Water wave interaction with a floating porous cylinder

The interaction of water waves with a freely floating circular cylinder possessing a side-wall that is porous over a portion of its draft is investigated theoretically. The porous side-wall region is bounded top and bottom by impermeable end caps thereby resulting in an enclosed fluid region within the structure. The problem is formulated based on potential flow and linear wave theory and assuming small-amplitude structural oscillations. An eigenfunction expansion approach is then used to obtain semi-analytical expressions for the hydrodynamic excitation and reaction loads on the structure. Numerical results are presented which illustrate the effects of the various wave and structural parameters on these quantities. It is found that the permeability, size and location of the porous region may have a significant influence on the horizontal components of the hydrodynamic excitation and reaction loads, while its influence on the vertical components in most cases is relatively minor.     

Wave interaction with cylindrical porous piles

The interaction of waves with arrays of porous circular cylinders is studied theoretically and, under the assumption of potential flow and linear wave theory, an analytical solution is derived. The solution is valid for either submerged or emerged structures. The extension to the cases of unidirectional and multidirectional waves is obtained by means of a transfer function. For specific conditions the model gives the same solution as those previously presented by other authors. Numerical results are presented which exemplify diverse wave and mechanical parameters on the wave transformation due to the presence of a system of circular cylinders.     

Water wave interaction with surface-piercing porous cylinders using the null-field integral equations

Following the successful experiences of solving water wave scattering problems for multiple impermeable cylinders by the authors' group, we extend the null-field integral formulation in conjunction with the addition theorem and the Fourier series to deal with the problems of surface-piercing porous cylinders in this paper. In the implementation, the null-field point can be exactly located on the real boundary free of calculating the Cauchy and Hadamard principal values, thanks to the introduction of degenerate kernels (or separable kernels) for fundamental solutions. This method is a semi-analytical approach, since errors attribute from the truncation of the Fourier series. Not only a systematic approach is proposed but also the effect on the near-trapped modes due to porous cylinders and disorder of layout is examined. Several advantages such as mesh-free generation, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence, over the conventional boundary element method (BEM) are achieved. It is found that the disorder has more influence to suppress the occurrence of near-trapped modes than the porosity. The free-surface elevation is consistent with the results of William and Li and those using the conventional BEM. Besides, the numerical results of the force on the surface of cylinders agree well with those of William and Li. Besides, the present method is a semi-analytical approach for problems containing circular and elliptical shapes at the same time.     

Short-crested wave interaction with a concentric porous cylindrical structure

In this paper, theoretical study is carried out to investigate the general 3D short-crested wave interaction with a concentric two-cylinder system. The interior cylinder is impermeable and the exterior cylinder is thin in thickness and porous to protect the interior cylinder. Both cylinders are surface-piercing and bottom mounted. Analytical solution is derived based on the linear potential theory. The effects of the wide range wave parameters and structure configuration including porosity of the exterior cylinder and the annular spacing on the wave forces, surface elevations and the diffracted wave contours are examined.     

Wave interaction with one or two rows of closely spaced rectangular cylinders

Experimental results are reported on the wave reflection from and transmission through one row or two rows of closely spaced rectangular cylinders. An empirical expression is proposed for the friction factor which models the head loss due to closely spaced rectangular cylinders. Algebraic expressions are presented to calculate the reflection and transmission coefficients of regular waves for a single slotted wall or double slotted walls. The model is validated by the published and present experimental results. The proposed method can be used for the preliminary design of slotted-wall breakwaters.     

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.     

Interaction between waves and an array of floating porous circular cylinders

The present study theoretically as well as experimentally investigates the interaction between waves and an array of porous circular cylinders with or without an inner porous plate based on the linear wave theory.To design more effective floating breakwaters,the transmission rate of waves propagating through the array is evaluated.Each cylinder in the array is partly made of porous materials.Specifically,it possesses a porous sidewall and an impermeable bottom.In addition,an inner porous plate is horizontally fixed inside the cylinders.It dissipates the wave more effectively and eliminates the sloshing phenomenon.The approach suggested by Kagemoto and Yue(1986) is adopted to solve the multiple-scatter problem,while a hierarchical interaction theory is adopted to deal with hydrodynamic interactions among a great number of bodies,which efficiently saves computation time.Meanwhile,a series of model tests with an array of porous cylinders is performed in a wave basin to validate the theoretical work and the calculated results.The draft of the cylinders,the location of the inner porous plate,and the spacing between adjacent cylinders are also adjusted to investigate their effects on wave dissipation.     

多向不规则波浪作用下群墩结构上爬高的计算研究

波浪的方向分布对波浪的传播及其与工程结构物的作用都具有明显影响,目前现有的研究大多是基于单向波浪进行的。为了研究方向分布对群墩结构上的爬高影响,基于规则波浪与群墩作用的理论解,结合多向不规则波浪的造波方法,建立了多向不规则波浪与群墩作用的计算模型,同时进行了物理模型试验对模型的有效性进行了验证。系统地对群墩周围及表面上的波浪爬高进行了计算分析,结果表明,方向分布对波浪爬高具有较大的影响,且不同位置处的影响并不相同,在实际的工程设计中如果按照单向波浪计算,可能低估或者高估群墩周围的爬高。     

Three dimensional wave scattering by arrays of elliptical and circular cylinders

Recently, Chatjigeorgiou and Mavrakos (2009, 2010a) provided an analytic solution for the three dimensional wave scattering by arrays of elliptical cylinders. The present paper extends the contents of the existing study to tackle the problem of the hydrodynamic interactions between elliptical and circular cylinders. The main task is to derive an analytic solution for the total velocity potential for an arbitrary body of the array and accordingly, to express the hydrodynamic pressure, the exciting forces and the wave elevation in compact analytic closed-forms.The solution method is rather complicated as it considers the circular cylinders as different geometries and not special cases of elliptical cylinders with zero elliptic eccentricity. Nevertheless, the adopted procedure enhances the mathematical reconstruction of the physical subject as it requires the derivation and the employment of addition theorems that transform expressions from elliptic to polar coordinate systems in all four possible combinations.     

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.     

Semi-analytical solution for the water wave diffraction by arrays of truncated circular cylinders in front of a vertical wall

The present study investigates the combined wave field that is induced by the continuous interaction of plane waves with an array of truncated circular cylinders in front of a rigid wall. The long-term goal of the study is the investigation of possible increase in the efficiency of cylindrical Wave Energy Converters (WECs) by putting in the vicinity of the array a barrier to propagation, a wall, that could assist the reflection of the incoming waves. The main task is to develop a generic solution method that is free of conceptual simplifications employed, e.g. by the method of images and the assumption of “pure” wave reflection. To cope with the set task, the proposed method relies on the semi-analytical formulation of the velocity potentials, while the solution is sought by combined expressions that involve polar and elliptical harmonics. The wall is represented as an elliptical cylinder with zero semi-minor axis. This assumption has eventually a beneficial effect to the underlying formulation given that it simplifies significantly the expansions of the involved diffraction potentials.     

Solitary wave interaction with a concentric porous cylinder system

Theoretical investigations on solitary waves interacting with a surface-piercing concentric porous cylinder system are presented in this paper. The outer cylinder is porous and considered thin in thickness, while the inner cylinder is solid. Both cylinders are rigidly fixed on the bottom. Following Isaacson's [Isaacson, Micheal de St. Q., 1983. Solitary wave diffraction around large cylinder. Journal of the Waterway, Port, Coastal and Ocean Engineering 109(1), 121–127.] approach, we obtained the solutions for free-surface elevation and the corresponding velocity potential in terms of Fourier integrals. Numerical results are presented to show the effects of incident wave condition, porosity of the outer cylinder and radius ratio on wave forces and wave elevations around the inner and outer cylinders.     

Interaction of regular waves with a group of dual porous circular cylinders

Diffraction of linear waves around a group of dual porous cylinders consisting of a thin and porous outer cylinder with an impermeable inner cylinder is investigated analytically based on the eigenfunction expansion method proposed by Spring and Monkmeyer [Spring BH, Monkmeyer PL. Interaction of plane waves with vertical cylinders. In: Proceedings 14th international coastal engineering conference. 1974. p. 1828–47] and further modified by Linton and Evans [Linton CM, Evans DV. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 1990;215:549–69]. The present formulation is an extension of the work of Wang and Ren [Wang KH, Ren X. Wave interaction with a concentric porous cylinder system. Ocean Engineering 1994;21(4):343–60], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. This paper aims at investigating the influence of multiple interactions between the cylinders in the group on the hydrodynamic wave forces, wave run-up and free-surface elevation in their vicinity. Further, the study focuses on the variation of the forces and run-up on the individual cylinders within the group compared to that on isolated cylinders.     

Short-crested waves interaction with a concentric porous cylinder system with partially porous outer cylinder

In this paper, based on the linear wave theory, the interaction of short-crested waves with a concentric dual cylindrical system with a partially porous outer cylinder is studied by using the scaled boundary finite element method (SBFEM), which is a novel semi-analytical method with the advantages of combining the finite element method (FEM) with the boundary element method (BEM). The whole solution domain is divided into one unbounded sub-domain and one bounded sub-domain by the exterior cylinder. By weakening the governing differential equation in the circumferential direction, the SBFEM equations for both domains can be solved analytically in the radial direction. Only the boundary on the circumference of the exterior porous cylinder is discretized with curved surface finite elements. Meanwhile, by introducing a variable porous-effect parameter G, non-homogeneous materials caused by the complex configuration of the exterior cylinder are modeled without additional efforts. Comparisons clearly demonstrate the excellent accuracy and computational efficiency associated with the present SBFEM. The effects of the wide range wave parameters and the structure configuration are examined. This parametric study will help determine the various hydrodynamic effects of the concentric porous cylindrical structure.     

Solitary wave interactions with an array of two vertical cylinders

This paper addresses a numerical investigation of nonlinear waves interactions with an array of two surface-piercing vertical cylinders and the corresponding nonlinear hydrodynamic loads on each individual cylinder. The primary interest of this study is concentrated on the problem of three-dimensional scattering of solitary waves by cylinder arrays and the nonlinear interactions between scattered waves. The theoretical model adopted for simulation is the generalized Boussinesq two-equation model. The boundary-fitted coordinate transformation and multiple-grid technique are utilized here to simplify the computation domain and to facilitate the applications of the boundary conditions on the cylinder surfaces. The velocity potential, free-surface elevation and subsequent evolution of the scattered wave field are numerically evaluated. The hydrodynamic forces on each cylinder during wave impact are also determined. A study of the sheltering effect by the neighboring structures on wave loads is conducted. It is found that the presence of the neighboring cylinder has shown significant influence on the wave loads and the scattering of the primary incident waves. For two transversely arranged cylinders, the transverse force coefficient increases as the separation distance decreases.     

Second-order resonance among an array of two rows of vertical circular cylinders

Experimental and theoretical works are conducted on the first-order and second-order wave interactions among an array of two rows of vertical circular cylinders.We show that both the first-order and the second-order resonance of dynamic free-surface displacement could in some cases be quite relevant among an array of two rows of vertical cylinders not only in theory but also in real phenomena. In some cases, on the other hand, we show that large free-surface displacement predicted theoretically is quite attenuated in reality probably due to viscous dissipation.     

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.     

波浪对阻抗型圆柱群的绕射

应用柱面上阻抗型边界条件分析单柱和圆柱群上波面高度和总波浪力的分布规律。随着阻抗值减小波面高度明显减小,柱上总的波浪力也随之减小。由于柱间干扰和阻抗影响,波浪力在一定的波数尺寸范围内出现急降区,阻抗型柱的变化平缓,而刚性光滑壁面柱降低显著,说明阻抗越小柱间波浪散射强度越小。     

A new approximate analytic solution for water wave scattering by a submerged horizontal porous disk

This study gives a new approximate analytic solution for water wave scattering by a submerged horizontal porous disk in the context of the linear potential theory. The solution is based on the domain decomposition method. The velocity potentials are determined by two different approaches. One approach is to adopt decompositions for velocity potentials, and the other is to expand the vertical derivative of the velocity potential on the porous disk along the radial direction. Hence the velocity potentials are determined by the matched eigenfunction expansions. Differing from previous solutions with respect to the porous disk, the present solution needs no complex dispersion relations. Thus the new solution is easier for numerical implementation. According to numerical examples, the convergence of the present solution is satisfactory. In addition, the present predictions of the wave surface elevation and the vertical wave force on the disk agree very well with previous results by different approaches. The present solution can also be extended to other structures involving disks, such as a fish cage, a porous disk with finite thickness, and a submerged elastic disk.     

A theory for waves interacting with porous structures with multiple regions

This study presents an analytical solution for the problem of waves passing a submerged porous structure, using a multi-region method in the solution scheme considering the characteristics of geometry and composing materials of the porous structure. Using the flux and pressure conditions on horizontal boundaries and interfaces, the orthogonal property of wave motion within the porous layers through water depth is derived, and applied in the solution process. The flux and pressure conditions on vertical boundaries and interfaces are integrated to give a set of linear matrix equations, through which the unknown coefficients are solved. Comparisons of the present method with previous studies are preceded in verification, which suggests the validity and practicability of the present study, with a further expectation of extending our work to build a mild-slope equation over multiple-layer porous medium in the future.