Floating pontoon breakwaters

The hydrodynamic properties of a pair of long floating pontoon breakwaters of rectangular section are investigated theoretically. The structures are partially restrained by linear symmetric moorings fore and aft. The fluid motion is idealized as linearized, two-dimensional potential flow. The breakwater motions are assumed to be two-dimensional, in surge, heave and pitch. The solution for the fluid motion is obtained by the boundary integral equation method using an appropriate Green's function. Numerical results are presented that illustrate the effects of the various wave and structural parameters on the efficiency of the breakwaters as barriers to wave action. It is found that the wave reflection properties of the structures depend strongly on their width, draft and spacing and the mooring line stiffnesses, while their excess buoyancy is of lesser importance.     

Simplified analytical solutions for wave interaction with absorbing-type caisson breakwaters

Simplified analytical solutions are presented to model the interaction of linear waves with absorbing-type caisson breakwaters, which possess one, or two, perforated or slotted front faces which result in one, or two, interior fluid regions (chambers). The perforated/slotted surfaces are idealized as thin porous plates. Energy dissipation in the interior fluid region(s) inside the breakwater is modelled through a damping function. Under the assumption of potential flow and linear wave theory a boundary-value problem may then be formulated to describe wave interaction with the idealized structure. A solution to this simplified problem may be obtained by an eigenfunction expansion technique and an explicit analytical expression may be obtained for the reflected wave height. Using the experimental work of previous authors, damping coefficients are determined for both single and double chamber absorbing-type caisson breakwaters. Based on the damping for a single perforated-wall breakwater, a methodology is proposed to enable the estimation of the damping coefficients for a breakwater with two chambers. The theoretical predictions of the reflection coefficients for the two-chamber structures using the present model are compared with those obtained from laboratory experiments by other authors. It is found that the inclusion of the damping in the interior fluid region gives rise to improved agreement between theory and experiment.     

波浪与抛石潜堤相互作用的MPS法数值模型研究

为了研究波浪与抛石潜堤相互作用过程中大自由表面变形和堤内渗流等强非线性紊流运动问题,利用改进的MPS法,建立了模拟波浪与抛石潜堤相互作用的MPS法数值计算模型。模型将抛石潜堤假定为均质多孔介质,采用Drew的二相流运动方程描述多孔介质内外的流体运动;通过在动量方程中增加非线性阻力项,并引入亚粒子尺度紊流模型,模拟波浪与可渗结构物相互作用过程中的紊流运动。选取“U”型管中多孔介质内渗流过程和孤立波与可渗潜堤相互作用两个典型的渗流问题,通过将数值计算结果与理论解和实测值的对比分析,对所提出的MPS法紊流渗流模型的模拟精度进行验证。结果表明:基于改进的MPS法构建的垂向二维紊流渗流模型可以很好地再现“U”型管中多孔介质内渗流以及波浪作用下可渗潜堤内外的复杂流场,显著缓解流-固界面处的压力震荡与粒子分布不均匀问题,实现了较高的模拟精度。     

Dual pontoon floating breakwater

The hydrodynamic properties of a dual pontoon floating breakwater consisting of a pair of floating cylinders of rectangular section, connected by a rigid deck, is investigated theoretically. The structure is partially restrained by linear symmetric moorings fore and aft. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of the breakwater is taken to be that of a two-dimensional rigid body undergoing surge, heave and pitch motions. The solution for the fluid motion is obtained by the boundary integral equation method using an appropriate Green's function. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the efficiency of the breakwater as a barrier to wave action. It is found that the wave reflection properties of the structure depend strongly on the width, draft and spacing of the pontoons and the mooring line stiffness, while the excess buoyancy of the system is of lesser importance.     

Mooring forces and motion responses of pontoon-type floating breakwaters

The experimental and theoretical investigations on the behaviour of pontoon-type floating breakwaters are presented. A two-dimensional finite element model is adopted to study the behaviour of pontoon-type floating breakwaters in beam waves. The stiffness coefficients of the slack mooring lines are idealized as the linear stiffness coefficients, which can be derived from the basic catenary equations of the cable. The theoretical model is supported by an experimental programme conducted in a wave flume. The motion responses and mooring forces are measured for three different mooring configurations, and the results are reported and discussed in detail in this paper. The wave attenuation characteristics are presented for the configurations studied.     

Performance of pile-restrained flexible floating breakwaters

The overall performance of pile-restrained flexible floating breakwaters is investigated under the action of linear monochromatic incident waves in the frequency domain. The aforementioned floating breakwaters undergo only vertical structural deflections along their length and are held in place by means of vertical piles. The total number of degrees of freedom equals the six conventional body modes, when the breakwater moves as a rigid body, plus the extra bending modes. These bending modes are introduced to represent the structural deflections of the floating breakwater and are described by the Bernoulli–Euler flexible beam equation. The number of bending modes introduced is determined through an appropriate iterative procedure. The hydrostatic coefficients corresponding to the bending modes are also derived. The numerical analysis of the flexible floating breakwaters is based on a three-dimensional hydrodynamic formulation of the floating body. A parametric study is carried out for a wide range of structural stiffness parameters and wave headings, to investigate their effect on the performance of flexible floating breakwaters. Moreover, this performance is compared with that of the corresponding pile-restrained rigid floating breakwater. Results indicated that the degree of structural stiffness and the wave heading strongly affect the performance of flexible floating breakwaters. The existence of an “optimum” value of structural stiffness is demonstrated for the entire wave frequency range.     

An effective wave-trapping system

This is a theoretical study of a breakwater-seawall wave-trapping system. The breakwater, being flexible, porous and thin beam-like, is held fixed in the sea bed and idealized as one-dimensional beam of uniform flexural rigidity and uniform mass per unit length. The seawall, being vertical, rigid and impermeable, is located behind the breakwater by a distance of L. The velocity potentials of the wave motion are coupled with the equation of motion of the breakwater. Analytical solutions in closed forms are obtained for the reflected and transmitted velocity potentials together with the displacement of the breakwater. The free-surface elevation, hydrodynamic forces acting on both the breakwater and the seawall are determined. It is found that the values of L, at which the minimum reflected-wave amplitudes reach, are in the range of λ to λ for breakwaters with different rigidity and permeability. It is shown that, when the spacing L maintains values in the range of λ to λ, the resultant amplitudes in both regions can be reduced to a favorable amount for any wave and structural parameters. It is also shown that the hydrodynamic forces on the breakwater decrease as the structural flexibility and porosity increase. However, with increases of the structural porosity and flexibility, the seawall experiences an increase of the hydrodynamic forces. Various results are presented in this paper to illustrate the effects of the structural and perous parameters together with the spacing on the response and efficiency of the breakwater-seawall wave-trapping system.     

Dynamic response and sliding distance of composite breakwaters under breaking and non-breaking wave attack

Over the last 15 years improved awareness of wave impact induced failures has focused attention on the need to account for the dynamic response of maritime structures to wave impact load. In this work a non-linear model is introduced that allows evaluating the effective design load and the potential sliding of caisson breakwater subject to both pulsating and impulsive wave loads. The caisson dynamics is modelled using a time-step numerical method to solve numerically the equations of motion for a rigid body founded on multiple non-linear springs having both horizontal and vertical stiffness. The model is first shown to correctly describe the dynamics of caisson breakwaters subject to wave attack, including nonlinear features of wave–structure–soil interaction. Predictions of sliding distances by the new method are then compared with measurements from physical model tests, showing very good agreement with observations. The model succeeds in describing the physics that stands behind the process and is fast, accurate and flexible enough to be suitable for performance design of caisson breakwaters.     

Reflection of Oblique Incident Waves by Breakwaters with Partially-Perforated Wall

The reflection of oblique incident waves from breakwaters with a partially-perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigenfunction expansion method is applied to expand velocity poten-tials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with experimental data. The effect of porosity, the relative chamber width, the relative water depth in the wave absorbing chamber and the water depth in front of the structure are discussed.     

透空式防波堤周围的非线性波浪传播的数值模拟

对非线形波浪在透空式防波堤周围的波浪变形进行了数值模拟,在Boussinesq波浪方程中加入与透空建筑物有关的新的耗散项,从而界定了透空建筑物引起的部分反射和透射,波浪折射衍射的传播过程通过控制方程求解。波浪控制方程通过有限差分方法求解。模型应用于模拟波浪经过具有部分反射的群桩式透空结构,结果表明透空式防波堤可以有效地衰减波浪,是重力式结构的一种替代形式。     

Performance of hemi-cylindrical and rectangular submerged breakwaters

A parametric experimental study is conducted to compare the reflection and transmission characteristics of submerged hemi-cylindrical and rectangular rigid and water-filled flexible breakwater models. The results show that, for the rigid breakwaters, rectangular models are more effective than hemi-cylindrical ones in terms of reduction of transmitted waves. As for the flexible breakwaters, the hemi-cylindrical models may give better wave reflection than rectangular ones. However, the energy loss induced by the rectangular breakwaters is much larger and more significant to result in an overall better efficiency in terms of reduction in wave transmission. The effects of internal pressure show that the lowest pressurized flexible models considered in this work are the most effective in the reduction of the transmitted wave height. Higher wave reflection, lower wave transmission and higher energy loss are obtained consistently at the lower submergence depth ratio.     

Meshless Method for Analysis of Permeable Breakwaters in the Proximity of A Vertical Wall

In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method(BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater's width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.     

近破波作用下沉箱式防波堤运动特性的模型实验研究

对近破波作用下沉箱式防波堤的运动特性进行了模型实验研究。实验中测量了沉箱模型与基床的摩擦系数、基床刚度和阻尼系数;不同水位情况下作用于沉箱模型上的近破波波压力时程;近破波作用下沉箱模型的位移和转角响应时程等,并与数学模型计算结果进行了比较分析。实验结果表明,若沉箱的滑移力大于沉箱与基床间的摩擦力,在连续波浪作用下,沉箱将连续出现间歇式滑移运动,数学模型可较好地模拟这一运动过程。     

The new wave overtopping database for coastal structures

Significant effort has been made to generate a homogeneous database on wave overtopping consisting of more than 10,000 irregular wave overtopping tests from more than 160 independent projects or test series, each described by means of 31 parameters. Many coastal structures, including dikes, rubble mound breakwaters, berm breakwaters, caisson structures and combinations have been considered and have been schematised for inclusion in the database. All these overtopping tests are represented by over 300,000 numbers in the database.     

Vibrating-Rocking Motion of Caisson Breakwater Under Breaking Wave Impact

The possible motions of a caisson breakwater under dynamic load excitation include vibrating, vibrating-sliding and vibrating-rocking motions. The models of vibrating motion and vibrating-sliding motion have been proposed in an early paper. In this paper, a model of vibrating-rocking motion of caisson breakwaters under breaking wave impact is presented, which can be used to simulate the histories of vibrating-rocking motion of caisson breakwaters. The effect of rocking motion on the displacement, rotation, sliding force and overturning moment of breakwaters is investigated. In case the overturning moment exceeds the stability moment of a caisson, the caisson may only rock. The caisson overturns only in case the rocking angle exceeds the critical angle. It is shown that the sliding force and overturning moment of breakwaters can be reduced effectively due to the rocking motion. It is proposed that some rocking motion should be allowed in breakwater design.     

A Probabilistic Method for Motion Analysis of Caisson Breakwaters

1 .IntroductionInrecent years ,especiallyfrom1994 when aninternational conference on breakwater design washeldinJapan,muchresearchonthe dynamic analysis of caisson breakwaters has been done ,and manyimportant progresses have been made .Oumeraci and Korten…     

Springing analysis of a seagoing vessel using fully coupled BEM-FEM in the time domain

The quasi-steady resonant vibration of a flexible seagoing vessel under resonant wave excitation force, called springing, is studied in this paper. A higher-order B-spline Rankine panel method is used to represent the effects of the fluid motion surrounding this flexible seagoing vessel, and a finite element formulation based on Vlasov beam is employed for structural response. The boundary integral equation and finite element equation, both for fluid and structural domains, are fully coupled with each other using an iterative implicit method in the time domain. Coupling between the two field equations is achieved by relying on fixed-point iteration with relaxation aided by Aitken's δ² process to maximize convergence speed. The steady-unsteady coupling term or m-term in the linearized body boundary condition derived by Timman and Newman is taken into account for accurate prediction of flexible body motion when forward speed is present. The 2nd derivative of basis potential in the m-term is obtained by modifying Nakos approach, which was originally developed using the Stokes theorem for rigid body ship motion problem. For the solution of the FE equation, instead of conventionally used modal superposition method, a direct integration scheme based on Newmark method is employed. It is believed that this technique is more attractive in the sense that it allows us free from the selection of optimum number of mode-shapes in the computation.     

Wave diffraction by elliptical breakwaters in shallow water

The scattering of waves by both floating and submerged stationary elliptical breakwaters is investigated by means of linearised shallow water wave theory. This formulation leads to solutions for the fluid velocity potential in terms of Mathieu functions of real argument. Expressions are derived for the wave-induced forces and moments on the structures and their total and differential scattering cross-sections. Numerical results are presented for a range of wave and structural parameters.The present analysis serves as a prelude to a more comprehensive study of the problem without the shallow water restriction.     

Analytical solution on the surge motion of tension-leg twin platform structural systems

In this study the wave induced surge motion of a twin platform of a pretension leg structural system is investigated. A set of equations along with boundary conditions are derived, and solutions are obtained analytically. The tension-legged twin platform structural system might better represent a platform system in the practical application in either idealized two-dimensional analysis or actual three-dimensional practice than a single platform system. In the analysis the coupling problem of a two-dimensional tension leg twin platform interacting with a monochromatic linear wave train in an inviscid and incompressible fluid is considered. The problem is considered as a combination of the scattering and radiation. These two boundary-value problems are first solved independently and then combined together to resolve for all unknowns. The analysis is focused on the wave induced surge motion of the twin platform and the reflection coefficient. Other than the wave-related parameters, the dimensional effect of the twin platform structure is examined and presented in numerical examples. From the analytical results, it is found that the behavior of the tension-leg twin platform is significantly influenced by dimensional factors of the platform system such as the dimension of each single platform and the spacing between two platforms. It is also realized that to simplify the analysis of a twin platform system into a single platform, it tends to underestimate the wave-induced response and then reduces the safety of the platform system.     

Numerical Wave Flume Study on Wave Motion Around Submerged Plates

1 .IntroductionApile supportedplatesubmergedatacertaindepthunderseasurfacewasdevelopedasanewtypeofunderwaterbreakwaterfortheprotectionofcoastlinesandharbors .Thisisbecauseitdoesnothinderthewaterexchangebetweentheopenseaandtheprotectedareanordoesithindertheviewovertheopensea .Besides,itislessdependentonthegeotechnicalconditionsoftheseabottomwherethestructureistobeinstalled ;however,itscostishigh ,particularlyinrelativelydeepwaters .Formanyapplicationsitispossibletoreducethewavemotionintheprotec…