weir control at the reef-edge. (The symbols are defined as follows: g is gravitational acceleration; h_r is still water depth over horizontal reef-top; H_o is offreef wave height (equivalent deep water value); q is discharge per unit length of reef edge; T is wave period and is maximum wave set-up on reef-top.)     

波浪与外壁透空双方形沉箱相互作用

在线性波浪理论下,利用复合边界元素法(composite BEM)数值解析在等水深、规则波浪入射二种外壁透空双方形沉箱的无因次波力及Kd绕射分布图,并分别与其他研究者所作双圆筒内、外圆柱无因次波力及绕射分布图的计算结果进行比较,都说明本模式的合理性和可行性。在考虑不同透水参数下,分别计算波浪作用在内、外结构物的波力及沉箱四周绕射系数大小分布图。计算结果显示:波浪作用于外壁透空全透水双方形沉箱,外方柱无因次最大波力值会随着透水参数增加而降低;内方柱无因次最大波力值则随着透水参数增加而增加。本研究结果可供设计外海透水方形沉箱结构交互作用参考。     

有顶板开孔沉箱所受波浪力的数值分析

利用流体体积(VOF)方法并结合k-ε模型以及等温状态下的气体状态方程数值计算规则波对有顶板开孔沉箱的作用,将数值计算结果与物理模型试验数据分别对总水平力、前开孔板和后实体板的压力分布以及顶板总力等物理量进行对比,验证了所建立的数学模型和数值计算方法的有效性和可靠性,为分析有顶板开孔沉箱的波浪力提供了有效的计算方法.     

Hydrodynamic behavior of a straight floating pipe under wave conditions

This paper examines the hydrodynamic behavior of a floating straight pipe under wave conditions. The main problem in calculating the forces acting on a small-sized floating structure is obtaining the correct force coefficients C_n and C_t, which differ from a submerged structure. For a floating straight pipe of small size, we simplify it into a 2D problem, where the pipe is set symmetrically under wave conditions. The force equations were deduced under wave conditions and a specific method proposed to resolve the wave forces acting on a straight floating pipe. Results of the numerical method were compared to those from model tests and the effects of C_n and C_t on numerical results studied. Suggestions for the selection of correct C_n and C_t values in calculating wave forces on a straight floating pipe are given. The results are valuable for research into the hydrodynamic behavior of the gravity cage system.     

Experimental investigation of wave slamming on an open structure supported elastically

The superstructures of marine structures supported by the elastic legs and located in the splash zone will subject to violent wave slamming and vibrate consequently during storms. A series of model tests are carried out to investigate the wave impacting on the open structures supported elastically. Three kinds of models with different natural frequencies are designed. The characteristics of the wave pressures on the three models are compared. The durations of the uplift forces and the corresponding accelerations of the structure during wave impact are analyzed simultaneously. The distributions of the peak impact pressures on the subfaces of the plates with different supporting stiffness are given. The relationship between the uplift force on the three models and the relative clearance are obtained. The spectral properties of the slamming loads on the three different structures are compared. The experimental results indicate that the behaviors of the impact pressures, the uplift forces and accelerations of the plates with small natural frequencies are obviously different from those of the plates with larger natural frequencies within the range of the experimental parameters.     

Probabilistic model for wave forces acting on a cylinder in random waves

Generally, the sea-state (random waves) is best described by a wave spectrum. A number of statistical models for wave spectra has been well established and a sea-state can be specified. Once the specified sea-state is established, the corresponding model for wave forces acting on a single cylinder or a group of cylinders can be formulated. Since peak force is of more practical value, a multivariate or joint probability density function for wave forces has been developed for the peak force distribution of wave forces. This theoretical force model derives the tri-variate probability density function P(F, F′, F″), where F is the peak force defined by Morison equation. This model is of wide-band in nature and is tested by wave flume experiments.     

Oblique and Multi-Directional Random Wave Loads on Vertical Breakwaters

1 .IntroductionTraditionally ,thedesignofcoastalstructuresisbasedontheformulaedevelopedforhead onuni directionalwaves .However,wavesusuallyattackabreakwaterobliquely ,formingshort crestedwavesinfrontofthebreakwater.Ontheotherhand ,asthehumanactivityareaisspreading ,thewaterdepthattheconstructionsiteforbreakwatershasatendencytobecomelarge ,andsomebreakwatershavebeenconstructedinwaterareasdeeperthan 6 0minJapan (Tanimotoetal.,1 988) .Theseawaveismulti directionalandrandom ,especiallyindeepwater…     

新型开孔工字板组合式防波堤波浪力特性试验研究

开孔工字板组合式防波堤是基于透空板式防波堤的一种新型结构形式,具有自重轻、材料省的特点。为充分了解新型开孔组合式防波堤的受力特性,基于室内水槽物理模型试验,测量新型开孔工字板组合式防波堤上的波压力与结构总力,研究相对波高H/d、相对波长L/B对该新型防波堤结构表面压力的影响,讨论了该新型防波堤所受波浪力荷载与相对波高H/d、相对波长L/B的关系。结果表明,相对波高H/d是决定新型防波堤结构表面波压力和结构总力的主要影响因素。该新型防波堤结构波浪力荷载以垂直方向受力为主,新型防波堤结构所受竖向总力远大于水平总力,最大可达到15倍。新型防波堤水平总力随相对波长L/B先增大后趋于稳定。相对波长L/B=3.617是防波堤结构水平总力变化幅度的分界点。