Hydrodynamic coefficients for a thick-walled bottomless cylindrical body floating in water of finite depth

The paper deals with the linearized hydrodynamic forces acting on a thick-walled, bottomless cylindrical body having vertical symmetry axis and oscillating in water of finite depth. For the solution of the radiation problem, the flow field around the structure is subdivided into ring-shaped fluid regions, in each of which an axisymmetric eigenfunction expansion for the velocity potential is made. By implementing Galerkin's method the various potential solutions are then matched and numerical results concerning the hydrodynamic coefficients for heave, surge and pitch motions, as well as the coupling terms between the last two modes are obtained.     

Wave radiation and diffraction by a two-dimensional floating body with an opening near a side wall

The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi-infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.     

Water entry of a finite width wedge near a floating body

The problem of a two-dimensional finite-width wedge entering water near a freely floating body is considered through the velocity potential theory for the incompressible liquid with the fully nonlinear boundary conditions on the free surface. The problem is solved by using the boundary element method in the time domain. The numerical process is divided into two phases based on whether the interaction between the wedge and floating body is significant. In the first phase, when the single wedge enters water at initial stage, only a small part near its tip is in the fluid, the problem is studied in a stretched coordinate system and the presence of the floating body has no major effect. In the second phase, the disturbance by water entry of the wedge has reached the floating body, and both are considered together in the physical system. The auxiliary function method is adopted to decouple the nonlinear mutual dependence between the motions of the wedge and floating body, both in three degrees of freedom, and the fluid flow, as well as the interaction effects between them. Case studies are undertaken for a wedge entering water in forced or free fall motion, vertically or obliquely. Results are provided for the accelerations, velocities, pressure distribution and free surface deformation, and the interaction effects are discussed.     

大深度分层流体中二维淹没浮体的波浪力分析

研究了大深度分层流体中二维任意形状淹没浮体的波浪力特性。首先基于一种合适的格林函数,采用边界积分方程法研究了流体中浮体对水波散射问题,然后通过单个淹没圆柱体的透射能和反射能与解析方法结果的比较,对所提出的方法进行了验证,最后分析了在不同的几何和物理条件下几种形状的浮体对波浪力的特有影响,得到了一些有意义的结果,这对分层海洋中淹没浮体的设计具有重要的参考价值。     

Energy characteristics of the hydroacoustic field in a nonuniform marine medium with a cylindrical body floating on the surface

By using the hydroacoustic field generated by a point source in a nonuniform marine medium with a cylindrical body floating on the surface and determined as a solution of the corresponding problem by the method of partial domains, we study the energy characteristics of the near and far fields. The asymptotics capable of improving the accuracy of calculations is proposed for the analysis of the posed problem for an infinite system of linear algebraic equations. We also present some results of numerical calculations for some special cases and their comparative analysis in the case of variation of the parameters of a waveguide within the ranges typical of the coastal zone of the sea. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 52–59, May–June, 2006.     

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 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.     

Inertial and hydrodynamic inertial loads on floating units

The analysis of the dynamic behavior of floating units usually employs a coordinate system with origin in the unit's center of gravity, which significantly simplifies the global mass matrix. Hydrodynamic coefficients are then computed considering the same coordinate system. However, to analyze other conditions of mass distribution and maintain the simplicity of a global mass matrix, it is necessary to determine again the hydrodynamic coefficients, thereby reducing the efficiency of the entire process. Another important point is that the geometries frequently used in floating units are such that the cross-terms of an added mass are relatively unimportant when compared with the main terms, and it is, therefore, common to use only some of them to analyze the unit's dynamic behavior. Recently, however, in the search for production systems suitable for water depths greater than 3000 m, other geometries have been considered in technical and economic feasibility studies. It is possible that for these new geometries all terms of the added mass matrix must be included in the analysis. This paper presents the full development used to determine the complete global mass matrix, the inertial and hydrodynamic inertial loads that make use of the added mass matrices considering any coordinate system and the six degrees of freedom, including all cross-terms.     

Oblique wave interaction with a floating structure near a wall with stepped bottom

Diffraction of obliquely incident waves by a floating structure near a wall with step-type bottom topography is investigated under the three-dimensional small amplitude wave theory. Full solution of the problem under the potential flow approach is obtained by the matched eigenfunction expansion method. The wave-induced forces on the structure and on the wall, the reflection and transmission characteristics and the wave elevations in the free surface regions are studied for different incident wave angles, water depth ratios and dimension of the structure and the distance of the wall from the center of the structure. The problem is reformulated under shallow water approximations and results are compared with the finite depth results.     

Wave diffraction on arc-shaped floating perforated breakwaters

An analytical method is developed to study the sheltering effects on arc-shaped floating perforated breakwaters. In the process of analysis, the floating breakwater is assumed to be rigid, thin, vertical, and immovable and located in water with constant depth. The fluid domain is divided into two regions by imaginary interface. The velocity potential in each region is expanded by eigenfunction in the context of linear theory. By satisfying continuity of pressure and normal velocity across the imaginary fluid interface, a set of linear algebraic equations can be obtained to determine the unknown coefficients for eigenfunction expansions. The accuracy of the present model was verified by a comparison with existing results for the case of arc-shaped floating breakwater. Numerical results, in the form of contour maps of the non-dimensional wave amplitude around the breakwater and diffracted wave amplitude at typical sections, are presented for a range of wave and breakwater parameters. Results show that the sheltering effects on the arc-shaped floating perforated breakwater are closely related to the incident wavelength, the draft and the porosity of the breakwater.     

斜向波对台阶地形上有限吃水半无限长弹性板的散射作用

基于线性势流理论和欧拉-伯努利梁理论,采用匹配特征函数展开法建立斜向波对台阶地形上有限吃水半无限长弹性板散射的解析解。与以往研究不同,本文同时考虑波浪入射角度、弹性板吃水、三种不同板端条件（自由板端、简支板端、固定板端）以及海底地形的影响。本文还直接将板端条件引入匹配边界条件,建立线性方程组求解速度势中的展开系数,计算过程简单、高效。计算结果表明：本文方法收敛性好,并满足能量守恒方程。将本文计算结果与文献中的特例结果进行对比,吻合良好。分析了波浪入射角度、弹性板吃水、不同板端条件以及海底地形对弹性板水动力参数的影响,研究结果可以为工程设计提供参考。     

Difference-frequency wave loads on a large body in multi-directional waves

The second-order difference-frequency wave forces on a large three-dimensional body in multi-directional waves are computed by the boundary integral equation method and the so-called FML formulation (assisting radiation potential method). Semi-analytic solutions for a bottom-mounted vertical circular cylinder are also developed to validate the numerical method. Difference-frequency wave loads on a bottom-mounted vertical cylinder and stationary four legs of the ISSC tension-leg platform (TLP) are presented for various combinations of incident wave frequencies and headings. These force quadratic transfer functions (QTF) can directly be used in studying slowly varying wave loads in irregular short-crested seas described by a particular directional spectrum. From our numerical results, it is seen that the slowly varying wave loads are in general very sensitive to the directional spreading function of the sea, and therefore wave directionality needs to be taken into account in relevant ocean engineering applications. It is also pointed out that the uni-directionality of the sea is not necessarily a conservative assumption when the second-order effects are concerned.     

Nonlinear hydroelastic analysis of a moored floating body

By integration of the second-order fluid pressure over the instantaneous wetted surface, the generalized first- and second-order fluid forces used in nonlinear hydroelastic analysis are obtained. The expressions for coefficients of the generalized first- and second-order hydrodynamic forces in irregular waves are also given. The coefficients of the restoring forces of a mooring system acting on a flexible floating body are presented. The linear and nonlinear three-dimensional hydroelastic equations of motion of a moored floating body in frequency domain are established. These equations include the second-order forces, induced by the rigid body rotations of large amplitudes in high waves, the variation of the instantaneous wetted surface and the coupling of the first order wave potentials. The first-order and second-order principal coordinates of the hydrelastic vibration of a moored floating body are calculated. The frequency characteristics of the principal coordinates are discussed. The numerical results indicate that the rigid resonance and the coupling resonance of a moored floating body can occur in low frequency domain while the flexible resonance can occur in high frequency domain. The hydroelastic responses of a moored box-type barge are also given in this paper. The effects of the second-order forces on the modes are investigated in detail.     

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。     

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.     

Wave loads on rubble mound breakwater crown walls

Crown walls are primarily built to reduce wave overtopping of mound breakwaters. Several methods have been proposed to calculate wave loads on the crown wall, e.g., Iribarren and Nogales [Iribarren, R., Nogales, C., 1964. Obras Marı́timas. Dossat (Ed.), Madrid, 376 pp.], Jensen [Jensen, O.J., 1984. A Monograph on Rubble Mound Breakwaters. Danish Hydraulic Institute] and Günbak and Gökce [Günbak, A.R., Gökce, T., 1984. Wave screen stability of rubble-mound breakwaters. International Symposium of Maritime Structures in the Mediterranean Sea. Athens, Greece, pp. 2.99–2.112]. In this paper, a new method based on those previous results, and on further experimental work, using monochromatic waves, is presented. The application of the new method requires waves breaking on the armour layer; i.e., only broken waves will reach the crown wall. The method is extended to irregular waves via the hypothesis of equivalence introduced by Saville [Saville, T., 1962. An approximation of the wave run-up frequency distribution. Proc. 8th International Conference on Coastal Engineering, Mexico City] and is applied to the crown walls of Gijón and Bilbao breakwaters in Spain. The comparison of the probability force distributions obtained by the present method to that measured by Burcharth et al. [Burcharth, H.F., Frigaard, P., Berenguer, J.M., Gonzalez, B., Uzcanga, J., Villanueva, J., 1995. Design of the Ciervana breakwater, Bilbao. In: T. Telford (Ed.), Proc. 4th Coastal Structures and Breakwaters, Chap. 3. Institution of Civil Engineers] and Jensen (1984) is relatively good.     

Wave reflection by a vertical wall with a horizontal submerged porous plate

By applying the linear water wave theory and the eigenfunction expansion method, the wave reflection by a vertical wall with a horizontal submerged porous plate is investigated in this paper. The numerical results, concerning the effects of the dimensionless plate length, the relative water depth, and the porous effect parameter of the plate on the wave loads on the plate and the wave height near the wall as well as the reflection coefficient, are discussed. It is found that the submerged plate increases the complexity of the phenomenon related to the wave reflection and refraction in the close region of the wall, and leads to the occurrence of the phenomenon of wave trapping. The results indicate that there may exist a process of focusing wave energy near the wall for small dimensionless porous effect parameters, whereas the increase of the dimensionless porous effect parameter decreases gradually the wave height until setdown occurs. The behavior of a larger plate with proper porosity is similar to that of a wave absorber which can significantly suppress not only the wave height above the plate but also the reflection waves. The ability of the porous plate to reduce the wave height on the wall surface is, in general, directly proportional to the dimensionless plate length and may be strongest for a proper value of the dimensionless porous effect parameter. It is also demonstrated that the wave loads on a porous plate are smaller than those on an impermeable plate.     

Wave radiation by a floating rectangular structure in oblique seas

The linear wave radiation by a long floating rectangular structure in oblique seas of finite depth is investigated by use of the method of separation of variables and the eigenfunction expansion matching method. Analytical expressions for the radiated potentials, wave forces and hydrodynamic coefficients are given. The correctness of these expressions is verified through two specific examples investigated previously by other numerical methods. Using the present analytical solution, the hydrodynamic effects of the angle of incidence, the draft and the width of the structure on the wave forces and hydrodynamic coefficients are discussed in detail which may provide some useful information for the design of rectangular structures in oblique seas.     

Nonlinear wave effect on the slow drift motion of a floating body

The slow drift motion of a floating body in a two-dimensional wave field has been investigated using a time-domain, fully nonlinear numerical model with non-reflective open boundaries. Preliminary computations were conducted for incident bichromatic waves, in which wave theories with different orders were applied in generating the waves required. The results show that the use of low-order theories generates undesirable free waves, and that fourth-order terms contribute markedly to low-frequency input. The motion of a rectangular floating body in response to nonlinear bichromatic waves was computed. The numerical results for small-amplitude incident waves agree reasonably well with the second-order approximation for both the steady and difference-frequency (Δσ) components in the body's motion. For relatively large waves, however, the 2Δσ component becomes predominant compared with the Δσ component. The motion of the body in irregular waves with different wave parameters has also been presented in order to discuss the validity range of a second-order approximation.