Water wave interaction with an array of bottom-mounted surface-piercing porous cylinders

The interaction of water waves with arrays of bottom-mounted, surface-piercing circular cylinders is investigated theoretically. The sidewall of each cylinder is porous and thin. Under the assumptions of potential flow and linear wave theory, a semi-analytical solution is obtained by an eigenfunction expansion approach first proposed for impermeable cylinders by Spring and Monkmeyer (1974), and later simplified by Linton and Evans (1990). Analytical expressions are developed for the wave motion in the exterior and all interior fluid regions. Numerical results are presented which illustrate the effects of various wave and structural parameters on the hydrodynamic loads and the diffracted wave field. It is found that the porosity of the structures may result in a significant reduction in both the hydrodynamic loads experienced by the cylinders and the associated wave runup.     

Interaction of cnoidal waves with an array of vertical concentric porous cylinders

An array of large concentric porous cylinder arrays is mounted in shallow water exposed to cnoidal waves. The interactions between waves and cylinders are studied theoretically using an eigenfunction expansion approach. Semi-analytical solutions of hydrodynamic loads and wave run-up on each cylinder are obtained using first approximation to cnoidal waves. The square array configuration of four-legged identical concentric porous cylinder is investigated in present study. Numerical results reveal the variation of dimensionless wave force and wave run-up on individual cylinder with angle of incidence, porosity parameter, spacing between outer and inner cylinders, spacing between concentric porous cylinders and wave parameter. Different mechanism of wave force is found under different range of scattering parameter.     

Forces and moment on a horizontal plate due to regular and irregular waves in the presence of current

This work presents an experimental study of a submerged plate used as a breakwater for coastal areas protection. Questions addressed concern the influence of current on the reflective power of the plate, and its influence on the hydrodynamic loads exerted on it. Results concern both monochromatic and irregular waves. Generally speaking, an influence of the current is found, changing the reflecting power of the structure up to 50%. A homogenized behavior of the loads and moments is found in the presence of currents, meaning that the load values become less sensitive to the frequency. Furthermore, the influence of waves reflected by the wave absorber, representing partially reflective conditions at the shore, is found to be of same order in the absence of current. In any case, the linear behavior of the breakwater is emphasized through the irregular waves approach.     

Wave interaction with a semi-porous cylindrical breakwater mounted on a storage tank

The interaction of linear water waves with a semi-porous cylindrical breakwater surrounding a rigid vertical circular cylinder mounted on a storage tank is investigated theoretically. The cylindrical breakwater structure is porous in the vicinity of the free-surface, while at some distance below the water surface it becomes impermeable. Under the assumptions of linearized potential flow, the coupled problem of flow in the interior and exterior fluid regions is solved by an eigenfunction expansion approach. Analytical expressions are obtained for the wave motion in both the interior and exterior flow regions. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the hydrodynamic loads and interior and exterior wave fields. It is found that for certain parameter combinations the semi-porous, cylindrical breakwater may result in a significant reduction in the wave field and hydrodynamic forces experienced by the interior structure.     

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.     

Hydrodynamic characteristics of semi-immersed breakwater with an attached porous plate

In the present study, wave interaction with a fixed, partially immersed breakwater of box type with a plate attached (impermeable-permeable) at the front part of the structure is investigated numerically and experimentally. The large scale laboratory experiments on the interaction of regular waves with the special breakwater were conducted in the wave flume of Laboratori d’Enginyeria Marνtima (LIM) at Universitat Politecnica de Catalunya (UPC) in Barcelona. Experimental results are compared with numerical results obtained with the use of the Cornell breaking Wave and Structures (COBRAS) wave model. The effects of an impermeable as well as a permeable plate attached to the bottom of the breakwater on its hydrodynamic characteristics (wave transmission, reflection, dissipation, velocity and turbulence kinetic energy) are investigated. Computed velocities and turbulence kinetic energy in the vicinity of the structure indicate the effects of the breakwater with the attached (impermeable/permeable) plate on the flow pattern and the turbulence structure. The attached impermeable plate at the front part of the breakwater enhances significantly the efficiency of the structure in attenuating the incident waves. The permeable plate reduces the efficiency of the structure since wave energy is transmitted through the porous body of the plate. Based on the hydrodynamic characteristics it is inferred that the breakwater with an impermeable plate attached to its bottom is more efficient. The comparison of horizontal and vertical forces acting on the breakwater for all cases examined reveals that plate porosity influences slightly vertical force and severely horizontal force acting on the structure, reducing maximum values in both cases.     

Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate

This study examines the hydrodynamic performance of a new perforated-wall breakwater. The breakwater consists of a perforated front wall, a solid back wall and a submerged horizontal porous plate installed between them. The horizontal porous plate enhances the stability and wave-absorbing capacity of the structure. An analytical solution based on linear potential theory is developed for the interaction of water waves with the new proposed breakwater. According to the division of the structure, the whole fluid domain is divided into three sub-domains, and the velocity potential in each domain is obtained using the matched eigenfunction method. Then the reflection coefficient and the wave forces and moments on the perforated front wall and the submerged horizontal porous plate are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a perforated-wall breakwater with a submerged horizontal solid plate [Yip, T.L., Chwang, A.T., 2000. Perforated wall breakwater with internal horiontal plate. Journal of Engineering Mechanics ASCE 126 (5), 533–538] and a vertical wall with a submerged horizontal porous plate [Wu, J.H., Wan, Z.P., Fang, Y., 1998. Wave reflection by a vertical wall with a horizontal submerged porous plate. Ocean Engineering 25 (9), 767–779]. Numerical results show that with suitable geometric porosity of the front wall and horizontal plate, the reflection coefficient will be always rather small if the relative wave absorbing chamber width (distance between the front and back walls versus incident wavelength) exceeds a certain small value. In addition, the wave force and moment on the horizontal plate decrease significantly with the increase of the plate porosity.     

Incompressible SPH flow model for wave interactions with porous media

The paper presents an Incompressible Smoothed Particle Hydrodynamics (ISPH) method to simulate wave interactions with a porous medium. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. The ISPH method employs a strict incompressible hydrodynamic formulation to solve the fluid pressure and the numerical solution is obtained by using a two-step semi-implicit scheme. The ISPH flow model solves the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the NS type model equations for the flows inside the porous media. The presence of porous media is considered by including additional friction forces into the equations. The developed ISPH model is first validated by the solitary and regular waves damping over a porous bed and the solitary wave interacting with a submerged porous breakwater. The convergence of the method and the sensitivity of relevant model parameters are discussed. Then the model is applied to the breaking wave interacting with a breakwater covered with a layer of porous materials. The computational results demonstrate that the ISPH flow model could provide a promising simulation tool in coastal hydrodynamic applications.     

Hydrodynamic performance of a dual cylindrical caisson breakwater

The hydrodynamic performance of a dual cylindrical caisson breakwater (DCBW) formed by a row of caissons each of which consisting of a porous outer cylinder circumscribing an impermeable inner cylinder has been theoretically investigated. The theoretical formulation is based on the eigenfunction expansion method proposed by Spring and Monkmeyer (1974) which was further modified by Linton and Evans [Linton, C.M., Evans, D.V., 1990. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 215, 549–569] for an array of impermeable cylinders. The present formulation is an extension of the work of Wang and Ren [Wang, K.H., Ren, X., 1994. Wave interaction with a concentric porous cylinder system. Ocean Engineering 21(4), 343–360], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. In the present study, the formulation has been extended to the case of a group of porous dual cylinder system. Parametric studies are carried out to study the influence of porosity (G₀) on the outer caisson, width of the doughnut chamber (a/b) and the angle of wave incidence on the variation in the hydrodynamic loading, wave run-up, free-surface elevation in its vicinity as well as the transmission on its lee-side. The importance of the presence of the inner cylinder in achieving the required hydrodynamic performance in terms of either protection or providing tranquility on its lee side keeping higher stability for the breakwater system is highlighted.     

Wave damping characteristics of vertically stratified porous structures under oblique wave action

The characteristics of wave damping for the vertically stratified porous breakwaters are investigated under oblique wave action. It is found that for common angles of incidence, the wave damping efficiency of a vertically stratified porous structure behaves very similar to a simple structure. The reflection coefficient decreases with increasing angle of incidence while the transmission coefficient only slightly increases as the angle of incidence increases. It is shown that the wave energy loss is in direct proportional to the structure thickness and its porosity regardless of the angle of incidence. Considering small transmission coefficient as a basic requirement and if a moderate reflection coefficient is accepted, a structure thickness of b/h=1 is proposed. In this situation, since the structure does not have a very large thickness, adopting a vertically stratified structure is not an effective way to improve its wave damping efficiency.     

聚焦波作用下平面网衣结构的水动力特性研究

由于沿海区域的限制以及愈加严重的环境污染,渔业养殖正从近海走向深远海。深远海海域的海况更加恶劣,给养殖装备的设计与性能评估带来新的挑战。为解决该问题,对极端波浪与养殖装备网衣结构的相互作用开展研究。基于waves2Foam建立数值波浪水池,极端波浪模拟采用基于NewWave理论的聚焦波模型,网衣结构模拟采用多孔介质模型,并通过与Morison模型计算的网衣受力等效分析,获得多孔介质模拟网衣结构阻力系数的直接估计方法。然后将多孔介质模型嵌入waves2Foam中,开展聚焦波与网衣结构相互作用的数值模拟,同时开展水槽试验,验证数值模拟的准确性。基于数值模拟结果,系统地分析了不同网衣密实度及不同波浪参数下网衣结构的升阻力特性以及网衣结构对波浪场的扰动规律。研究表明：聚焦波波峰幅值和网衣密实度对网衣结构的升阻力影响较大,且升力峰值出现在阻力为0的时刻;网衣结构对聚焦波的时空演化特性有影响,改变了聚焦波波形。     

On-line identification and convergence analysis of excitation-force and drag-force models for moored floating structures

This work presents an approach to identify hydrodynamic models for incident, diffraction and viscous forces acting on a moored floating structure. An important aspect treated here is the analysis of the unknown initial condition of the hydrodynamic state for the potential-radiation force. There is established its influence on the parameter convergence and the long-term effects. Afterwards the persistency of excitation of the regressor is analyzed in the case of both poor and rich excitation conditions. Theoretical results show that asymptotic convergence of the estimates takes place under arbitrary conditions of the wave excitation. A case study consisting in the identification of a moored semisubmersible is carried out to exemplify the application of the approach.     

Experimental study on wave transmission coefficient, mooring lines and module connector forces with different designs of floating breakwaters

This paper presents the results and conclusions obtained from the physical model tests carried out with four different designs of floating breakwaters. Changes from a basic design have been introduced in order to evaluate the improvement in the efficiency as a coastal protection structure. Incident and transmitted waves have been measured, as well as the efforts in the mooring lines and module connectors. It has been found that the width of the pontoons is one of the key design parameters, while small modifications in the floating breakwater's cross section shape are less determinant in its hydrodynamic behaviour and in mechanical loads in the discussed ranges. 2D and 3D tests were conducted, observing the great influence that the wave obliquity has in the module connector forces.     

A coupled numerical model for simulation of wave breaking and hydraulic performances of a composite seawall

A numerical model is developed by combining a porous flow model and a two-phase flow model to simulate wave transformation in porous structure and hydraulic performances of a composite type low-crest seawall. The structure consists of a wide submerged reef, a porous terrace at the top and an impermeable rear wall. The porous flow model is based on the extended Navier-Stokes equations for wave motion in porous media and k−ε turbulence equations. The two-phase flow model combines the water domain with the air zone of finite thickness above water surface. A unique solution domain is established by satisfying kinematic boundary condition at the interface of air and water. The free surface advection of water wave is modeled by the volume of fluid method with newly developed fluid advection algorithm. Comparison of computed and measured wave properties shows reasonably good agreement. The influence of terrace width and structure porosity is investigated based on numerical results. It is concluded that there exist optimum value of terrace width and porosity that can maximize hydraulic performances. The velocity distributions inside and in front of the structure are also investigated.     

A parametric study of wave loads on trimaran ships traveling in waves

In this paper, we present a spectral analysis based on wave loads to select suitable side-hull arrangements for a trimaran ship traveling in waves. Neglecting the steady flow effect, the three-dimensional source-distribution method, using a pulsating source potential incorporating the panel method, is adopted to solve the corresponding hydrodynamic coefficients. The significant values for wave loads, including shear forces, bending moments, and torsion moments at different locations on the main hull and connected deck with respect to different staggers and clearances, are derived by the spectral analysis. Several ship speeds and wave headings are also considered for comparison. This study offers more information for selecting the side-hull arrangement from the viewpoint of wave loads on trimaran ships, which may be regarded as helpful references for seakeeping design of these types of ships.     

Characteristics of breaking irregular wave forces on a monopile

The substructures of offshore wind turbines are subjected to extreme breaking irregular wave forces. The present study is focused on investigating breaking irregular wave forces on a monopile using a computational fluid dynamics (CFD) based numerical model. The breaking irregular wave forces on a monopile mounted on a slope are investigated with a numerical wave tank. The experimental and numerical irregular free surface elevations are compared in the frequency-domain for the different locations in the vicinity of the cylinder. A numerical analysis is performed for different wave steepness cases to understand the influence of wave steepness on the breaking irregular wave loads. The wave height transformation and energy level evolution during the wave shoaling and wave breaking processes is investigated. The higher-frequency components generated during the wave breaking process are observed to play a significant role in initiating the secondary force peaks. The free surface elevation skewness and spectral bandwidth during the wave transformation process are analysed and an investigation is performed to establish a correlation of these parameters with the breaking irregular wave forces. The role of the horizontal wave-induced water particle velocity at the free surface and free surface pressure in determining the breaking wave loads is highlighted. The higher-frequency components in the velocity and pressure spectrum are observed to be significant in influencing the secondary peaks in the breaking wave force spectrum.     

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.     

Experimental study of wave loads on a small vehicle in close proximity to a large vessel

Operations involving the launch or recovery of a smaller vessel from a larger one are extremely dangerous in high sea states and, therefore, they are normally carried out in low to moderate sea states. However, this can be severely restrictive and in some situations, carrying out such operations in high sea states is unavoidable. Here we report on a detailed investigation of the interaction between two vessels of different size in order to characterise their hydrodynamic interaction under different conditions and to provide insight for operational purposes. Model experiments were conducted to investigate the hydrodynamic interaction between two vessels in close proximity in waves. Previous studies into this interaction have focused on two vessels with comparable size/displacement. This study focused on the interaction between vessels of very different sizes, a platform supply vessel and a lifeboat, at various separation distances between the two models and wave headings. It is found that the effect of the hydrodynamic interaction on the wave loads on the lifeboat model is substantial. The load responses show a strong non-linearity (high order harmonic components). In head waves, the effect of the hydrodynamic interaction on the wave loads is greater in the transverse modes (sway, roll and yaw) than in the longitudinal modes (surge, heave and pitch). The sheltering effects of the larger model on the lifeboat model were also evident from the experiments. The results of this investigation may be used to inform the planning of marine operations, such as the launch and recovery of a lifeboat or an Autonomous Underwater Vehicle (AUV) from a mothership and the transfer of equipment or personnel between vessels. The data will also provide a useful resource for validation of Computational Fluid Dynamics (CFD) codes and other numerical simulations, and can be used to better understand the limitations and potential widening of the operational weather windows and to ensure that operations are carried out safely.     

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。     

An Improved Time Domain Approach for Analysis of Floating Bridges Based on Dynamic Finite Element Method and State-Space Model

The floating bridge bears the dead weight and live load with buoyancy, and has wide application prospect in deep-water transportation infrastructure. The structural analysis of floating bridge is challenging due to the complicated fluid-solid coupling effects of wind and wave. In this research, a novel time domain approach combining dynamic finite element method and state-space model (SSM) is established for the refined analysis of floating bridges. The dynamic coupled effects induced by wave excitation load, radiation load and buffeting load are carefully simulated. High-precision fitted SSMs for pontoons are established to enhance the calculation efficiency of hydrodynamic radiation forces in time domain. The dispersion relation is also introduced in the analysis model to appropriately consider the phase differences of wave loads on pontoons. The proposed approach is then employed to simulate the dynamic responses of a scaled floating bridge model which has been tested under real wind and wave loads in laboratory. The numerical results are found to agree well with the test data regarding the structural responses of floating bridge under the considered environmental conditions. The proposed time domain approach is considered to be accurate and effective in simulating the structural behaviors of floating bridge under typical environmental conditions.